defined assignment method

Assignment Problem: Meaning, Methods and Variations | Operations Research

After reading this article you will learn about:- 1. Meaning of Assignment Problem 2. Definition of Assignment Problem 3. Mathematical Formulation 4. Hungarian Method 5. Variations.

Meaning of Assignment Problem:

An assignment problem is a particular case of transportation problem where the objective is to assign a number of resources to an equal number of activities so as to minimise total cost or maximize total profit of allocation.

The problem of assignment arises because available resources such as men, machines etc. have varying degrees of efficiency for performing different activities, therefore, cost, profit or loss of performing the different activities is different.

Thus, the problem is “How should the assignments be made so as to optimize the given objective”. Some of the problem where the assignment technique may be useful are assignment of workers to machines, salesman to different sales areas.

Definition of Assignment Problem:

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Suppose there are n jobs to be performed and n persons are available for doing these jobs. Assume that each person can do each job at a term, though with varying degree of efficiency, let c ij be the cost if the i-th person is assigned to the j-th job. The problem is to find an assignment (which job should be assigned to which person one on-one basis) So that the total cost of performing all jobs is minimum, problem of this kind are known as assignment problem.

The assignment problem can be stated in the form of n x n cost matrix C real members as given in the following table:

What is an Assignment Method?

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Assignment method.

In accounting and finance, the assignment method is a technique used for allocating or assigning resources, costs, or tasks among different departments, employees, or projects. The assignment method aims to optimize resource allocation to achieve maximum efficiency, cost savings, or other desired outcomes. It is often used in cost accounting, project management, and operations research.

For example, in cost accounting , the assignment method can be used to allocate indirect costs (such as overhead) to various cost centers or cost objects based on certain allocation criteria, like the proportion of direct labor hours or machine hours. This helps in determining the total cost of each product or service and aids in decision-making related to pricing, production levels, or resource allocation.

Another example is in project management, where the assignment method can be used to allocate tasks to team members based on their skills, availability, or other relevant factors. This helps in efficient task distribution, ensuring timely project completion, and optimal utilization of resources.

In summary, the assignment method is a technique used for allocating resources, costs, or tasks to optimize efficiency and achieve desired outcomes.

Example of an Assignment Method

Let’s take an example from cost accounting , specifically in a manufacturing company.

Suppose a manufacturing company produces three products: Product A, Product B, and Product C. The company has a total indirect overhead cost of $90,000. The indirect overhead cost needs to be allocated to each product based on machine hours used in production.

The machine hours used for each product are as follows:

• Product A: 600 hours
• Product B: 900 hours
• Product C: 1,500 hours

Total machine hours used: 3,000 hours (600 + 900 + 1,500)

Now, we will use the assignment method to allocate the indirect overhead costs based on the proportion of machine hours used for each product.

• Calculate the overhead rate per machine hour: \(\text{Overhead rate} = \frac{\text{Total overhead cost}}{\text{Total machine hours}} \) \(\text{Overhead rate} = \frac{90,000}{3,000 \text{ hours}} \) Overhead rate = $30 per machine hour
• Allocate the overhead cost to each product based on the machine hours used:
• Product A: 600 hours * $30 = $18,000
• Product B: 900 hours * $30 = $27,000
• Product C: 1,500 hours * $30 = $45,000

So, using the assignment method, the allocated overhead costs for Product A, Product B, and Product C are $18,000, $27,000, and $45,000, respectively. This allocation helps the company understand the total cost of producing each product and make informed decisions about pricing, production levels, and resource allocation.

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Pedagogy - Diversifying Your Teaching Methods, Learning Activities, and Assignments

Definition of Pedagogy 

In the most general sense, pedagogy is all the ways that instructors and students work with the course content. The fundamental learning goal for students is to be able to do “something meaningful” with the course content. Meaningful learning typically results in students working in the middle to upper levels of Bloom’s Taxonomy . We sometimes find that novice instructors conflate course content with pedagogy. This often results in “teaching as talking” where the presentation of content by the instructor is confused with the learning of content by the students. Think of your course content as clay and pedagogy as the ways you ask students to make “something meaningful” from that clay. Pedagogy is the combination of teaching methods (what instructors do), learning activities (what instructors ask their students to do), and learning assessments (the assignments, projects, or tasks that measure student learning).

Key Idea for Pedagogy

Diversify your pedagogy by varying your teaching methods, learning activities, and assignments. Critically assess your pedagogy through the lens of BIPOC students’ experiences at a PWI . We visualize these two related practices as a cycle because they are iterative and ongoing. Diversifying your pedagogy likely means shedding some typical ways of teaching in your discipline, or the teaching practices you inherited. It likely means doing more active learning and less traditional lecturing. Transforming good pedagogy into equitable pedagogy means rethinking your pedagogy in light of the PWI context and considering the ways your pedagogy may help or hinder learning for BIPOC students. 

PWI Assumptions for Pedagogy

Understanding where students are on the spectrum of novice to expert learning in your discipline or course is a key challenge to implementing effective and inclusive pedagogy (National Research Council 2000). Instructors are typically so far removed from being a novice learner in their disciplines that they struggle to understand where students are on that spectrum. A key PWI assumption is that students understand how your disciplinary knowledge is organized and constructed . Students typically do not understand your discipline or the many other disciplines they are working in during their undergraduate years. Even graduate students may find it puzzling to explain the origins, methodologies, theories, logics, and assumptions of their disciplines. A second PWI assumption is that students are (or should be) academically prepared to learn your discipline . Students may be academically prepared for learning in some disciplines, but unless their high school experience was college preparatory and well supported, students (especially first-generation college students) are likely finding their way through a mysterious journey of different disciplinary conventions and modes of working and thinking (Nelson 1996).

A third PWI assumption is that instructors may confuse students’ academic underpreparation with their intelligence or capacity to learn . Academic preparation is typically a function of one’s high school experience including whether that high school was well resourced or under funded. Whether or not a student receives a quality high school education is usually a structural matter reflecting inequities in our K12 educational systems, not a reflection of an individual student’s ability to learn. A final PWI assumption is that students will learn well in the ways that the instructor learned well . Actually most instructors in higher education self-selected into disciplines that align with their interests, skills, academic preparation, and possibly family and community support. Our students have broader and different goals for seeking a college education and bring a range of skills to their coursework, which may or may not align with instructors’ expectations of how students learn. Inclusive teaching at a PWI means supporting the learning and career goals of our students.

Pedagogical Content Knowledge as a Core Concept

Kind and Chan (2019) propose that Pedagogical Content Knowledge (PCK) is the synthesis of Content Knowledge (expertise about a subject area) and Pedagogical Knowledge (expertise about teaching methods, assessment, classroom management, and how students learn). Content Knowledge (CK) without Pedagogical Knowledge (PK) limits instructors’ ability to teach effectively or inclusively. Novice instructors that rely on traditional lectures likely have limited Pedagogical Knowledge and may also be replicating their own inherited teaching practices. While Kind and Chan (2019) are writing from the perspective of science education, their concepts apply across disciplines. Moreover, Kind and Chan (2019) support van Driel et al.’s assertion that:

high-quality PCK is not characterized by knowing as many strategies as possible to teach a certain topic plus all the misconceptions students may have about it but by knowing when to apply a certain strategy in recognition of students’ actual learning needs and understanding why a certain teaching approach may be useful in one situation (quoted in Kind and Chan 2019, 975). 

As we’ve stressed throughout this guide, the teaching context matters, and for inclusive pedagogy, special attention should be paid to the learning goals, instructor preparation, and students’ point of entry into course content. We also argue that the PWI context shapes what instructors might practice as CK, PK, and PCK. We recommend instructors become familiar with evidence-based pedagogy (or the Scholarship of Teaching and Learning , SoTL) in their fields. Moreover, we advise instructors to find and follow those instructors and scholars that specifically focus on inclusive teaching in their fields in order to develop an inclusive, flexible, and discipline-specific Pedagogical Content Knowledge.

Suggested Practices for Diversifying + Assessing Pedagogy

Although diversifying and critically assessing teaching methods, learning activities, and assignments will vary across disciplines, we offer a few key starting points. Diversifying your pedagogy is easier than critically assessing it through a PWI lens, but both steps are essential. In general, you can diversify your pedagogy by learning about active learning, peer learning, team-based learning, experiential learning, problem-based learning, and case-based learning, among others . There is extensive evidence-based pedagogical literature and practical guides readily available for these methods. And you can also find and follow scholars in your discipline that use these and other teaching methods.

Diversifying Your Pedagogy

Convert traditional lectures into interactive (or active) lectures.

For in-person or synchronous online courses, break a traditional lecture into “mini-lectures” of 10-15 minutes in length. After each mini-lecture, ask your students to process their learning using a discussion or problem prompt, a Classroom Assessment Technique (CAT), a Think-Pair-Share, or another brief learning activity. Read Lecturing from Center for Teaching , Vanderbilt University.

Structure small group discussions

Provide both a process and concrete questions or tasks to guide student learning (for example, provide a scenario with 3 focused tasks such as identify the problem, brainstorm possible solutions, and list the pros/cons for each solution). Read How to Hold a Better Class Discussion , The Chronicle of Higher Education .

Integrate active learning

Integrate active learning, especially into courses that are conceptual, theoretical, or otherwise historically challenging (for example, calculus, organic chemistry, statistics, philosophy). For gateway courses, draw upon the research of STEM and other education specialists on how active learning and peer learning improves student learning and reduces disparities. Read the Association of American Universities STEM Network Scholarship .  

Include authentic learning

Include authentic learning, learning activities and assignments that mirror how students will work after graduation. What does it mean to think and work like an engineer? How do project teams work together? How does one present research in an educational social media campaign? Since most students seeking a college education will not become academic researchers or faculty, what kinds of things will they do in the “real world?” Help students practice and hone those skills as they learn the course content. Read Edutopia’s PBL: What Does It Take for a Project to Be Authentic?

Vary assignments and provide options

Graded assignments should range from low to high stakes. Low stakes assignments allow students to learn from their mistakes and receive timely feedback on their learning. Options for assignments allow students to demonstrate their learning, rather than demonstrate their skill at a particular type of assessment (such as a multiple choice exam or an academic research paper). Read our guide, Create Assessments That Promote Learning for All Students .

Critically Assess Your Pedagogy

Critically assessing your pedagogy through the PWI lens with attention to how your pedagogy may affect the learning of BIPOC students is more challenging and highly contextual. Instructors will want to review and apply the concepts and principles discussed in the earlier sections of this guide on Predominantly White Institutions (PWIs), PWI Assumptions, and Class Climate. 

Reflect on patterns

Reflect on patterns of participation, progress in learning (grade distributions), and other course-related evidence. Look at your class sessions and assignments as experimental data. Who participated? What kinds of participation did you observe? Who didn’t participate? Why might that be? Are there a variety of ways for students to participate in the learning activities (individually, in groups, via discussion, via writing, synchronously/in-person, asynchronously/online)?

Respond to feedback on climate

Respond to feedback on climate from on-going check-ins and Critical Incident Questionnaires (CIQs) as discussed in the Climate Section (Ongoing Practices). Students will likely disengage from your requests for feedback if you do not respond to their feedback. Use this feedback to re-calibrate and re-think your pedagogy. 

Seek feedback on student learning

Seek feedback on student learning in the form of Classroom Assessment Techniques (CATs), in-class polls, asynchronous forums, exam wrappers, and other methods.  Demonstrate that you care about your students’ learning by responding to this feedback as well. Here’s how students in previous semesters learned this material … I’m scheduling a problem-solving review session in the next class in response to the results of the exam …

Be diplomatic but clear when correcting mistakes and misconceptions

First-generation college students, many of whom may also identify as BIPOC, have typically achieved a great deal with few resources and significant barriers (Yosso 2005). However, they may be more likely to internalize their learning mistakes as signs that they don’t belong at the university. When correcting, be sure to normalize mistakes as part of the learning process. The correct answer is X, but I can see why you thought it was Y. Many students think it is Y because … But the correct answer is X because … Thank you for helping us understand that misconception.

Allow time for students to think and prepare for participation in a non-stressful setting

This was already suggested in the Climate Section (Race Stressors), but it is worth repeating. BIPOC students and multilingual students may need more time to prepare, not because of their intellectual abilities, but because of the effects of race stressors and other stressors increasing their cognitive load. Providing discussion or problem prompts in advance will reduce this stress and make space for learning. Additionally both student populations may experience stereotype threat, so participation in the “public” aspects of the class session may be stressful in ways that are not true for the majority white and domestic students. If you cannot provide prompts in advance, be sure to allow ample individual “think time” during a synchronous class session.

Avoid consensus models or majority rules processes

This was stated in the Climate Section (Teaching Practices to Avoid), but it’s such an entrenched PWI practice that it needs to be spotlighted and challenged. If I am a numerical “minority” and I am asked to come to consensus or agreement with a numerical “majority,” it is highly likely that my perspective will be minimized or dismissed. Or, I will have to expend a lot of energy to persuade my group of the value of my perspective, which is highly stressful. This is an unacceptable burden to put on BIPOC students and also may result in BIPOC students being placed in the position of teaching white students about a particular perspective or experience. The resulting tensions may also damage BIPOC students’ positive relationships with white students and instructors. When suitable for your content, create a learning experience that promotes seeking multiple solutions to problems, cases, or prompts. Rather than asking students to converge on one best recommendation, why not ask students to log all possible solutions (without evaluation) and then to recommend at least two solutions that include a rationale? Moreover, for course content dealing with policies, the recommended solutions could be explained in terms of their possible effects on different communities. If we value diverse perspectives, we need to structure the consideration of those perspectives into our learning activities and assignments. 

We recognize the challenges of assessing your pedagogy through the PWI lens and doing your best to assess the effects on BIPOC student learning. This is a complex undertaking. But we encourage you to invite feedback from your students as well as to seek the guidance of colleagues, including advisors and other student affairs professionals, to inform your ongoing practices of teaching inclusively at a PWI. In the next section, we complete our exploration of the Inclusive Teaching at a PWI Framework by exploring the importance of auditing, diversifying, and critically assessing course content.

Pedagogy References

Kind, Vanessa and Kennedy K.H. Chan. 2019. “Resolving the Amalgam: Connecting Pedagogical Content Knowledge, Content Knowledge and Pedagogical Knowledge.” International Journal of Science Education . 41(7): 964-978.

Howard, Jay. N.D. “How to Hold a Better Class Discussion: Advice Guide.” The Chronicle of Higher Education . https://www.chronicle.com/article/how-to-hold-a-better-class-discussion/#2 

National Research Council. 2000. “How Experts Differ from Novices.” Chap 2 in How People Learn: Brain, Mind, Experience, and School: Expanded Edition . Washington D.C.: The National Academies Press. https://nap.nationalacademies.org/catalog/9853/how-people-learn-brain-mind-experience-and-school-expanded-edition

Nelson, Craig E. 1996. “Student Diversity Requires Different Approaches to College Teaching, Even in Math and Science.” The American Behavioral Scientist . 40 (2): 165-175.

Sathy, Viji and Kelly A. Hogan. N.D.  “How to Make Your Teaching More Inclusive: Advice Guide.” The Chronicle of Higher Education . https://www.chronicle.com/article/how-to-make-your-teaching-more-inclusive/?cid=gen_sign_in

Yosso, Tara J. 2005. “Whose Culture Has Capital? A Critical Race Theory Discussion of Community Cultural Wealth.” Race, Ethnicity and Education . 8 (1): 69-91.

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Random Assignment in Psychology: Definition & Examples

Julia Simkus

Editor at Simply Psychology

BA (Hons) Psychology, Princeton University

Julia Simkus is a graduate of Princeton University with a Bachelor of Arts in Psychology. She is currently studying for a Master's Degree in Counseling for Mental Health and Wellness in September 2023. Julia's research has been published in peer reviewed journals.

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Saul Mcleod, PhD

Editor-in-Chief for Simply Psychology

BSc (Hons) Psychology, MRes, PhD, University of Manchester

Saul Mcleod, PhD., is a qualified psychology teacher with over 18 years of experience in further and higher education. He has been published in peer-reviewed journals, including the Journal of Clinical Psychology.

Olivia Guy-Evans, MSc

Associate Editor for Simply Psychology

BSc (Hons) Psychology, MSc Psychology of Education

Olivia Guy-Evans is a writer and associate editor for Simply Psychology. She has previously worked in healthcare and educational sectors.

In psychology, random assignment refers to the practice of allocating participants to different experimental groups in a study in a completely unbiased way, ensuring each participant has an equal chance of being assigned to any group.

In experimental research, random assignment, or random placement, organizes participants from your sample into different groups using randomization. 

Random assignment uses chance procedures to ensure that each participant has an equal opportunity of being assigned to either a control or experimental group.

The control group does not receive the treatment in question, whereas the experimental group does receive the treatment.

When using random assignment, neither the researcher nor the participant can choose the group to which the participant is assigned. This ensures that any differences between and within the groups are not systematic at the onset of the study. 

In a study to test the success of a weight-loss program, investigators randomly assigned a pool of participants to one of two groups.

Group A participants participated in the weight-loss program for 10 weeks and took a class where they learned about the benefits of healthy eating and exercise.

Group B participants read a 200-page book that explains the benefits of weight loss. The investigator randomly assigned participants to one of the two groups.

The researchers found that those who participated in the program and took the class were more likely to lose weight than those in the other group that received only the book.

Importance 

Random assignment ensures that each group in the experiment is identical before applying the independent variable.

In experiments , researchers will manipulate an independent variable to assess its effect on a dependent variable, while controlling for other variables. Random assignment increases the likelihood that the treatment groups are the same at the onset of a study.

Thus, any changes that result from the independent variable can be assumed to be a result of the treatment of interest. This is particularly important for eliminating sources of bias and strengthening the internal validity of an experiment.

Random assignment is the best method for inferring a causal relationship between a treatment and an outcome.

Random Selection vs. Random Assignment 

Random selection (also called probability sampling or random sampling) is a way of randomly selecting members of a population to be included in your study.

On the other hand, random assignment is a way of sorting the sample participants into control and treatment groups. 

Random selection ensures that everyone in the population has an equal chance of being selected for the study. Once the pool of participants has been chosen, experimenters use random assignment to assign participants into groups. 

Random assignment is only used in between-subjects experimental designs, while random selection can be used in a variety of study designs.

Random Assignment vs Random Sampling

Random sampling refers to selecting participants from a population so that each individual has an equal chance of being chosen. This method enhances the representativeness of the sample.

Random assignment, on the other hand, is used in experimental designs once participants are selected. It involves allocating these participants to different experimental groups or conditions randomly.

This helps ensure that any differences in results across groups are due to manipulating the independent variable, not preexisting differences among participants.

When to Use Random Assignment

Random assignment is used in experiments with a between-groups or independent measures design.

In these research designs, researchers will manipulate an independent variable to assess its effect on a dependent variable, while controlling for other variables.

There is usually a control group and one or more experimental groups. Random assignment helps ensure that the groups are comparable at the onset of the study.

How to Use Random Assignment

There are a variety of ways to assign participants into study groups randomly. Here are a handful of popular methods: 

• Random Number Generator : Give each member of the sample a unique number; use a computer program to randomly generate a number from the list for each group.
• Lottery : Give each member of the sample a unique number. Place all numbers in a hat or bucket and draw numbers at random for each group.
• Flipping a Coin : Flip a coin for each participant to decide if they will be in the control group or experimental group (this method can only be used when you have just two groups) 
• Roll a Die : For each number on the list, roll a dice to decide which of the groups they will be in. For example, assume that rolling 1, 2, or 3 places them in a control group and rolling 3, 4, 5 lands them in an experimental group.

When is Random Assignment not used?

• When it is not ethically permissible: Randomization is only ethical if the researcher has no evidence that one treatment is superior to the other or that one treatment might have harmful side effects. 
• When answering non-causal questions : If the researcher is just interested in predicting the probability of an event, the causal relationship between the variables is not important and observational designs would be more suitable than random assignment. 
• When studying the effect of variables that cannot be manipulated: Some risk factors cannot be manipulated and so it would not make any sense to study them in a randomized trial. For example, we cannot randomly assign participants into categories based on age, gender, or genetic factors.

Drawbacks of Random Assignment

While randomization assures an unbiased assignment of participants to groups, it does not guarantee the equality of these groups. There could still be extraneous variables that differ between groups or group differences that arise from chance. Additionally, there is still an element of luck with random assignments.

Thus, researchers can not produce perfectly equal groups for each specific study. Differences between the treatment group and control group might still exist, and the results of a randomized trial may sometimes be wrong, but this is absolutely okay.

Scientific evidence is a long and continuous process, and the groups will tend to be equal in the long run when data is aggregated in a meta-analysis.

Additionally, external validity (i.e., the extent to which the researcher can use the results of the study to generalize to the larger population) is compromised with random assignment.

Random assignment is challenging to implement outside of controlled laboratory conditions and might not represent what would happen in the real world at the population level. 

Random assignment can also be more costly than simple observational studies, where an investigator is just observing events without intervening with the population.

Randomization also can be time-consuming and challenging, especially when participants refuse to receive the assigned treatment or do not adhere to recommendations. 

What is the difference between random sampling and random assignment?

Random sampling refers to randomly selecting a sample of participants from a population. Random assignment refers to randomly assigning participants to treatment groups from the selected sample.

Does random assignment increase internal validity?

Yes, random assignment ensures that there are no systematic differences between the participants in each group, enhancing the study’s internal validity .

Does random assignment reduce sampling error?

Yes, with random assignment, participants have an equal chance of being assigned to either a control group or an experimental group, resulting in a sample that is, in theory, representative of the population.

Random assignment does not completely eliminate sampling error because a sample only approximates the population from which it is drawn. However, random sampling is a way to minimize sampling errors. 

When is random assignment not possible?

Random assignment is not possible when the experimenters cannot control the treatment or independent variable.

For example, if you want to compare how men and women perform on a test, you cannot randomly assign subjects to these groups.

Participants are not randomly assigned to different groups in this study, but instead assigned based on their characteristics.

Does random assignment eliminate confounding variables?

Yes, random assignment eliminates the influence of any confounding variables on the treatment because it distributes them at random among the study groups. Randomization invalidates any relationship between a confounding variable and the treatment.

Why is random assignment of participants to treatment conditions in an experiment used?

Random assignment is used to ensure that all groups are comparable at the start of a study. This allows researchers to conclude that the outcomes of the study can be attributed to the intervention at hand and to rule out alternative explanations for study results.

Further Reading

• Bogomolnaia, A., & Moulin, H. (2001). A new solution to the random assignment problem .  Journal of Economic theory ,  100 (2), 295-328.
• Krause, M. S., & Howard, K. I. (2003). What random assignment does and does not do .  Journal of Clinical Psychology ,  59 (7), 751-766.

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What Is Activity-Based Costing (ABC)?

How activity-based costing (abc) works, requirements for activity-based costing (abc), benefits of activity-based costing (abc).

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Activity-Based Costing (ABC): Method and Advantages Defined with Example

Activity-based costing (ABC) is a costing method that assigns overhead and indirect costs to related products and services. This accounting method of costing recognizes the relationship between costs, overhead activities, and manufactured products, assigning indirect costs to products less arbitrarily than traditional costing methods. However, some indirect costs, such as management and office staff salaries, are difficult to assign to a product.

Key Takeaways

• Activity-based costing (ABC) is a method of assigning overhead and indirect costs—such as salaries and utilities—to products and services. 
• The ABC system of cost accounting is based on activities, which are considered any event, unit of work, or task with a specific goal.
• An activity is a cost driver , such as purchase orders or machine setups. 
• The cost driver rate, which is the cost pool total divided by cost driver, is used to calculate the amount of overhead and indirect costs related to a particular activity. 

ABC is used to get a better grasp on costs, allowing companies to form a more appropriate pricing strategy. 

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Activity-based costing (ABC) is mostly used in the manufacturing industry since it enhances the reliability of cost data, hence producing nearly true costs and better classifying the costs incurred by the company during its production process.

This costing system is used in target costing, product costing, product line profitability analysis, customer profitability analysis, and service pricing. Activity-based costing is used to get a better grasp on costs, allowing companies to form a more appropriate pricing strategy. 

The formula for activity-based costing is the cost pool total divided by cost driver, which yields the cost driver rate. The cost driver rate is used in activity-based costing to calculate the amount of overhead and indirect costs related to a particular activity. 

The ABC calculation is as follows:  

• Identify all the activities required to create the product. 
• Divide the activities into cost pools, which includes all the individual costs related to an activity—such as manufacturing. Calculate the total overhead of each cost pool.
• Assign each cost pool activity cost drivers, such as hours or units. 
• Calculate the cost driver rate by dividing the total overhead in each cost pool by the total cost drivers. 
• Divide the total overhead of each cost pool by the total cost drivers to get the cost driver rate. 
• Multiply the cost driver rate by the number of cost drivers. 

As an activity-based costing example, consider Company ABC that has a $50,000 per year electricity bill. The number of labor hours has a direct impact on the electric bill. For the year, there were 2,500 labor hours worked, which in this example is the cost driver. Calculating the cost driver rate is done by dividing the $50,000 a year electric bill by the 2,500 hours, yielding a cost driver rate of $20. For Product XYZ, the company uses electricity for 10 hours. The overhead costs for the product are $200, or $20 times 10.

Activity-based costing benefits the costing process by expanding the number of cost pools that can be used to analyze overhead costs and by making indirect costs traceable to certain activities. 

The ABC system of cost accounting is based on activities, which are any events, units of work, or tasks with a specific goal, such as setting up machines for production, designing products, distributing finished goods, or operating machines. Activities consume overhead resources and are considered cost objects.

Under the ABC system, an activity can also be considered as any transaction or event that is a cost driver. A cost driver, also known as an activity driver, is used to refer to an allocation base. Examples of cost drivers include machine setups, maintenance requests, consumed power, purchase orders, quality inspections, or production orders.

There are two categories of activity measures: transaction drivers, which involve counting how many times an activity occurs, and duration drivers, which measure how long an activity takes to complete.

Unlike traditional cost measurement systems that depend on volume count, such as machine hours and/or direct labor hours, to allocate indirect or overhead costs to products, the ABC system classifies five broad levels of activity that are, to a certain extent, unrelated to how many units are produced. These levels include batch-level activity , unit-level activity, customer-level activity, organization-sustaining activity, and product-level activity.

Activity-based costing (ABC) enhances the costing process in three ways. First, it expands the number of cost pools that can be used to assemble overhead costs. Instead of accumulating all costs in one company-wide pool, it pools costs by activity. 

Second, it creates new bases for assigning overhead costs to items such that costs are allocated based on the activities that generate costs instead of on volume measures, such as machine hours or direct labor costs. 

Finally, ABC alters the nature of several indirect costs, making costs previously considered indirect—such as depreciation , utilities, or salaries—traceable to certain activities. Alternatively, ABC transfers overhead costs from high-volume products to low-volume products, raising the unit cost of low-volume products.

Chartered Global Management Accountant. " Activity-Based Costing (ABC) ."

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Types of Assignments

Cristy Bartlett and Kate Derrington

Introduction

As discussed in the previous chapter, assignments are a common method of assessment at university. You may encounter many assignments over your years of study, yet some will look quite different from others. By recognising different types of assignments and understanding the purpose of the task, you can direct your writing skills effectively to meet task requirements. This chapter draws on the skills from the previous chapter, and extends the discussion, showing you where to aim with different types of assignments.

The chapter begins by exploring the popular essay assignment, with its two common categories, analytical and argumentative essays. It then examines assignments requiring case study responses , as often encountered in fields such as health or business. This is followed by a discussion of assignments seeking a report (such as a scientific report) and reflective writing assignments, common in nursing, education and human services. The chapter concludes with an examination of annotated bibliographies and literature reviews. The chapter also has a selection of templates and examples throughout to enhance your understanding and improve the efficacy of  your assignment writing skills.

Different Types of Written Assignments

At university, an essay is a common form of assessment. In the previous chapter Writing Assignments we discussed what was meant by showing academic writing in your assignments. It is important that you consider these aspects of structure, tone and language when writing an essay.

Components of an essay

Essays should use formal but reader friendly language and have a clear and logical structure. They must include research from credible academic sources such as peer reviewed journal articles and textbooks. This research should be referenced throughout your essay to support your ideas (See the chapter Working with Information ).

If you have never written an essay before, you may feel unsure about how to start.  Breaking your essay into sections and allocating words accordingly will make this process more manageable and will make planning the overall essay structure much easier.

• An essay requires an introduction, body paragraphs and a conclusion.
• Generally, an introduction and conclusion are approximately 10% each of the total word count.
• The remaining words can then be divided into sections and a paragraph allowed for each area of content you need to cover.
• Use your task and criteria sheet to decide what content needs to be in your plan

An effective essay introduction needs to inform your reader by doing four basic things:

Table 20.1 An effective essay

An effective essay body paragraph needs to:

An effective essay conclusion needs to:

Common types of essays

You may be required to write different types of essays, depending on your study area and topic. Two of the most commonly used essays are analytical and argumentative .  The task analysis process discussed in the previous chapter Writing Assignments will help you determine the type of essay required. For example, if your assignment question uses task words such as analyse, examine, discuss, determine or explore, you would be writing an analytical essay . If your assignment question has task words such as argue, evaluate, justify or assess, you would be writing an argumentative essay . Despite the type of essay, your ability to analyse and think critically is important and common across genres.  

Analytical essays

These essays usually provide some background description of the relevant theory, situation, problem, case, image, etcetera that is your topic. Being analytical requires you to look carefully at various components or sections of your topic in a methodical and logical way to create understanding.

The purpose of the analytical essay is to demonstrate your ability to examine the topic thoroughly. This requires you to go deeper than description by considering different sides of the situation, comparing and contrasting a variety of theories and the positives and negatives of the topic. Although in an analytical essay your position on the topic may be clear, it is not necessarily a requirement that you explicitly identify this with a thesis statement, as is the case with an argumentative essay. If you are unsure whether you are required to take a position, and provide a thesis statement, it is best to check with your tutor.

Argumentative essays

These essays require you to take a position on the assignment topic. This is expressed through your thesis statement in your introduction. You must then present and develop your arguments throughout the body of your assignment using logically structured paragraphs. Each of these paragraphs needs a topic sentence that relates to the thesis statement. In an argumentative essay, you must reach a conclusion based on the evidence you have presented.

Case Study Responses

Case studies are a common form of assignment in many study areas and students can underperform in this genre for a number of key reasons.

Students typically lose marks for not:

• Relating their answer sufficiently to the case details
• Applying critical thinking
• Writing with clear structure
• Using appropriate or sufficient sources
• Using accurate referencing

When structuring your response to a case study, remember to refer to the case. Structure your paragraphs similarly to an essay paragraph structure but include examples and data from the case as additional evidence to support your points (see Figure 20.5 ). The colours in the sample paragraph below show the function of each component.

The Nursing and Midwifery Board of Australia (NMBA) Code of Conduct and Nursing Standards (2018) play a crucial role in determining the scope of practice for nurses and midwives. A key component discussed in the code is the provision of person-centred care and the formation of therapeutic relationships between nurses and patients (NMBA, 2018). This ensures patient safety and promotes health and wellbeing (NMBA, 2018). The standards also discuss the importance of partnership and shared decision-making in the delivery of care (NMBA, 2018, 4). Boyd and Dare (2014) argue that good communication skills are vital for building therapeutic relationships and trust between patients and care givers. This will help ensure the patient is treated with dignity and respect and improve their overall hospital experience. In the case, the therapeutic relationship with the client has been compromised in several ways. Firstly, the nurse did not conform adequately to the guidelines for seeking informed consent before performing the examination as outlined in principle 2.3 (NMBA, 2018). Although she explained the procedure, she failed to give the patient appropriate choices regarding her health care. 

Topic sentence | Explanations using paraphrased evidence including in-text references | Critical thinking (asks the so what? question to demonstrate your student voice). | Relating the theory back to the specifics of the case. The case becomes a source of examples as extra evidence to support the points you are making.

Reports are a common form of assessment at university and are also used widely in many professions. It is a common form of writing in business, government, scientific, and technical occupations.

Reports can take many different structures. A report is normally written to present information in a structured manner, which may include explaining laboratory experiments, technical information, or a business case.  Reports may be written for different audiences including clients, your manager, technical staff, or senior leadership within an organisation. The structure of reports can vary, and it is important to consider what format is required. The choice of structure will depend upon professional requirements and the ultimate aims of the report. Consider some of the options in the table below (see Table 20.2 ).

Table 20.2 Explanations of different types of reports

Reflective writing.

Reflective writing is a popular method of assessment at university. It is used to help you explore feelings, experiences, opinions, events or new information to gain a clearer and deeper understanding of your learning. A reflective writing task requires more than a description or summary.  It requires you to analyse a situation, problem or experience, consider what you may have learnt and evaluate how this may impact your thinking and actions in the future. This requires critical thinking, analysis, and usually the application of good quality research, to demonstrate your understanding or learning from a situation. Essentially, reflective practice is the process of looking back on past experiences and engaging with them in a thoughtful way and drawing conclusions to inform future experiences. The reflection skills you develop at university will be vital in the workplace to assist you to use feedback for growth and continuous improvement. There are numerous models of reflective writing and you should refer to your subject guidelines for your expected format. If there is no specific framework, a simple model to help frame your thinking is What? So what? Now what?   (Rolfe et al., 2001).

Table 20.3 What? So What? Now What? Explained.

The Gibbs’ Reflective Cycle

The Gibbs’ Cycle of reflection encourages you to consider your feelings as part of the reflective process. There are six specific steps to work through. Following this model carefully and being clear of the requirements of each stage, will help you focus your thinking and reflect more deeply. This model is popular in Health.

The 4 R’s of reflective thinking

This model (Ryan and Ryan, 2013) was designed specifically for university students engaged in experiential learning.  Experiential learning includes any ‘real-world’ activities including practice led activities, placements and internships.  Experiential learning, and the use of reflective practice to heighten this learning, is common in Creative Arts, Health and Education.

Annotated Bibliography

What is it.

An annotated bibliography is an alphabetical list of appropriate sources (books, journals or websites) on a topic, accompanied by a brief summary, evaluation and sometimes an explanation or reflection on their usefulness or relevance to your topic. Its purpose is to teach you to research carefully, evaluate sources and systematically organise your notes. An annotated bibliography may be one part of a larger assessment item or a stand-alone assessment piece. Check your task guidelines for the number of sources you are required to annotate and the word limit for each entry.

How do I know what to include?

When choosing sources for your annotated bibliography it is important to determine:

• The topic you are investigating and if there is a specific question to answer
• The type of sources on which you need to focus
• Whether they are reputable and of high quality

What do I say?

Important considerations include:

• Is the work current?
• Is the work relevant to your topic?
• Is the author credible/reliable?
• Is there any author bias?
• The strength and limitations (this may include an evaluation of research methodology).

Literature Reviews

It is easy to get confused by the terminology used for literature reviews. Some tasks may be described as a systematic literature review when actually the requirement is simpler; to review the literature on the topic but do it in a systematic way. There is a distinct difference (see Table 20.4 ). As a commencing undergraduate student, it is unlikely you would be expected to complete a systematic literature review as this is a complex and more advanced research task. It is important to check with your lecturer or tutor if you are unsure of the requirements.

Table 20.4 Comparison of Literature Reviews

Generally, you are required to establish the main ideas that have been written on your chosen topic. You may also be expected to identify gaps in the research. A literature review does not summarise and evaluate each resource you find (this is what you would do in an annotated bibliography). You are expected to analyse and synthesise or organise common ideas from multiple texts into key themes which are relevant to your topic (see Figure 20.10 ). Use a table or a spreadsheet, if you know how, to organise the information you find. Record the full reference details of the sources as this will save you time later when compiling your reference list (see Table 20.5 ).

Overall, this chapter has provided an introduction to the types of assignments you can expect to complete at university, as well as outlined some tips and strategies with examples and templates for completing them. First, the chapter investigated essay assignments, including analytical and argumentative essays. It then examined case study assignments, followed by a discussion of the report format. Reflective writing , popular in nursing, education and human services, was also considered. Finally, the chapter briefly addressed annotated bibliographies and literature reviews. The chapter also has a selection of templates and examples throughout to enhance your understanding and improve the efficacy of your assignment writing skills.

• Not all assignments at university are the same. Understanding the requirements of different types of assignments will assist in meeting the criteria more effectively.
• There are many different types of assignments. Most will require an introduction, body paragraphs and a conclusion.
• An essay should have a clear and logical structure and use formal but reader friendly language.
• Breaking your assignment into manageable chunks makes it easier to approach.
• Effective body paragraphs contain a topic sentence.
• A case study structure is similar to an essay, but you must remember to provide examples from the case or scenario to demonstrate your points.
• The type of report you may be required to write will depend on its purpose and audience. A report requires structured writing and uses headings.
• Reflective writing is popular in many disciplines and is used to explore feelings, experiences, opinions or events to discover what learning or understanding has occurred. Reflective writing requires more than description. You need to be analytical, consider what has been learnt and evaluate the impact of this on future actions.
• Annotated bibliographies teach you to research and evaluate sources and systematically organise your notes. They may be part of a larger assignment.
• Literature reviews require you to look across the literature and analyse and synthesise the information you find into themes.

Gibbs, G. (1988). Learning by doing: A guide to teaching and learning methods. Further Education Unit, Oxford Brookes University, Oxford.

Rolfe, G., Freshwater, D., Jasper, M. (2001). Critical reflection in nursing and the helping professions: a user’s guide . Basingstoke: Palgrave Macmillan.

Ryan, M. & Ryan, M. (2013). Theorising a model for teaching and assessing reflective learning in higher education.  Higher Education Research & Development , 32(2), 244-257. doi: 10.1080/07294360.2012.661704

Academic Success Copyright © 2021 by Cristy Bartlett and Kate Derrington is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License , except where otherwise noted.

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Assignment methods in unified routing

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Use assignment methods to determine how to assign work items. You can use the out-of-the-box assignment methods or build custom assignment rules by configuring the prioritization rules and assignment rulesets.

How auto assignment works

The auto-assignment process in unified routing matches incoming work items with the best-suited agents based on the configured assignment rules. This continuous process consists of multiple assignment cycles and a default block size of work items.

Each cycle picks up the top unassigned work items in the applicable default block size and attempts to match each work item with an appropriate agent. Work items that aren't assigned to agents because of unavailability of agents or right skill match wasn't found are routed back to the queue.

The next assignment cycle picks up the next block of the top-priority items that includes new work items.

When eligible agents aren't found for the work items, the assignment cycle keeps retrying to assign the top number of default sized block items as applicable for the channel.

For digital messaging and voice, the default block size is 100 work items of top priority.

For the records channel,

• The number of work items prioritized per queue are 10,000
• The number of work items processed for assignment are 2,000 by default

Cross-queue prioritization isn't available in unified routing.

For more information, see best practices to manage queues .

Types of assignment methods

The following assignment methods are available out of the box:

Highest capacity : Assigns a work item to an agent with the highest available capacity. This agent has the skills that are identified during the classification stage and presence that matches one of the allowed presences in the workstream. The work items are prioritized in the first-in, first-out manner—that is, the work item that was created first is assigned first. If more than one agent is available with the same capacity, the work item is assigned based on the round-robin order of the agents whose highest capacity is the same.

If you want to use skill-based routing and,

Set Default skill matching algorithm in the workstream as Exact Match , then the system filters agents using exact skill match, workstream’s presence, and capacity requirements, and orders the filtered agents by available capacity.

Set Default skill matching algorithm in the workstream as Closest Match , then the system filters agents based on the workstream's presence and capacity requirements and orders the filtered agents by closest match and not available capacity. More information: Closest match

If you need to distribute work fairly among agents, then you should consider switching to a round robin assignment strategy.

When you modify a rating model, the ongoing conversations or open work items that have skills with the rating model continue to have the existing rating. Sometimes, this might result in no agents who match the assignment criteria.

Advanced round robin : Assigns a work item to the agent who matches the criteria for skills, presence, and capacity. The initial order is based on when a user is added to the queue. Then, the order is updated based on assignments. Similar to how work items are assigned in the highest capacity method, in round robin assignment, the work items are prioritized in the first-in, first-out manner—that is, the work item that was created first is assigned first.

The ordering for round robin assignment is maintained queue wise. Some agents can be a part of multiple queues. Therefore, depending on the agent's last assignment timestamp in a queue, the agents might be assigned back-to-back or concurrent work items but from different queues.

In scenarios when multiple agents match the work item requirement, and there's a tie in the "order by", like, multiple matched agents with the same available capacity, the system resolves the assignment using round robin based on the earliest time of the last assignment.

For example, three agents, Lesa, Alicia, and Alan, are available with the coffee refund skill and can handle up to three chats at a time. Their last assignment time stamps are 10:30 AM, 10:35 AM, and 10:37 AM, respectively. A work item about a coffee refund arrives in the queue at 10:40 AM. With the order by set to "profile-based available capacity", all the agents at 10:40 AM have the same available capacity of 2 each. To break the tie between the agents, the system uses round robin. Therefore, the incoming chat is assigned to Lesa because her last assignment was the earliest at 10:30 AM. Later at 10:45 AM, if another coffee refund work item comes in, the system assigns it to Alicia. This is also based on the round robin order of assignment between Alicia and Alan because their available capacities are 2 each and Alicia had an earlier assignment than Alan at 10:35 AM.

Least active : Assigns a work item to the agent who has been least active among all the agents who match the required skills, presence, and capacity.

The assignment method uses "the time since last capacity is released for a voice call" and the wrap-up settings configured in the workstream to determine the least-active agent and route the next incoming call to them. For example, consider two agents in a queue. The first agent completes a call five minutes ago while the second agent has just completed their call. When a new call comes in, the system assigns it to the first agent who has finished their activity first.

Routing to the least-active agent assignment strategy helps in a balanced distribution of work items across agents, and results in higher agent efficiency and improved customer satisfaction.

You can also build a custom report to track an agent's "last capacity release time" and understand the assignment distribution across agents.

The least-active assignment method is available for the voice channel only and is the default selection when you create a voice queue.

This feature is intended to help customer service managers or supervisors enhance their team’s performance and improve customer satisfaction. This feature is not intended for use in making—and should not be used to make—decisions that affect the employment of an employee or group of employees, including compensation, rewards, seniority, or other rights or entitlements. Customers are solely responsible for using Dynamics 365, this feature, and any associated feature or service in compliance with all applicable laws, including laws relating to accessing individual employee analytics and monitoring, recording, and storing communications with end users. This also includes adequately notifying end users that their communications with agents may be monitored, recorded, or stored and, as required by applicable laws, obtaining consent from end users before using the feature with them. Customers are also encouraged to have a mechanism in place to inform their agents that their communications with end users may be monitored, recorded, or stored.

You can also create a custom assignment method to suit your business needs.

Create new : Lets you create and use your own rulesets and rules to configure priority, severity, and capacity for choosing the queues to which work items need to be routed. You can create the following rulesets:

• Prioritization rulesets : Lets you define the order in which the work items are assigned to agents when they're available to take more work.
• Assignment rulesets : Represent a set of conditions that are used to select agents and use an order by option to sort the matching agents.
• You must configure presence, capacity, and skill-matching rules in the custom assignment method because the default settings defined for the workstream won't be used in custom assignment method.
• The out-of-the-box assignment strategies don't consider the agent operating hours. You must write a custom assignment method by using the "is_working" operator in the rule definition.

Assignment cycle

Assignment cycle is the prioritization of work items, their selection, and their assignment to the best-suited agent based on the assignment rules. Unified routing optimizes the assignment cycles across the multiple queues in the organization for best performance.

The assignment cycle starts with one of the following triggers:

• Arrival of a new work item in the queue.
• Change to agent presence.
• Updates to agent capacity.
• Addition of an agent to the queue.
• Periodic trigger every five minutes for record type of work item.

How prioritization rulesets work

A prioritization ruleset is an ordered list of prioritization rules. Every prioritization rule represents a priority bucket in the queue. In a prioritization rule, you can specify a set of conditions and order by attributes. During evaluation, the prioritization rules are run in the order they're listed. For the first prioritization rule, the work items in the queue that match its conditions are put in the same priority bucket. In the priority bucket, the items are further sorted by the order specified in the prioritization rule. The second rule runs on the rest of the items in the queue, to identify the next priority bucket, and sorts the bucket by the Order by attribute until all rules are evaluated.

You can create one prioritization ruleset only per queue.

As an example, consider the prioritization ruleset as seen in the following screenshot with four rules.

During any assignment cycle, this prioritization ruleset runs, and the rules within the ruleset run in the order they're listed.

The first rule, "High priority and premium," finds all work items in the queue where the associated case priority is "High" and the case category is "Premium". The system creates the top priority bucket with those work items and sorts them in the "First in and first out" manner as specified in the Order by attribute. The first work item to be assigned from the queue is the oldest item in this bucket.

The next priority bucket is the work items where case category is "Premium". The work items with "Premium" case category and "High" priority have already been put in top bucket as per the preceding rule, so this rule only considers other work items with "Premium" case priority. The Order by attribute in this case also is "First in and first out".

The next priority bucket consists of work items where case priority is high and they haven't been bucketed already. Here the work items are ordered by their "First Response By" field in the ascending order—that is, the work items that require the first response at the earliest are prioritized first.

Some important points about prioritization rules are as follows:

• You can create only one prioritization ruleset per queue.
• Prioritization rules are run during every assignment cycle. If you change any attributes of the work item, such as the priority of the case, that change is considered during the next assignment cycle.
• By default, the queue is sorted on a "first in and first out" manner. If you don't create a prioritization rule, then the oldest work item is assigned first.
• In normal scenarios, when a sufficient number of agents are available to take up the work items, the processing period is a couple of seconds only. The agents are assigned work items in the priority order. However, if work items pile up because of fewer eligible agents, and then an agent becomes available during the processing period, the agent is offered the next work item according to the priority order. This strategy might create a perception that the highest priority item wasn't assigned; especially after some top-priority items are attempted for assignment and yet remain in the queue.
• The work items that don't match the criteria of any of the prioritization rulesets are kept in the last priority bucket, and are ordered by "first in first out".
• Prioritization rules are skipped for affinity work items and such work items is assigned before other work items in the queue. For information about affinity, go to Agent affinity .

How assignment rulesets work

The assignment ruleset is an ordered list of assignment rules. Each assignment rule represents a set of conditions that is used to determine the agents to select and an order-by field to sort the matching agents. At runtime, the assignment rule with the top order is evaluated first. The agents are matched as per the conditions specified in the rule. If more than one matching agent exists, they're sorted by the order by field, and the top agent is assigned the work. If no agents are matched, then the next assignment rule in the ruleset is evaluated. This method can be thought of as a gradual relaxation of constraints in the assignment, such that first, the strictest criteria are applied, and then the conditions are reduced so that the best agent is found. If no matching agents are found, then the work item remains in the queue.

In the assignment rule, the system user attributes are matched with the requirement of the work item. When you select static match, the condition is formed on the System User entity attribute and static values. When you select dynamic match, the conditions on the left are based on the system user root entity and the conditions on the right are based on the conversation root entity. You can drill down to two levels on the conversation root entity to form the rule conditions. An assignment rule with the dynamic match and static match is as follows.

Components of an assignment rule

The assignment rules are composed of the following items:

Order : Specifies the order in which the assignment rule is evaluated in a ruleset. The lower-order rules are run first. If any rule results in matching a user, then the next set of rules isn't evaluated.

Name : The unique rule name.

Condition : The expressions that are evaluated to match the users with the attributes of incoming work. The conditions have three parts:

User attribute : Properties of the users that can be used for comparing the user with the incoming work. The user attributes can be one of the following:

• Select attributes on the System User table.
• Presence Status : Maintained by the unified routing service based on user workloads and manual selection.
• Capacity : Maintained by the unified routing service based on user workloads and manual selection.
• User skills : Represents the skills associated with the user that can be used for doing skill-based assignment.
• Calendar Schedule : Schedule of the user as represented in the user service scheduling calendars.
• Bot attributes : Can be used only when you have configured bots as users and want to do some comparisons on them.

Operators : Define the comparison relationship between the User attribute and incoming work item attributes.

Unified routing filters the attribute-specific operators for you to choose from. Some special operators that are available for the attribute types are as follows.

Value : The user attributes are compared against this value to find the right agent. The value can be static, such as Address 1: County equals "USA". The value can also be dynamic, so that you can compare the user attribute dynamically with the values on the work item. In dynamic values, you can select any attribute on the work item or related records. For example, the following condition finds users whose country is the same as that of the customer associated with the case.

For some operators, values aren't required. They can be conditions, such as "Contains data," "Does not contain data," and "Calendar schedule: is working."

For user skills, the values are predefined for the operators. More information: Set up skill-based routing

Order by : If multiple agents match the conditions in a rule, you can use the "Order by" clause to find the best-suited one. You can specify the following order by clauses:

Ordering Attributes :

• Least active : Is available for voice queues only. The work item is routed to the agent who is least active among all the agents who match skills, presence, and capacity. For more information, see the Types of assignment methods section.
• Round robin
• Unit-based available capacity
• Profile-based available capacity
• Proficiency
• Skill count

User Attributes : These attributes are defined on the system user entity.

A sample assignment rule is explained in the following scenario with a screenshot.

The first condition specifies the "user skills" on which the operator is an exact match. Then the user attributes are evaluated. The different user attributes are specified with operators, and values for each attribute, such as the Presence status attribute, should be equal to "Available" or "Busy". On the right of the operator, you can specify the value that you want the attribute to be matched against. The values can be "static," such as "presence status equals Available or Busy". If you specify "dynamic," the condition is matched at runtime based on the expression you specify. For example, if you specify "Preferred Customer Type Equals Conversation.Contact.Membership Level," the "preferred customer type" of every agent is matched against the dynamically calculated membership level of the customer associated with the chat.

Dynamic match reduces the effort of having to write and maintain multiple static rules for each permutation and combination of the possible value.

Limits on offering a work item repeatedly to an agent

When agents are offered a work item through automatic assignment, they typically can accept or decline. Both rejection and time out of the notification is considered as a decline. An agent who declines the same work item thrice won't be considered for further auto assignment for the specific work item. The system tries to offer the declined work item to other agents in the queue if they're eligible.

For example, agent Serena Davis rejects a chat from customer Ana Bowman twice and the assignment notification times out in the third attempt. The system considers it as three declines and auto assignment won't offer the same chat to Serena Davis again. But the system offers the chat from Ana Bowman to other eligible agents. Also, Serena Davis is considered for other incoming conversations except the declined chat from Ana Bowman.

If all matching agents decline the work item because agent availability is low or the work requires a very specific skill and proficiency, the work remains in the queue. Similarly, if 100 agents decline a particular work item, auto assignment won't consider the work item in further assignment cycles. It can be manually assigned by supervisors or can be picked up by agents including those who rejected it.

You can update the default limit of three declines to a value between one and five based on your org requirement. The limit is applicable to all channels in the org.

You can make an OData call as follows to check the limit for your organization.

<org-url>/api/data/v9.0/msdyn_omnichannelconfigurations?$select=msdyn_number_of_declines_allowed

If this OData call returns the null value, it means that the decline limit is set to a default value of 3.

You can update the OData call as follows to modify the limit.

var data = { "msdyn_number_of_declines_allowed": 3 } // update the record Xrm.WebApi.updateRecord("msdyn_omnichannelconfiguration", "d4d91600-6f21-467b-81fe-6757a2791fa1", data).then( function success(result) { console.log("Omnichannel Configuration updated"); // perform operations on record update }, function (error) { console.log(error.message); // handle error conditions } );

Configure assignment methods and rules FAQ about unified routing in Customer Service, Omnichannel for Customer Service Diagnostics for unified routing Create workstreams Create queues Set up unified routing for records Set up skill-based routing for unified routing

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Assignment – Types, Examples and Writing Guide

Table of Contents

Definition:

Assignment is a task given to students by a teacher or professor, usually as a means of assessing their understanding and application of course material. Assignments can take various forms, including essays, research papers, presentations, problem sets, lab reports, and more.

Assignments are typically designed to be completed outside of class time and may require independent research, critical thinking, and analysis. They are often graded and used as a significant component of a student’s overall course grade. The instructions for an assignment usually specify the goals, requirements, and deadlines for completion, and students are expected to meet these criteria to earn a good grade.

History of Assignment

The use of assignments as a tool for teaching and learning has been a part of education for centuries. Following is a brief history of the Assignment.

• Ancient Times: Assignments such as writing exercises, recitations, and memorization tasks were used to reinforce learning.
• Medieval Period : Universities began to develop the concept of the assignment, with students completing essays, commentaries, and translations to demonstrate their knowledge and understanding of the subject matter.
• 19th Century : With the growth of schools and universities, assignments became more widespread and were used to assess student progress and achievement.
• 20th Century: The rise of distance education and online learning led to the further development of assignments as an integral part of the educational process.
• Present Day: Assignments continue to be used in a variety of educational settings and are seen as an effective way to promote student learning and assess student achievement. The nature and format of assignments continue to evolve in response to changing educational needs and technological innovations.

Types of Assignment

Here are some of the most common types of assignments:

An essay is a piece of writing that presents an argument, analysis, or interpretation of a topic or question. It usually consists of an introduction, body paragraphs, and a conclusion.

Essay structure:

• Introduction : introduces the topic and thesis statement
• Body paragraphs : each paragraph presents a different argument or idea, with evidence and analysis to support it
• Conclusion : summarizes the key points and reiterates the thesis statement

Research paper

A research paper involves gathering and analyzing information on a particular topic, and presenting the findings in a well-structured, documented paper. It usually involves conducting original research, collecting data, and presenting it in a clear, organized manner.

Research paper structure:

• Title page : includes the title of the paper, author’s name, date, and institution
• Abstract : summarizes the paper’s main points and conclusions
• Introduction : provides background information on the topic and research question
• Literature review: summarizes previous research on the topic
• Methodology : explains how the research was conducted
• Results : presents the findings of the research
• Discussion : interprets the results and draws conclusions
• Conclusion : summarizes the key findings and implications

A case study involves analyzing a real-life situation, problem or issue, and presenting a solution or recommendations based on the analysis. It often involves extensive research, data analysis, and critical thinking.

Case study structure:

• Introduction : introduces the case study and its purpose
• Background : provides context and background information on the case
• Analysis : examines the key issues and problems in the case
• Solution/recommendations: proposes solutions or recommendations based on the analysis
• Conclusion: Summarize the key points and implications

A lab report is a scientific document that summarizes the results of a laboratory experiment or research project. It typically includes an introduction, methodology, results, discussion, and conclusion.

Lab report structure:

• Title page : includes the title of the experiment, author’s name, date, and institution
• Abstract : summarizes the purpose, methodology, and results of the experiment
• Methods : explains how the experiment was conducted
• Results : presents the findings of the experiment

Presentation

A presentation involves delivering information, data or findings to an audience, often with the use of visual aids such as slides, charts, or diagrams. It requires clear communication skills, good organization, and effective use of technology.

Presentation structure:

• Introduction : introduces the topic and purpose of the presentation
• Body : presents the main points, findings, or data, with the help of visual aids
• Conclusion : summarizes the key points and provides a closing statement

Creative Project

A creative project is an assignment that requires students to produce something original, such as a painting, sculpture, video, or creative writing piece. It allows students to demonstrate their creativity and artistic skills.

Creative project structure:

• Introduction : introduces the project and its purpose
• Body : presents the creative work, with explanations or descriptions as needed
• Conclusion : summarizes the key elements and reflects on the creative process.

Examples of Assignments

Following are Examples of Assignment templates samples:

Essay template:

I. Introduction

• Hook: Grab the reader’s attention with a catchy opening sentence.
• Background: Provide some context or background information on the topic.
• Thesis statement: State the main argument or point of your essay.

II. Body paragraphs

• Topic sentence: Introduce the main idea or argument of the paragraph.
• Evidence: Provide evidence or examples to support your point.
• Analysis: Explain how the evidence supports your argument.
• Transition: Use a transition sentence to lead into the next paragraph.

III. Conclusion

• Restate thesis: Summarize your main argument or point.
• Review key points: Summarize the main points you made in your essay.
• Concluding thoughts: End with a final thought or call to action.

Research paper template:

I. Title page

• Title: Give your paper a descriptive title.
• Author: Include your name and institutional affiliation.
• Date: Provide the date the paper was submitted.

II. Abstract

• Background: Summarize the background and purpose of your research.
• Methodology: Describe the methods you used to conduct your research.
• Results: Summarize the main findings of your research.
• Conclusion: Provide a brief summary of the implications and conclusions of your research.

III. Introduction

• Background: Provide some background information on the topic.
• Research question: State your research question or hypothesis.
• Purpose: Explain the purpose of your research.

IV. Literature review

• Background: Summarize previous research on the topic.
• Gaps in research: Identify gaps or areas that need further research.

V. Methodology

• Participants: Describe the participants in your study.
• Procedure: Explain the procedure you used to conduct your research.
• Measures: Describe the measures you used to collect data.

VI. Results

• Quantitative results: Summarize the quantitative data you collected.
• Qualitative results: Summarize the qualitative data you collected.

VII. Discussion

• Interpretation: Interpret the results and explain what they mean.
• Implications: Discuss the implications of your research.
• Limitations: Identify any limitations or weaknesses of your research.

VIII. Conclusion

• Review key points: Summarize the main points you made in your paper.

Case study template:

• Background: Provide background information on the case.
• Research question: State the research question or problem you are examining.
• Purpose: Explain the purpose of the case study.

II. Analysis

• Problem: Identify the main problem or issue in the case.
• Factors: Describe the factors that contributed to the problem.
• Alternative solutions: Describe potential solutions to the problem.

III. Solution/recommendations

• Proposed solution: Describe the solution you are proposing.
• Rationale: Explain why this solution is the best one.
• Implementation: Describe how the solution can be implemented.

IV. Conclusion

• Summary: Summarize the main points of your case study.

Lab report template:

• Title: Give your report a descriptive title.
• Date: Provide the date the report was submitted.
• Background: Summarize the background and purpose of the experiment.
• Methodology: Describe the methods you used to conduct the experiment.
• Results: Summarize the main findings of the experiment.
• Conclusion: Provide a brief summary of the implications and conclusions
• Background: Provide some background information on the experiment.
• Hypothesis: State your hypothesis or research question.
• Purpose: Explain the purpose of the experiment.

IV. Materials and methods

• Materials: List the materials and equipment used in the experiment.
• Procedure: Describe the procedure you followed to conduct the experiment.
• Data: Present the data you collected in tables or graphs.
• Analysis: Analyze the data and describe the patterns or trends you observed.

VI. Discussion

• Implications: Discuss the implications of your findings.
• Limitations: Identify any limitations or weaknesses of the experiment.

VII. Conclusion

• Restate hypothesis: Summarize your hypothesis or research question.
• Review key points: Summarize the main points you made in your report.

Presentation template:

• Attention grabber: Grab the audience’s attention with a catchy opening.
• Purpose: Explain the purpose of your presentation.
• Overview: Provide an overview of what you will cover in your presentation.

II. Main points

• Main point 1: Present the first main point of your presentation.
• Supporting details: Provide supporting details or evidence to support your point.
• Main point 2: Present the second main point of your presentation.
• Main point 3: Present the third main point of your presentation.
• Summary: Summarize the main points of your presentation.
• Call to action: End with a final thought or call to action.

Creative writing template:

• Setting: Describe the setting of your story.
• Characters: Introduce the main characters of your story.
• Rising action: Introduce the conflict or problem in your story.
• Climax: Present the most intense moment of the story.
• Falling action: Resolve the conflict or problem in your story.
• Resolution: Describe how the conflict or problem was resolved.
• Final thoughts: End with a final thought or reflection on the story.

How to Write Assignment

Here is a general guide on how to write an assignment:

• Understand the assignment prompt: Before you begin writing, make sure you understand what the assignment requires. Read the prompt carefully and make note of any specific requirements or guidelines.
• Research and gather information: Depending on the type of assignment, you may need to do research to gather information to support your argument or points. Use credible sources such as academic journals, books, and reputable websites.
• Organize your ideas : Once you have gathered all the necessary information, organize your ideas into a clear and logical structure. Consider creating an outline or diagram to help you visualize your ideas.
• Write a draft: Begin writing your assignment using your organized ideas and research. Don’t worry too much about grammar or sentence structure at this point; the goal is to get your thoughts down on paper.
• Revise and edit: After you have written a draft, revise and edit your work. Make sure your ideas are presented in a clear and concise manner, and that your sentences and paragraphs flow smoothly.
• Proofread: Finally, proofread your work for spelling, grammar, and punctuation errors. It’s a good idea to have someone else read over your assignment as well to catch any mistakes you may have missed.
• Submit your assignment : Once you are satisfied with your work, submit your assignment according to the instructions provided by your instructor or professor.

Applications of Assignment

Assignments have many applications across different fields and industries. Here are a few examples:

• Education : Assignments are a common tool used in education to help students learn and demonstrate their knowledge. They can be used to assess a student’s understanding of a particular topic, to develop critical thinking skills, and to improve writing and research abilities.
• Business : Assignments can be used in the business world to assess employee skills, to evaluate job performance, and to provide training opportunities. They can also be used to develop business plans, marketing strategies, and financial projections.
• Journalism : Assignments are often used in journalism to produce news articles, features, and investigative reports. Journalists may be assigned to cover a particular event or topic, or to research and write a story on a specific subject.
• Research : Assignments can be used in research to collect and analyze data, to conduct experiments, and to present findings in written or oral form. Researchers may be assigned to conduct research on a specific topic, to write a research paper, or to present their findings at a conference or seminar.
• Government : Assignments can be used in government to develop policy proposals, to conduct research, and to analyze data. Government officials may be assigned to work on a specific project or to conduct research on a particular topic.
• Non-profit organizations: Assignments can be used in non-profit organizations to develop fundraising strategies, to plan events, and to conduct research. Volunteers may be assigned to work on a specific project or to help with a particular task.

Purpose of Assignment

The purpose of an assignment varies depending on the context in which it is given. However, some common purposes of assignments include:

• Assessing learning: Assignments are often used to assess a student’s understanding of a particular topic or concept. This allows educators to determine if a student has mastered the material or if they need additional support.
• Developing skills: Assignments can be used to develop a wide range of skills, such as critical thinking, problem-solving, research, and communication. Assignments that require students to analyze and synthesize information can help to build these skills.
• Encouraging creativity: Assignments can be designed to encourage students to be creative and think outside the box. This can help to foster innovation and original thinking.
• Providing feedback : Assignments provide an opportunity for teachers to provide feedback to students on their progress and performance. Feedback can help students to understand where they need to improve and to develop a growth mindset.
• Meeting learning objectives : Assignments can be designed to help students meet specific learning objectives or outcomes. For example, a writing assignment may be designed to help students improve their writing skills, while a research assignment may be designed to help students develop their research skills.

When to write Assignment

Assignments are typically given by instructors or professors as part of a course or academic program. The timing of when to write an assignment will depend on the specific requirements of the course or program, but in general, assignments should be completed within the timeframe specified by the instructor or program guidelines.

It is important to begin working on assignments as soon as possible to ensure enough time for research, writing, and revisions. Waiting until the last minute can result in rushed work and lower quality output.

It is also important to prioritize assignments based on their due dates and the amount of work required. This will help to manage time effectively and ensure that all assignments are completed on time.

In addition to assignments given by instructors or professors, there may be other situations where writing an assignment is necessary. For example, in the workplace, assignments may be given to complete a specific project or task. In these situations, it is important to establish clear deadlines and expectations to ensure that the assignment is completed on time and to a high standard.

Characteristics of Assignment

Here are some common characteristics of assignments:

• Purpose : Assignments have a specific purpose, such as assessing knowledge or developing skills. They are designed to help students learn and achieve specific learning objectives.
• Requirements: Assignments have specific requirements that must be met, such as a word count, format, or specific content. These requirements are usually provided by the instructor or professor.
• Deadline: Assignments have a specific deadline for completion, which is usually set by the instructor or professor. It is important to meet the deadline to avoid penalties or lower grades.
• Individual or group work: Assignments can be completed individually or as part of a group. Group assignments may require collaboration and communication with other group members.
• Feedback : Assignments provide an opportunity for feedback from the instructor or professor. This feedback can help students to identify areas of improvement and to develop their skills.
• Academic integrity: Assignments require academic integrity, which means that students must submit original work and avoid plagiarism. This includes citing sources properly and following ethical guidelines.
• Learning outcomes : Assignments are designed to help students achieve specific learning outcomes. These outcomes are usually related to the course objectives and may include developing critical thinking skills, writing abilities, or subject-specific knowledge.

Advantages of Assignment

There are several advantages of assignment, including:

• Helps in learning: Assignments help students to reinforce their learning and understanding of a particular topic. By completing assignments, students get to apply the concepts learned in class, which helps them to better understand and retain the information.
• Develops critical thinking skills: Assignments often require students to think critically and analyze information in order to come up with a solution or answer. This helps to develop their critical thinking skills, which are important for success in many areas of life.
• Encourages creativity: Assignments that require students to create something, such as a piece of writing or a project, can encourage creativity and innovation. This can help students to develop new ideas and perspectives, which can be beneficial in many areas of life.
• Builds time-management skills: Assignments often come with deadlines, which can help students to develop time-management skills. Learning how to manage time effectively is an important skill that can help students to succeed in many areas of life.
• Provides feedback: Assignments provide an opportunity for students to receive feedback on their work. This feedback can help students to identify areas where they need to improve and can help them to grow and develop.

Limitations of Assignment

There are also some limitations of assignments that should be considered, including:

• Limited scope: Assignments are often limited in scope, and may not provide a comprehensive understanding of a particular topic. They may only cover a specific aspect of a topic, and may not provide a full picture of the subject matter.
• Lack of engagement: Some assignments may not engage students in the learning process, particularly if they are repetitive or not challenging enough. This can lead to a lack of motivation and interest in the subject matter.
• Time-consuming: Assignments can be time-consuming, particularly if they require a lot of research or writing. This can be a disadvantage for students who have other commitments, such as work or extracurricular activities.
• Unreliable assessment: The assessment of assignments can be subjective and may not always accurately reflect a student’s understanding or abilities. The grading may be influenced by factors such as the instructor’s personal biases or the student’s writing style.
• Lack of feedback : Although assignments can provide feedback, this feedback may not always be detailed or useful. Instructors may not have the time or resources to provide detailed feedback on every assignment, which can limit the value of the feedback that students receive.

About the author

Muhammad Hassan

Researcher, Academic Writer, Web developer

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Part III: Travel Demand Modeling

13 Last Step of Four Step Modeling (Trip Assignment Models)

Chapter overview.

Chapter 13 presents trip assignment, the last step of the Four-Step travel demand Model (FSM). This step determines which paths travelers choose for moving between each pair of zones. Additionally, this step can yield numerous results, such as traffic volumes in different transportation corridors, the patterns of vehicular movements, total vehicle miles traveled (VMT) and vehicle travel time (VTT) in the network, and zone-to-zone travel costs. Identification of the heavily congested links is crucial for transportation planning and engineering practitioners. This chapter begins with some fundamental concepts, such as the link cost functions. Next, it presents some common and useful trip assignment methods with relevant examples. The methods covered in this chapter include all-or-nothing (AON), user equilibrium (UE), system optimum (SO), feedback loop between distribution and assignment (LDA),  incremental increase assignment, capacity restrained assignment, and stochastic user equilibrium assignment.

Learning Objectives

•  Describe the reasons for performing trip assignment models in FSM and relate these models’ foundation through the cost-function concept.
• Compare static and dynamic trip assignment models and infer the appropriateness of each model for different situations.
• Explain Wardrop principles and relate them to traffic assignment algorithms.
• Complete simple network traffic assignment models using static models such as the all-or-nothing and user equilibrium models.
• Solve modal split analyses manually for small samples using the discrete choice modeling framework and multinominal logit models.

Introduction

In this chapter, we continue the discussion about FSM and elaborate on different methods of traffic assignment, the last step in the FSM model after trip generation, trip distribution, and modal split. The traffic assignment step, which is also called route assignment or route choice , simulates the choice of route selection from a set of alternatives between the origin and the destination zones (Levinson et al., 2014). The first three FSM steps determine the number of trips produced between each zone and the proportion completed by different transportation modes. The purpose of the final step is to determine the routes or links in the study area that are likely to be used. For example, when updating a Regional Transportation Plan (RTP), traffic assignment is helpful in determining how much shift or diversion in daily traffic happens with the introduction an additional transit line or extension a highway corridor (Levinson et al., 2014). The output from the last step can provide modelers with numerous valuable results. By analyzing the results, the planner can gain insight into the strengths and weaknesses of different transportation plans. The results of trip assignment analysis can be:

• The traffic flows in the transportation system and the pattern of vehicular movements.
• The volume of traffic on network links.
• Travel costs between trip origins and destinations (O-D).
• Aggregated network metrics such as total vehicle flow, vehicle miles traveled (VMT) , and vehicle travel time (VTT).
• Zone-to-zone travel costs (travel time) for a given level of demand.
• Modeled link flows highlighting congested corridors.
• Analysis of turning movements for future intersection design.
• Determining the Origin-Destination (O-D) pairs using a specific link or path.
• Simulation of the individual choice for each pair of origins and destinations (Mathew & Rao, 2006).

Link Performance Function

Building a link performance function is one of the most important and fundamental concepts of the traffic assignment process. This function is usually used for estimating travel time, travel cost, and speed on the network based on the relationship between speed and travel flow. While this function can take different forms, such as linear, polynomial , exponential , and hyperbolic , one of the most common functions is the link performance function which represents generalized travel costs (United States Bureau of Public Roads, 1964). This equation estimates travel time on a free-flow road (travel with speed limit) adding a function that exponentially increases travel time as the road gets more congested. The road volume-to-capacity ratio can represent congestion (Meyer, 2016).

While transportation planners now recognize that intersection delays contribute to link delays, the following sections will focus on the traditional function. Equation (1) is the most common and general formula for the link performance function.

• t and x are the travel time and vehicle flow;
• t 0 is the link free flow travel time;
• k is the link capacity;
• α and β are parameters for specific type of links and calibrated using the field data. In the absence of any field data, it is usually assumed = 0.15, and β= 4.0.

α and β are the coefficients for this formula and can take different values (model parameters). However, most studies and planning practices use the same value for them. These values can be locally calibrated for the most efficient results.

Figure 13.1 demonstrates capacity as the relationship between flow and travel time. In this plot, the travel time remains constant as vehicle volumes increase until the turning point , which indicates that the link’s volume is approaching its capacity.

The following example shows how the link performance function helps us to determine the travel time according to flow and capacity.

Performance Function Example

Assume the traffic volume on a path between zone i and j was 525. The travel time recorded on this path is 15 minutes. If the capacity of this path would be 550, then calculate the new travel time for future iteration of the model.

Based on the link performance function, we have:

Now we have to plug in the numbers into the formula to determine the new travel time:

Traffic Assignment Models

Typically, traffic assignment is calculated for private cars and transit systems independently. Recall that the impedance function differs for drivers and riders, and thus simulating utility maximization behavior should be approached differently. For public transit assignment, variables such as fare, stop or transfer, waiting time, and trip times define the utility (equilibrium) (Sheffi, 1985). For private car assignment, however, in some cases, the two networks are related when public buses share highways with cars, and congestion can also affect the performance.

Typically, private car traffic assignment models the path choice of trip makers using:

• algorithms like all-or-nothing
• user equilibrium
• system optimum assignment

Of the assignment models listed above, user equilibrium is widely adopted in the U.S. (Meyer, 2016). User equilibrium relies on the premise that travelers aim to minimize their travel costs. This algorithm achieves equilibrium when no user can decrease their travel time or cost by altering their travel path.

• incremental
• capacity-restrained
• iterative feedback loop
• Stochastic user equilibrium assignment
• Dynamic traffic assignment

All-or-nothing Model

Through the all-or-nothing (AON) assignment, it is assumed that the impedance of a road or path between each origin and destination is constant and equal to the free-flow level of service. This means that the traffic time is not affected by the traffic flow on the path. The only logic behind this model is that each traveler uses the shortest path from his or her origin to the destination, and no vehicle is assigned to other paths (Hui, 2014). This method is called the all-or-nothing assignment model and is the simplest one among all assignment models. This method is also called the 0-1 assignment model, and its advantage is its simple procedure and calculation. The assumptions of this method are:

• Congestion does not affect travel time or cost, meaning that no matter how much traffic is loaded on the route, congestion does not take place.
• Since the method assigns one route to any travel between each pair of OD, all travelers traveling from a particular zone to another particular zone choose the same route (Hui, 2014).

To run the AON model, the following process can be followed:

• Step 0: Initialization. Use free flow travel costs Ca=Ca(0) , for each link a on the empty network. Ɐ
• Step 1: Path finding. Find the shortest path P for each zonal pair.
• Step 2: Path flows assigning. Assign both passenger trips (hppod) and freight trips (hfpod) in PCEs from zonal o to d to path P.
• Step 3: Link flows computing. Sum the flows on all paths going through a link as total flows of this link.

Example 2 illustrates the above-mentioned process for the AON model

All-or-nothing Example

Table 13.1 shows a trip distribution matrix with 4 zones. Using the travel costs between each pair of them shown in Figure 13.2, assign the traffic to the network. Load the vehicle trips from the trip distribution table shown below using the AON technique. After assigning the traffic, illustrate the links and the traffic volume on each on them.

Table 13.1 Trip Distribution Results.

To solve this problem, we need to find the shortest path among all alternatives for each pair of zones. The result of this procedure would be 10 routes in total, each of which bears a specific amount of travels. For instance, the shortest path between zone 1 and 2 is the straight line with 5 min travel time. All other routes like 1 to 4 to 2 or 1 to 4 to 3 to 2 would be empty from travelers going from zone 1 to zone 2. The results are shown in Table 13.2.

As you can see, some of the routes remained unused. This is because in all-or-nothing if a route has longer travel time or higher costs, then it is assumed it would not be used at all.

User Equilibrium

The next method for traffic assignment is called User Equilibrium (UE). The rule or algorithm is adapted from the well-known Wardrop equilibrium (1952) conditions (Correa & Stier-Moses, 2011). In this algorithm, it is assumed that travelers will always choose the shortest path, and equilibrium conditions are realized when no traveler is able to decrease their travel impedance by changing paths (Levinson et al., 2014).

As we discussed, the UE method is based on the first principle of Wardrop : “for each origin- destination (OD) pair, with UE, the travel time on all used paths is equal and less than or equally to the travel time that would be experienced by a single vehicle on any unused path”( Jeihani Koohbanani, 2004, p. 10). The mathematical format of this principle is shown in equation (3):

For a given OD pair, the UE condition can be expressed in equation (3):

This model assumes that all paths have equal travel time. Additionally, the model includes the following general assumptions:

• The users possess all the knowledge needed about different paths.
• The users have perfect knowledge of the path cost.
• Travel time in a route is subject to change only by the cost flow function of that route.
• Travel times increases as we load travel into the network (Mathew & Rao, 2006).

Hence, the UE assignment comes to an optimization problem that can be formulated using equation (4):

k  is the path x a equilibrium flow in link a t a  travel time on link a f k rs  flow on path  connecting OD pairs q rs  trip rate between  and δ a, k rs is constraint function defined as 1 if link a belongs to path k and 0 otherwise

Example 3 shows how the UE method can be applied for the traffic assignment step. This example is a very simple network consisting of two zones with two possible paths between them.

UE Example 

In this example, t 1 and t 2 are travel times measured by min on each route, and x 1 and x 2 are traffic flows on each route measured by (Veh/Hour).

Using the UE method, assign 4,500 Veh/Hour to the network and calculate travel time on each route after assignment, traffic volume, and system total travel time.

According to the information provided, total flow (X 1 +X 2 ) is equal to 4,500 (4.5).

First, we need to check, with all traffic assigned to one route, whether that route is still the shortest path. Thus we have:

T 1 (4.5)=23min

T 2 (0)=3min

if all traffic is assigned to route 2:

T 1 (0)=3min

T 2 (4.5)=43.5 min

Step 2: Wardrope equilibrium rule: t 1 =t 2        5+4x 1 =3+ 2x 2 2         and we have x 1 =4.5-x 2

Now the equilibrium equation can be written as: 6 + 4(4.5 − x2)=4+ x222

x 1 = 4.5 − x 2 = 1.58

Now the updated average travel times are: t 1 =5+4(1.58)=11.3min and T 2 =3+2(2.92)2=20.05min

Now the total system travel time is:

Z(x)=X 1 T 1 (X 1 )+X 2 T 2 (X 2 )=2920 veh/hr(11.32)+1585 veh/hr(20.05)=33054+31779=64833 min

System Optimum Assignment

One traffic assignment model is similar to the previous one and is called system optimum (SO). The second principle of the Wardrop defines the model’s logic. Based on this principle, drivers’ rationale for choosing a path is to minimize total system costs with one another to minimize total system travel time (Mathew & Rao, 2006). Using the SO traffic assignment, one can solve various problems, such as optimizing the departure time for a single commuting route, minimizing the total travel time from multiple origins to a single destination, or minimizing travel time in stochastic time-dependent O-D flows from several origins to a single destination ( Jeihani & Koohbanani, 2004).

One other traffic assignment model similar to the previous one is called system optimum (SO) in which the second principle of the Wardrop defines the logic of the model. Based on this principle, drivers’ rationale for choosing a path is to minimize total system costs with one another in order to minimize total system travel time (Mathew & Rao, 2006). Using the SO traffic assignment, problems like optimizing departure time for a single commuting route, minimizing total travels from multiple origins to one destination, or minimizing travel time in stochastic time-dependent OD flows from several origins to a single destination can be solved (Jeihani Koohbanani, 2004).

The basic mathematical formula for this model that satisfies the principle of the model is shown in equation (5):

In example 4, we will use the same network we described in the UE example in order to compare the results for the two models.

In that simple two-zone network, we had:

T 1 =5+4X 1    T2=3+2X 2 2

Now, based on the principle of the model we have:

Z(x)=x 1 t 1 (x 1 )+x 2 t 2 (x 2 )

Z(x)=x 1 (5+4x 1 )+x 2 (3+2x 2 2 )

Z(x)=5x 1 +4x 1 2 +3x 2 +2x 2 3

From the flow conservation. we have: x 1 +x 2 =4.5     x 1 =4.5-x 2

Z(x)=5(4.5-x 2 )+4(4.5-x 2 )2+4x 2 +x 2 3

Z(x)=x 3 2 +4x 2 2 -27x 2 +103.5

In order to minimize the above equation, we have to take derivatives and equate it to zero. After doing the calculations, we have:

Based on our finding, the system travel time would be:

T 1 =5+4*1.94=12.76min     T 2 =3+ 2(2.56)2=10.52 min

And the total travel time of the system would be:

Z(x)=X 1 T 1 (X 1 )+X 2 T 2 (X 2 )=1940 veh/hr(12.76)+2560 veh/hr(10.52)=24754+26931=51685 min

Incremental Increase model

Incremental increase is based on the logic of the AON model and models a process designed with multiple steps. In each step or level, a fraction of the total traffic volume is assigned, and travel time is calculated based on the allocated traffic volume. Through this incremental addition of traffic, the travel time of each route in step (n) is the updated travel time from the previous step (n-1) (Rojo, 2020).

The steps for the incremental increase traffic assignment model are:

• Finding the shortest path between each pair of O-Ds (Origin Destination).
• Assigning a portion of the trips according to the matrix (usually 40, 30, 20 and 10 percent to the shortest path).
• Updating the travel time after each iteration (each incremental increase).
• Continuing until all trips are assigned.
• Summing the results.

The example below illustrates the implementation process of this method.

A hypothetical network accommodates two zones with three possible links between them. Perform an incremental increase traffic assignment model for assigning 200 trips between the two zones with increments of: 30%, 30%, 20%, 20%. (The capacity is 50 trips.)

Incremental Increase Example

Step 1 (first iteration): Using the method of AON, we now assign the flow to the network using the function below:

Since the first route has the shortest travel time, the first 30% of the trips will be assigned to route 1. The updated travel time for this path would be:

And the remaining route will be empty, and thus their travel times are unchanged.

Step 2 (second iteration): Now, we can see that the second route has the shortest travel time, with 30% of the trips being assigned to this route, and the new travel time would be:

Step 3 (third iteration): In the third step, the 20% of the remaining trips will be assigned to the shortest path, which in this case is the first route again. The updated travel time for this route is:

Step 4 (fourth iteration): In the last iteration, the remaining 10% would be assigned to first route, and the time is:

Finally, we can see that route 1 has a total of 140 trips with a 8.85 travel time, the second route has a total of 60 trips with a 9.17 travel time, and the third route was never used.

Capacity Restraint Assignment

So far, all the presented algorithms or rules have considered the model’s link capacity. The flow is assigned to a link based on travel time as the only factor. In this model, after each iteration, the total number of trips is compared with the capacity to observe how much increase in travel time was realized by the added volume. In this model, the iteration stops if the added volume in step (n) does not change the travel time updated in step (n-1). With the incorporation of such a constraint, the cost or performance function would be different from the cost functions discussed in previous algorithms (Mathew & Rao, 2006). Figure 13.6 visualizes the relationship between flow and travel time with a capacity constraint.

Based on this capacity constraint specific to each link, the α, β can be readjusted for different links such as highways, freeways, and other roads.

Feedback Loop Model (Combined Traffic Assignment and Trip Distribution)

The feedback loop model defines an interaction between the trip distribution route choice step with several iterations. The model allows travelers to change their destination if a route is congested. For example, the feedback loop models that the traveler has a choice of similar destinations, such as shopping malls, in the area. In other words, in a real-world situation, travelers usually simultaneously decide about their travel characteristics (Qasim, 2012).

The chart below shows how the combination of these two modes can take place:

Equation (6), shown below for this model, ensures convergence at the end of the model is:

where C a (t) is the same as previous

P a , is total personal trip flows on link a,

f a ; is total freight trip flows on link a,

T od is the total flow from node o to node d,

p od is personal trip from node o to node d,

F od is freight trip from node o to node d,

ζ is a parameter estimated from empirical data,

K is a parameter depending on the type of gravity model used to calculate T od , Evans (1976) proved that K’ equals to 1 for distribution using doubly constrained gravity model and it equals to 1 plus attractiveness for distribution using singly constrained model. Florian et al. (1975) ignored K for distribution using a doubly constrained gravity model because it is a constant.

Stochastic User Equilibrium Traffic Assignment

Stochastic user equilibrium traffic assignment is a sophisticated and more realistic model in which the level of uncertainty regarding which link should be used based on a measurement of utility function is introduced. This model performs a discrete choice analysis through a logistic model. Based on the first Wardrop principle, this model assumes that all drivers perceive the costs of traveling in each link identically and choose the route with minimum cost. In stochastic UE, however, the model allows different individuals to have different perceptions about the costs, and thus, they may choose non-minimum cost routes (Mathew & Rao, 2006). In this model, flow is assigned to all links from the beginning, unlike previous models, which is closer to reality. The probability of using each path is calculated with the following logit formula shown in equation (7):

P i is the probability of using path i

U i is the utility function for path i

In the following, an example of a simple network is presented.

Stochastic User Equilibrium Example

There is a flow of 200 trips between two points and their possible path, each of which has a travel time specified in Figure 13.7.

Using the mentioned logit formula for these paths, we have:

Based on the calculated probabilities, the distribution of the traffic flow would be:

Q 1 =175 trips

Q 2 =24 trips

Q 3 =1 trips

Dynamic Traffic Assignment

Recall the first Wardrop principle, in which travelers are believed to choose their routes with the minimum cost. Dynamic traffic assignment is based on the same rule, but the difference is that delays result from congestion. In this way, not only travelers’ route choice affects the network’s level of service, but also the network’s level of service affects travelers’ choice. However, it is not theoretically proven that an equilibrium would result under such conditions (Mathew & Rao, 2006).

Today, various algorithms are developed to solve traffic assignment problems. In any urban transportation system, travelers’ route choice and different links’ level of service have a dynamic feedback loop and affect each other simultaneously. However, a lot of these rules are not present in the models presented here. In real world cases, there can be more than thousands of nodes and links in the network, and therefore more sensitivity to dynamic changes is required for a realistic traffic assignment (Meyer, 2016). Also, the travel demand model applies a linear sequence of the four steps, which is unlike reality. Additionally, travelers may have only a limited knowledge of all possible paths, modes, and opportunities and may not make rational decisions.

In this last chapter of landuse/transportation modeling book, we reviewed the basic concepts and principles of traffic assignment models as the last step in travel demand modeling. Modeling the route choice and other components of travel behavior and demand for transportation proven to be very challenging and can incorporate multiple factors. For instance, going from AON to incremental increase assignment, we factor in the capacity and volume (and resulting delays) relationship in the assignment to make more realistic models.  Multiple-time-period assignments for multiple classes, separate specification of facilities like high-occupancy vehicle (HOV) and high-occupancy toll (HOT) lanes; and, independent transit assignment using congested highway travel times to estimate a bus ridership assignment, are some of the new extensions and variation of algorithms that take into account more realities within transportation network. A new prospect in traffic assignment models that adds several capabilities for such efforts is emergence of ITS such as data that can be collected from connected vehicles or autonomous vehicles. Using these data, perceived utility or impedances of different modes or infrastructure from individuals perspective can be modeled accurately, leading to more accurate assignment models, which are crucial planning studies such as growth and land use control efforts, environmental studies, transportation economies, etc.

Route choice is the process of choosing a certain path for a trip from a very large choice sets.

Regional Transportation Plan is long term planning document for a region’s transportation usually updated every five years.

Vehicles (VMT) is the aggregate number of miles deriven from in an area in particular time of day.

• Total vehicle travel time is the aggregate amount of time spent in transportation usually in minutes.

Link performance function is function used for estimating travel time, travel cost, and speed on the network based on the relationship between speed and travel flow.

Hyperbolic function is a function used for linear differential equations like calculating distances and angels in hyperbolic geometry.

Free-flow road is situation where vehicles can travel with the maximum allowed travel speed.

• Algorithms like all-or-nothing an assignment model where we assume that the impedance of a road or path between each origin and destination is constant and is equal to free-flow level of service, meaning that the traffic time is not affected by the traffic flow on the path.

Capacity-restrained is a model which takes into account the capacity of a road compared to volume and updates travel times.

User equilibrium is a traffic assignment model where we assume that travelers will always choose the shortest path and equilibrium condition would be realized when no traveler is able to decrease their travel impedance by changing paths.

System optimum assignment is an assignment model based on the principle that drivers’ rationale for choosing a path is to minimize total system costs with one another in order to minimize total system travel time.

• Static user-equilibrium assignment algorithm is an iterative traffic assignment process which assumes that travelers chooses the travel path with minimum travel time subject to constraints.
• Iterative feedback loop is a model that iterates between trip distribution and route choice step based on the rational that if a path gets too congested, the travel may alter travel destination.

First principle of Wardrop is the assumption that for each origin-destination (OD) pair, with UE, the travel time on all used paths is equal and less than or equally to the travel time that would be experienced by a single vehicle on any unused path.

System optimum (SO) is a condition in trip assignment model where total travel time for the whole area is at a minimum.

• Stochastic time-dependent OD is a modeling framework where generation and distribution of trips are randomly assigned to the area.

Incremental increase is AON-based model with multiple steps in each of which, a fraction of the total traffic volume is assigned, and travel time is calculated based on the allocated traffic volume.

Stochastic user equilibrium traffic assignment employs a probability distribution function that controls for uncertainties when drivers compare alternative routes and make decisions.

Dynamic traffic assignment is a model based on Wardrop first principle in which delays resulted from congestion is incorporated in the algorithm.

Key Takeaways

In this chapter, we covered:

• Traffic assignment is the last step of FSM, and the link cost function is a fundamental concept for traffic assignment.
• Different static and dynamic assignments and how to perform them using a simplistic transportation network.
• Incorporating stochastic decision-making about route choice and how to solve assignment problems with regard to this feature.

Prep/quiz/assessments

• Explain what the link performance function is in trip assignment models and how it is related to link capacity.
• Name a few static and dynamic traffic assignment models and discuss how different their rules or algorithms are.
• How does stochastic decision-making on route choice affect the transportation level of service, and how it is incorporated into traffic assignment problems?
• Name one extension of the all-or-nothing assignment model and explain how this extension improves the model results.

Correa, J.R., & Stier-Moses, N.E.(2010).Wardrope equilibria. In J.J. Cochran( Ed.), Wiley encyclopedia of operations research and management science (pp.1–12). Hoboken, NJ: John Wiley & Sons. http://dii.uchile.cl/~jcorrea/papers/Chapters/CS2010.pdf

Hui, C. (2014). Application study of all-or-nothing assignment method for determination of logistic transport route in urban planning. Computer Modelling & New Technologies , 18 , 932–937. http://www.cmnt.lv/upload-files/ns_25crt_170vr.pdf

Jeihani Koohbanani, M. (2004).  Enhancements to transportation analysis and simulation systems (Unpublished Doctoral dissertation, Virginia Tech). https://vtechworks.lib.vt.edu/bitstream/handle/10919/30092/dissertation-final.pdf?sequence=1&isAllowed=y

Levinson, D., Liu, H., Garrison, W., Hickman, M., Danczyk, A., Corbett, M., & Dixon, K. (2014). Fundamentals of transportation . Wikimedia. https://upload.wikimedia.org/wikipedia/commons/7/79/Fundamentals_of_Transportation.pdf

Mathew, T. V., & Rao, K. K. (2006). Introduction to transportation engineering. Civil engineering–Transportation engineering. IIT Bombay, NPTEL ONLINE, Http://Www. Cdeep. Iitb. Ac. in/Nptel/Civil% 20Engineering .

Meyer, M. D. (2016). Transportation planning handbook . John Wiley & Sons.

Qasim, G. (2015). Travel demand modeling: AL-Amarah city as a case study . [Unpublished Doctoral dissertation , the Engineering College University of Baghdad]

Rojo, M. (2020). Evaluation of traffic assignment models through simulation. Sustainability , 12 (14), 5536. https://doi.org/10.3390/su12145536

Sheffi, Y. (1985). Urban transportation networks: Equilibrium analysis with mathematical programming method . Prentice-Hall. http://web.mit.edu/sheffi/www/selectedMedia/sheffi_urban_trans_networks.pdf

US Bureau of Public Roads.  (1964). Traffic assignment manual for application with a large, high speed computer . U.S. Department of Commerce, Bureau of Public Roads, Office of Planning, Urban Planning Division.

https://books.google.com/books/about/Traffic_Assignment_Manual_for_Applicatio.html?id=gkNZAAAAMAAJ

Wang, X., & Hofe, R. (2008). Research methods in urban and regional planning . Springer Science & Business Media.

Polynomial is distribution that involves the non-negative integer powers of a variable.

Hyperbolic function is a function that the uses the variable values as the power to the constant of e.

A point on the curve where the derivation of the function becomes either maximum or minimum.

all-or-nothing is an assignment model where we assume that the impedance of a road or path between each origin and destination is constant and is equal to free-flow level

Incremental model is a model that the predictions or estimates or fed into the model for forecasting incrementally to account for changes that may occur during each increment.

Iterative feedback loop is a model that iterates between trip distribution and route choice step based on the rational that if a path gets too congested, the travel may alter travel destination

Wardrop equilibrium is a state in traffic assignment model where are drivers are reluctant to change their path because the average travel time is at a minimum.

second principle of the Wardrop is a principle that assumes drivers’ rationale for choosing a path is to minimize total system costs with one another in order to minimize total system travel time

Stochastic time-dependent OD is a modeling framework where generation and distribution of trips are randomly assigned to the area

feedback loop model is type of dynamic traffic assignment model where an iteration between route choice and traffic assignment step is peformed, based on the assumption that if a particular route gets heavily congested, the travel may change the destination (like another shopping center).

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Assignment problem in linear programming : introduction and assignment model.

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Assignment problem is a special type of linear programming problem which deals with the allocation of the various resources to the various activities on one to one basis. It does it in such a way that the cost or time involved in the process is minimum and profit or sale is maximum. Though there problems can be solved by simplex method or by transportation method but assignment model gives a simpler approach for these problems.

In a factory, a supervisor may have six workers available and six jobs to fire. He will have to take decision regarding which job should be given to which worker. Problem forms one to one basis. This is an assignment problem.

1. Assignment Model :

Suppose there are n facilitates and n jobs it is clear that in this case, there will be n assignments. Each facility or say worker can perform each job, one at a time. But there should be certain procedure by which assignment should be made so that the profit is maximized or the cost or time is minimized.

In the table, Co ij is defined as the cost when j th job is assigned to i th worker. It maybe noted here that this is a special case of transportation problem when the number of rows is equal to number of columns.

Mathematical Formulation:

Any basic feasible solution of an Assignment problem consists (2n – 1) variables of which the (n – 1) variables are zero, n is number of jobs or number of facilities. Due to this high degeneracy, if we solve the problem by usual transportation method, it will be a complex and time consuming work. Thus a separate technique is derived for it. Before going to the absolute method it is very important to formulate the problem.

Suppose x jj is a variable which is defined as

1 if the i th job is assigned to j th machine or facility

0 if the i th job is not assigned to j th machine or facility.

Now as the problem forms one to one basis or one job is to be assigned to one facility or machine.

The total assignment cost will be given by

The above definition can be developed into mathematical model as follows:

Determine x ij > 0 (i, j = 1,2, 3…n) in order to

Subjected to constraints

and x ij is either zero or one.

Method to solve Problem (Hungarian Technique):

Consider the objective function of minimization type. Following steps are involved in solving this Assignment problem,

1. Locate the smallest cost element in each row of the given cost table starting with the first row. Now, this smallest element is subtracted form each element of that row. So, we will be getting at least one zero in each row of this new table.

2. Having constructed the table (as by step-1) take the columns of the table. Starting from first column locate the smallest cost element in each column. Now subtract this smallest element from each element of that column. Having performed the step 1 and step 2, we will be getting at least one zero in each column in the reduced cost table.

3. Now, the assignments are made for the reduced table in following manner.

(i) Rows are examined successively, until the row with exactly single (one) zero is found. Assignment is made to this single zero by putting square □ around it and in the corresponding column, all other zeros are crossed out (x) because these will not be used to make any other assignment in this column. Step is conducted for each row.

(ii) Step 3 (i) in now performed on the columns as follow:- columns are examined successively till a column with exactly one zero is found. Now , assignment is made to this single zero by putting the square around it and at the same time, all other zeros in the corresponding rows are crossed out (x) step is conducted for each column.

(iii) Step 3, (i) and 3 (ii) are repeated till all the zeros are either marked or crossed out. Now, if the number of marked zeros or the assignments made are equal to number of rows or columns, optimum solution has been achieved. There will be exactly single assignment in each or columns without any assignment. In this case, we will go to step 4.

4. At this stage, draw the minimum number of lines (horizontal and vertical) necessary to cover all zeros in the matrix obtained in step 3, Following procedure is adopted:

(iii) Now tick mark all the rows that are not already marked and that have assignment in the marked columns.

(iv) All the steps i.e. (4(i), 4(ii), 4(iii) are repeated until no more rows or columns can be marked.

(v) Now draw straight lines which pass through all the un marked rows and marked columns. It can also be noticed that in an n x n matrix, always less than ‘n’ lines will cover all the zeros if there is no solution among them.

5. In step 4, if the number of lines drawn are equal to n or the number of rows, then it is the optimum solution if not, then go to step 6.

6. Select the smallest element among all the uncovered elements. Now, this element is subtracted from all the uncovered elements and added to the element which lies at the intersection of two lines. This is the matrix for fresh assignments.

7. Repeat the procedure from step (3) until the number of assignments becomes equal to the number of rows or number of columns.

Related Articles:

• Two Phase Methods of Problem Solving in Linear Programming: First and Second Phase
• Linear Programming: Applications, Definitions and Problems

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Hungarian Method

The Hungarian method is a computational optimization technique that addresses the assignment problem in polynomial time and foreshadows following primal-dual alternatives. In 1955, Harold Kuhn used the term “Hungarian method” to honour two Hungarian mathematicians, Dénes Kőnig and Jenő Egerváry. Let’s go through the steps of the Hungarian method with the help of a solved example.

Hungarian Method to Solve Assignment Problems

The Hungarian method is a simple way to solve assignment problems. Let us first discuss the assignment problems before moving on to learning the Hungarian method.

What is an Assignment Problem?

A transportation problem is a type of assignment problem. The goal is to allocate an equal amount of resources to the same number of activities. As a result, the overall cost of allocation is minimised or the total profit is maximised.

Because available resources such as workers, machines, and other resources have varying degrees of efficiency for executing different activities, and hence the cost, profit, or loss of conducting such activities varies.

Assume we have ‘n’ jobs to do on ‘m’ machines (i.e., one job to one machine). Our goal is to assign jobs to machines for the least amount of money possible (or maximum profit). Based on the notion that each machine can accomplish each task, but at variable levels of efficiency.

Hungarian Method Steps

Check to see if the number of rows and columns are equal; if they are, the assignment problem is considered to be balanced. Then go to step 1. If it is not balanced, it should be balanced before the algorithm is applied.

Step 1 – In the given cost matrix, subtract the least cost element of each row from all the entries in that row. Make sure that each row has at least one zero.

Step 2 – In the resultant cost matrix produced in step 1, subtract the least cost element in each column from all the components in that column, ensuring that each column contains at least one zero.

Step 3 – Assign zeros

• Analyse the rows one by one until you find a row with precisely one unmarked zero. Encircle this lonely unmarked zero and assign it a task. All other zeros in the column of this circular zero should be crossed out because they will not be used in any future assignments. Continue in this manner until you’ve gone through all of the rows.
• Examine the columns one by one until you find one with precisely one unmarked zero. Encircle this single unmarked zero and cross any other zero in its row to make an assignment to it. Continue until you’ve gone through all of the columns.

Step 4 – Perform the Optimal Test

• The present assignment is optimal if each row and column has exactly one encircled zero.
• The present assignment is not optimal if at least one row or column is missing an assignment (i.e., if at least one row or column is missing one encircled zero). Continue to step 5. Subtract the least cost element from all the entries in each column of the final cost matrix created in step 1 and ensure that each column has at least one zero.

Step 5 – Draw the least number of straight lines to cover all of the zeros as follows:

(a) Highlight the rows that aren’t assigned.

(b) Label the columns with zeros in marked rows (if they haven’t already been marked).

(c) Highlight the rows that have assignments in indicated columns (if they haven’t previously been marked).

(d) Continue with (b) and (c) until no further marking is needed.

(f) Simply draw the lines through all rows and columns that are not marked. If the number of these lines equals the order of the matrix, then the solution is optimal; otherwise, it is not.

Step 6 – Find the lowest cost factor that is not covered by the straight lines. Subtract this least-cost component from all the uncovered elements and add it to all the elements that are at the intersection of these straight lines, but leave the rest of the elements alone.

Step 7 – Continue with steps 1 – 6 until you’ve found the highest suitable assignment.

Hungarian Method Example

Use the Hungarian method to solve the given assignment problem stated in the table. The entries in the matrix represent each man’s processing time in hours.

\(\begin{array}{l}\begin{bmatrix} & I & II & III & IV & V \\1 & 20 & 15 & 18 & 20 & 25 \\2 & 18 & 20 & 12 & 14 & 15 \\3 & 21 & 23 & 25 & 27 & 25 \\4 & 17 & 18 & 21 & 23 & 20 \\5 & 18 & 18 & 16 & 19 & 20 \\\end{bmatrix}\end{array} \)

With 5 jobs and 5 men, the stated problem is balanced.

\(\begin{array}{l}A = \begin{bmatrix}20 & 15 & 18 & 20 & 25 \\18 & 20 & 12 & 14 & 15 \\21 & 23 & 25 & 27 & 25 \\17 & 18 & 21 & 23 & 20 \\18 & 18 & 16 & 19 & 20 \\\end{bmatrix}\end{array} \)

Subtract the lowest cost element in each row from all of the elements in the given cost matrix’s row. Make sure that each row has at least one zero.

\(\begin{array}{l}A = \begin{bmatrix}5 & 0 & 3 & 5 & 10 \\6 & 8 & 0 & 2 & 3 \\0 & 2 & 4 & 6 & 4 \\0 & 1 & 4 & 6 & 3 \\2 & 2 & 0 & 3 & 4 \\\end{bmatrix}\end{array} \)

Subtract the least cost element in each Column from all of the components in the given cost matrix’s Column. Check to see if each column has at least one zero.

\(\begin{array}{l}A = \begin{bmatrix}5 & 0 & 3 & 3 & 7 \\6 & 8 & 0 & 0 & 0 \\0 & 2 & 4 & 4 & 1 \\0 & 1 & 4 & 4 & 0 \\2 & 2 & 0 & 1 & 1 \\\end{bmatrix}\end{array} \)

When the zeros are assigned, we get the following:

The present assignment is optimal because each row and column contain precisely one encircled zero.

Where 1 to II, 2 to IV, 3 to I, 4 to V, and 5 to III are the best assignments.

Hence, z = 15 + 14 + 21 + 20 + 16 = 86 hours is the optimal time.

Practice Question on Hungarian Method

Use the Hungarian method to solve the following assignment problem shown in table. The matrix entries represent the time it takes for each job to be processed by each machine in hours.

\(\begin{array}{l}\begin{bmatrix}J/M & I & II & III & IV & V \\1 & 9 & 22 & 58 & 11 & 19 \\2 & 43 & 78 & 72 & 50 & 63 \\3 & 41 & 28 & 91 & 37 & 45 \\4 & 74 & 42 & 27 & 49 & 39 \\5 & 36 & 11 & 57 & 22 & 25 \\\end{bmatrix}\end{array} \)

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Frequently Asked Questions on Hungarian Method

What is hungarian method.

The Hungarian method is defined as a combinatorial optimization technique that solves the assignment problems in polynomial time and foreshadowed subsequent primal–dual approaches.

What are the steps involved in Hungarian method?

The following is a quick overview of the Hungarian method: Step 1: Subtract the row minima. Step 2: Subtract the column minimums. Step 3: Use a limited number of lines to cover all zeros. Step 4: Add some more zeros to the equation.

What is the purpose of the Hungarian method?

When workers are assigned to certain activities based on cost, the Hungarian method is beneficial for identifying minimum costs.

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• Implementing Subledger Accounting

Accounting Method

Accounting methods group subledger journal entry rule sets. This facilitates the definition of consistent accounting treatment for each accounting event class, and accounting event type, for all subledger applications.

This grouping enables a set of subledger journal entry rule sets to be assigned collectively to a ledger.

For example:

A subledger accounting method can be defined to group subledger journal entry rule sets that adhere to and comply with US Generally Accepted Accounting Principles (GAAP) criteria.

By assigning a different subledger accounting method to each related ledger, you can create multiple accounting representations of transactions.

Accounting rules can be defined with either a top-down, or a bottom-up approach.

Top-Down: Define the accounting method, followed by components of each rule that must be assigned to it.

Bottom-Up: Define components for each rule and then assign them as required.

The Create Accounting process uses the accounting method definition with active journal entry rule set assignments to create subledger journal entries.

When an accounting method is initially defined its status changes to Incomplete. The status will also be Incomplete after modifying a component of any accounting rule associated with the assigned journal entry rule set.

The following definitions are used to define the journal entries, and are applied as updates to the accounting method:

Updates to the predefined accounting method

Assignment of journal entry rule sets for an accounting event class and accounting event type from the accounting methods page

Assignment of accounting methods to ledgers

Activation of subledger journal entry rule set assignments

Updates to the Predefined Accounting Method

You may update a predefined accounting method by end dating the existing assignment and creating an assignment with an effective start date.

Assignment of Journal Entry Rule Set for Accounting Event Class and Accounting Event Type

You create the assignment of a journal entry rule set for an accounting event class and accounting event type using the accounting method page.

The following should be considered for assigning rule sets:

If the accounting method has an assigned chart of accounts you can use journal entry rule sets that:

Use the same chart of accounts

Are not associated with any chart of accounts

You can assign to existing journal entry rule sets or create a new one.

Assignment of Accounting Methods to Ledgers

If the accounting method has an assigned chart of accounts, it may only be used by ledgers that use the same chart of accounts.

If the accounting method doesn't have an assigned chart of accounts, the accounting method can be assigned to any ledger.

Activation of Subledger Journal Entry Rule Set Assignments

You can activate the subledger journal entry rule set assignments from the Accounting Method page. You can also submit the Activate Subledger Journal Entry Rule Set Assignments process to validate and activate your accounting set ups.

Accounting Method and Accounting Rules

This figure illustrates the relationship of the components used in an accounting method.

Related Topics

• Subledger Journal Entry Rule Set
• Journal Line Rules
• Account Rules
• Description Rules