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  • How to Define a Research Problem | Ideas & Examples

How to Define a Research Problem | Ideas & Examples

Published on November 2, 2022 by Shona McCombes and Tegan George. Revised on May 31, 2023.

A research problem is a specific issue or gap in existing knowledge that you aim to address in your research. You may choose to look for practical problems aimed at contributing to change, or theoretical problems aimed at expanding knowledge.

Some research will do both of these things, but usually the research problem focuses on one or the other. The type of research problem you choose depends on your broad topic of interest and the type of research you think will fit best.

This article helps you identify and refine a research problem. When writing your research proposal or introduction , formulate it as a problem statement and/or research questions .

Table of contents

Why is the research problem important, step 1: identify a broad problem area, step 2: learn more about the problem, other interesting articles, frequently asked questions about research problems.

Having an interesting topic isn’t a strong enough basis for academic research. Without a well-defined research problem, you are likely to end up with an unfocused and unmanageable project.

You might end up repeating what other people have already said, trying to say too much, or doing research without a clear purpose and justification. You need a clear problem in order to do research that contributes new and relevant insights.

Whether you’re planning your thesis , starting a research paper , or writing a research proposal , the research problem is the first step towards knowing exactly what you’ll do and why.

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assignment problem in research

As you read about your topic, look for under-explored aspects or areas of concern, conflict, or controversy. Your goal is to find a gap that your research project can fill.

Practical research problems

If you are doing practical research, you can identify a problem by reading reports, following up on previous research, or talking to people who work in the relevant field or organization. You might look for:

  • Issues with performance or efficiency
  • Processes that could be improved
  • Areas of concern among practitioners
  • Difficulties faced by specific groups of people

Examples of practical research problems

Voter turnout in New England has been decreasing, in contrast to the rest of the country.

The HR department of a local chain of restaurants has a high staff turnover rate.

A non-profit organization faces a funding gap that means some of its programs will have to be cut.

Theoretical research problems

If you are doing theoretical research, you can identify a research problem by reading existing research, theory, and debates on your topic to find a gap in what is currently known about it. You might look for:

  • A phenomenon or context that has not been closely studied
  • A contradiction between two or more perspectives
  • A situation or relationship that is not well understood
  • A troubling question that has yet to be resolved

Examples of theoretical research problems

The effects of long-term Vitamin D deficiency on cardiovascular health are not well understood.

The relationship between gender, race, and income inequality has yet to be closely studied in the context of the millennial gig economy.

Historians of Scottish nationalism disagree about the role of the British Empire in the development of Scotland’s national identity.

Next, you have to find out what is already known about the problem, and pinpoint the exact aspect that your research will address.

Context and background

  • Who does the problem affect?
  • Is it a newly-discovered problem, or a well-established one?
  • What research has already been done?
  • What, if any, solutions have been proposed?
  • What are the current debates about the problem? What is missing from these debates?

Specificity and relevance

  • What particular place, time, and/or group of people will you focus on?
  • What aspects will you not be able to tackle?
  • What will the consequences be if the problem is not resolved?

Example of a specific research problem

A local non-profit organization focused on alleviating food insecurity has always fundraised from its existing support base. It lacks understanding of how best to target potential new donors. To be able to continue its work, the organization requires research into more effective fundraising strategies.

Once you have narrowed down your research problem, the next step is to formulate a problem statement , as well as your research questions or hypotheses .

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If you want to know more about the research process , methodology , research bias , or statistics , make sure to check out some of our other articles with explanations and examples.

Methodology

  • Sampling methods
  • Simple random sampling
  • Stratified sampling
  • Cluster sampling
  • Likert scales
  • Reproducibility

 Statistics

  • Null hypothesis
  • Statistical power
  • Probability distribution
  • Effect size
  • Poisson distribution

Research bias

  • Optimism bias
  • Cognitive bias
  • Implicit bias
  • Hawthorne effect
  • Anchoring bias
  • Explicit bias

All research questions should be:

  • Focused on a single problem or issue
  • Researchable using primary and/or secondary sources
  • Feasible to answer within the timeframe and practical constraints
  • Specific enough to answer thoroughly
  • Complex enough to develop the answer over the space of a paper or thesis
  • Relevant to your field of study and/or society more broadly

Writing Strong Research Questions

Research questions anchor your whole project, so it’s important to spend some time refining them.

In general, they should be:

  • Focused and researchable
  • Answerable using credible sources
  • Complex and arguable
  • Feasible and specific
  • Relevant and original

Your research objectives indicate how you’ll try to address your research problem and should be specific:

A research aim is a broad statement indicating the general purpose of your research project. It should appear in your introduction at the end of your problem statement , before your research objectives.

Research objectives are more specific than your research aim. They indicate the specific ways you’ll address the overarching aim.

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Assignment Problem: Meaning, Methods and Variations | Operations Research

assignment problem in 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:

assignment problem in research

Research Problem Statement — Find out how to write an impactful one!

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Table of Contents

What Is a Research Problem Statement?

A research problem statement is a clear, concise, and specific statement that describes the issue or problem that the research project addresses. It should be written in a way that is easily understandable to both experts and non-experts in the field.

To write a research problem statement, you should:

  • Identify the general area of interest: Start by identifying the general area of research that interests you.
  • Define the specific problem: Narrow down the general area of interest to a specific problem or issue.
  • Explain the significance of the problem: Provide context for the problem by explaining why it is important to study and what gap in current knowledge or understanding it fills.
  • Provide a clear and concise statement: State the problem in a clear and concise manner, making sure to use language that is easily understood by your intended audience.
  • Use a scientific and objective tone: The problem statement should be written in a neutral and objective tone, avoiding any subjective language and personal bias .

An Example of a Research Problem Statement

“The increasing prevalence of obesity in children is a growing public health concern. Despite the availability of information on healthy eating and physical activity, many children are still not engaging in healthy lifestyle behaviors. The problem this study addresses is the lack of understanding of the barriers and facilitators to healthy lifestyle behaviors in children.”

When to Write a Problem Statement in Research?

A research problem statement should be written at the beginning of the research process, before any data collection or analysis takes place. This is because the statement sets the foundation for the entire research project by clearly defining the problem that the research is trying to address.

Writing a problem statement early in the research process helps to guide the research design and methodology , and ensures that the research is focused on addressing the specific problem at hand. It also helps to ensure that the research is relevant and addresses a gap in current knowledge or understanding.

In addition, a well-written problem statement effectively communicates the purpose and significance of the research to potential funders, collaborators, and other stakeholders. It also generates interest and support for the research project.

It’s also important to note that, during the research process, the statement can be refined or updated as new information is discovered or as the research progresses. This is normal and it’s a good idea to revise the statement as needed to ensure that it remains clear and concise and that it accurately reflects the current focus of the research project.

What Does a Research Problem Statement Include?

A research problem statement typically includes the following elements:

1. The research topic:

The general area of interest or field of study that the research project addresses.

2. The specific problem or issue:

A clear and concise statement of the problem or issue that the research project aims to address.

3. The significance of the problem:

A discussion of why the problem is important and what gap in current knowledge or understanding it fills.

4. The research questions:

A set of questions that the research project aims to answer, in order to address the problem or issue.

5. The research objectives:

A set of specific and measurable objectives that the research project aims to achieve.

6. The scope of the research:

A description of the specific population, setting, or context that the research project will focus on.

7. The theoretical framework:

A discussion of the theoretical concepts and principles that inform the research project.

8. The research design:

A description of the research methodologies that will be used to collect and analyze data in order to address the research questions and objectives.

It’s important to note that the problem statement is usually brief and concise, typically a few sentences or a short paragraph. But it should provide enough information to convey the main idea of the research project.

Important Features of Research Problem Statement

The problem statement should be clear and easy to understand. Write it in a way that is accessible to both experts and non-experts in the field.

2. Specificity

The statement should be specific and clearly define the problem or issue that the research project aims to address. It should be narrow enough to be manageable, but broad enough to be of interest to others in the field.

3. Significance

The statement should explain why the problem is important and what gap in current knowledge or understanding it fills. It should provide context for the research project and help to justify its importance.

4. Relevance

The statement should be relevant to the field of study and address an issue that is currently of concern to researchers.

5. Research questions

The statement should include a set of research questions that the research project aims to answer in order to address the problem or issue.

6. Research objectives

The statement should include a set of specific and measurable objectives that the research project aims to achieve.

The statement should define the specific population, setting, or context that the research project will focus on.

8. Theoretical framework

The statement should provide an overview of the theoretical concepts and principles that inform the research project.

9. Research design

The statement should provide an overview of the research methodologies. This will be useful collect and analyze data in order to address the research questions and objectives.

Difference Between a Thesis Statement and a Problem Statement

A thesis statement and a problem statement are related but distinct elements of a research project.

A thesis statement is a statement that summarizes the central argument or claim of a research paper or essay. It presents the main idea of the paper and sets the direction for the rest of the content. It’s usually located at the end of the introduction, and it’s often one sentence.

A problem statement, on the other hand, is a statement that describes a specific problem or issue that the research project aims to address. It sets the foundation for the entire research project by clearly defining the research problem. It is usually located at the beginning of a research paper or proposal, and is of one or a few paragraphs.

In summary, a thesis statement is a summary of the main point or key argument of the research paper. A problem statement describes the specific issue that the research project aims to address. A thesis statement is more focused on the final outcome of the research. While a problem statement is focused on the current state of knowledge and the gap in understanding that the research project aims to fill.

In Conclusion

A problem statement is a critical component of the research project, as it provides a clear and concise roadmap for the research, and helps to ensure that the research is well-designed and addresses a significant and relevant issue.

We hope this blog has clarified your doubts and confusion associated with research problem statement and helps you write an effective statement for your research project!

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Assignment Problem

5.1  introduction.

The assignment problem is one of the special type of transportation problem for which more efficient (less-time consuming) solution method has been devised by KUHN (1956) and FLOOD (1956). The justification of the steps leading to the solution is based on theorems proved by Hungarian mathematicians KONEIG (1950) and EGERVARY (1953), hence the method is named Hungarian.

5.2  GENERAL MODEL OF THE ASSIGNMENT PROBLEM

Consider n jobs and n persons. Assume that each job can be done only by one person and the time a person required for completing the i th job (i = 1,2,...n) by the j th person (j = 1,2,...n) is denoted by a real number C ij . On the whole this model deals with the assignment of n candidates to n jobs ...

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Problem statement overview.

The dissertation problem needs to be very focused because everything else from the dissertation research logically flows from the problem. You may say that the problem statement is the very core of a dissertation research study. If the problem is too big or too vague, it will be difficult to scope out a purpose that is manageable for one person, given the time available to execute and finish the dissertation research study.

Through your research, your aim is to obtain information that helps address a problem so it can be resolved. Note that the researcher does not actually solve the problem themselves by conducting research but provides new knowledge that can be used toward a resolution. Typically, the problem is solved (or partially solved) by practitioners in the field, using input from researchers.

Given the above, the problem statement should do three things:

  • Specify and describe the problem (with appropriate citations)
  • Explain the consequences of NOT solving the problem

Explain the knowledge needed to solve the problem (i.e., what is currently unknown about the problem and its resolution – also referred to as a gap )

What is a problem?

The world is full of problems! Not all problems make good dissertation research problems, however, because they are either too big, complex, or risky for doctorate candidates to solve. A proper research problem can be defined as a specific, evidence-based, real-life issue faced by certain people or organizations that have significant negative implications to the involved parties.

Example of a proper, specific, evidence-based, real-life dissertation research problem:

“Only 6% of CEOs in Fortune 500 companies are women” (Center for Leadership Studies, 2019).

Specific refers to the scope of the problem, which should be sufficiently manageable and focused to address with dissertation research. For example, the problem “terrorism kills thousands of people each year” is probably not specific enough in terms of who gets killed by which terrorists, to work for a doctorate candidate; or “Social media use among call-center employees may be problematic because it could reduce productivity,” which contains speculations about the magnitude of the problem and the possible negative effects.

Evidence-based here means that the problem is well-documented by recent research findings and/or statistics from credible sources. Anecdotal evidence does not qualify in this regard. Quantitative evidence is generally preferred over qualitative ditto when establishing a problem because quantitative evidence (from a credible source) usually reflects generalizable facts, whereas qualitative evidence in the form of research conclusions tend to only apply to the study sample and may not be generalizable to a larger population. Example of a problem that isn’t evidence-based: “Based on the researcher’s experience, the problem is that people don’t accept female leaders;” which is an opinion-based statement based on personal (anecdotal) experience.

Real-life means that a problem exists regardless of whether research is conducted or not. This means that “lack of knowledge” or “lack of research” cannot be used as the problem for a dissertation study because it’s an academic issue or a gap; and not a real-life problem experienced by people or organizations.  Example of a problem that doesn’t exist in real life: “There is not enough research on the reasons why people distrust minority healthcare workers.” This type of statement also reveals the assumption that people actually do mistrust minority healthcare workers; something that needs to be supported by actual, credible evidence to potentially work as an underlying research problem.

What are consequences?

Consequences are negative implications experienced by a group of people or organizations, as a result of the problem. The negative effects should be of a certain magnitude to warrant research. For example, if fewer than 1% of the stakeholders experience a negative consequence of a problem and that consequence only constitutes a minor inconvenience, research is probably not warranted. Negative consequences that can be measured weigh stronger than those that cannot be put on some kind of scale.

In the example above, a significant negative consequence is that women face much larger barriers than men when attempting to get promoted to executive jobs; or are 94% less likely than men to get to that level in Corporate America.

What is a gap?

To establish a complete basis for a dissertation research study, the problem has to be accompanied by a gap . A gap is missing knowledge or insights about a particular issue that contributes to the persistence of the problem. We use gaps to “situate” new research in the existing literature by adding to the knowledge base in the business research field, in a specific manner (determined by the purpose of the research). Identifying gaps requires you to review the literature in a thorough fashion, to establish a complete understanding of what is known and what isn’t known about a certain problem.  In the example from above about the underrepresentation of female CEOs, a gap may be that male-dominated boards have not been studied extensively in terms of their CEO hiring decisions, which might then warrant a study of such boards, to uncover implicit biases and discriminatory practices against female candidates.

How to Write a Problem Statement

How to write a problem statement.

  • Here is one way to construct a problem section (keep in mind you have a 250-300 word limit, but you can write first and edit later):

It is helpful to begin the problem statement with a sentence :  “The problem to be addressed through this study is… ”  Then, fill out the rest of the paragraph with elaboration of that specific problem, making sure to “document” it, as NU reviewers will look for research-based evidence that it is indeed a problem (emphasis also on timeliness of the problem, supported by citations within the last 5 years).

Next, write a paragraph explaining the consequences of NOT solving the problem. Who will be affected? How will they be affected? How important is it to fix the problem? Again, NU reviewers will want to see research-based citations and statistics that indicate the negative implications are significant.

In the final paragraph, you will explain what information (research) is needed in order to fix the problem. This paragraph shows that the problem is worthy of doctoral-level research. What isn’t known about the problem? Ie, what is the gap? Presumably, if your problem and purpose are aligned, your research will try to close or minimize this gap by investigating the problem. Have other researchers investigated the issue? What has their research left unanswered?

  • Another way to tackle the Statement of the Problem:

The Statement of the Problem section is a very clear, concise identification of the problem. It must stay within the template guidelines of 250-300 words but more importantly, must contain four elements as outlined below. A dissertation worthy problem should be able to address all of the following points:

-->identification of the problem itself--what is "going wrong" (Ellis & Levy, 2008)

-->who is affected by the problem

-->the consequences that will result from a continuation of the problem

-->a brief discussion of 1) at least 3 authors’ research related to the problem; and 2)   their stated suggestion/recommendation for further research related to the problem

Use the following to work on the Statement of the Problem by first outlining the section as follows:

1. One clear, concise statement that tells the reader what is not working, what is “going wrong”. Be specific and support it with current studies.

2. Tell who is affected by the problem identified in #1. 

3. Briefly tell what will happen if the problem isn’t addressed.

4. Find at least 3 current studies and write a sentence or two for each study that

i. briefly discusses the author(s)’ work, what they studied, and

ii. state their recommendation for further research about the problem

  • Finally, you can follow this simple 3-part outline when writing the statement of the problem section:

Your problem statement is a short (250-300 words), 3 paragraph section, in which you

  • Explain context and state problem (“the problem is XYZ”), supported by statistics and/or recent research findings
  • Explain the negative consequences of the problem to stakeholders, supported by statistics and/or recent research findings
  • Explain the gap in the literature.

Example of a problem statement that follows the 3-part outline (295 words):

The problem to be addressed by this study is the decline of employee well-being for followers of novice mid-level managers and the corresponding rise in employee turnover faced by business leaders across the financial services industry (Oh et al., 2014).  Low levels of employee well-being are toxic for morale and result in expensive turnover costs, dysfunctional work environments, anemic corporate cultures, and poor customer service (Compdata, 2018; Oh et al., 2014).  According to Ufer (2017), the financial services industry suffers from one of the highest turnover rates among millennial-aged employees in all industries in the developed world, at 18.6% annually.  Starkman (2015) reported that 50% of those surveyed in financial services were not satisfied with a single one of the four key workplace aspects: job, firm, pay or career path. 

Low levels of employee well-being interrupt a financial services’ company’s ability to deliver outstanding customer service in a world increasingly dependent on that commodity (Wladawsky-Berger, 2018).Mid-level managers play an essential role in support of the success of many of top businesses today (Anicich & Hirsh, 2017). 

The current body of literature does not adequately address the well-being issue in the financial services industry from the follower’s perspective (Uhl-Bien, Riggio, Lowe, & Carsten, 2014). Strategic direction flows top-down from senior executives and passes through mid-level leadership to individual contributors at more junior grades.  The mid-level managers’ teams are tasked with the achievement of core tasks and the managers themselves are expected to maintain the workforce’s morale, motivation and welfare (Anicich & Hirsh, 2017).  Unless industry leaders better understand the phenomenon of employee well-being from the follower perspective and its role in positioning employees to provide a premium client experience, they may be handicapped from preserving their most significant principal market differentiator: customer service (Wladawsky-Berger, 2018). 

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Home » Problem Statement – Writing Guide, Examples and Types

Problem Statement – Writing Guide, Examples and Types

Table of Contents

Problem Statement

Problem Statement

Definition:

Problem statement is a clear, concise, and well-defined statement that outlines the issue or challenge that needs to be addressed. It is a crucial element in any project or research as it provides a clear understanding of the problem, its context, and its potential impact.

Types of Problem Statements

There are various types of problem statements, and the type of problem statement used depends on the context and purpose of the project or research. Some common types of problem statements are:

Business Problem Statement

Business Problem Statement identifies a problem or challenge within an organization that needs to be solved. It typically includes the impact of the problem on the organization and its stakeholders, such as customers, employees, or shareholders.

Research Problem Statement

Research Problem Statement outlines the research question or problem that the study aims to address. It describes the research objectives, the significance of the research, and the potential impact of the research findings.

Design Problem Statement

Design Problem Statement defines the problem or challenge that a design project aims to solve. It includes the user’s needs, the design constraints, and the desired outcomes of the design project.

Social Problem Statement

Social Problem Statement describes a problem or challenge in society that needs to be addressed. It typically includes the social, economic, or political impact of the problem and its effect on individuals or communities.

Technical Problem Statement

Technical Problem Statement defines a problem or challenge related to technology or engineering. It includes the technical requirements, constraints, and potential solutions to the problem.

Components of Problem Statement

The components of a problem statement may vary depending on the context and purpose of the project or research, but some common components include:

  • Problem description : This component provides a clear and concise description of the problem, its context, and its impact. It should explain what the problem is, who is affected by it, and why it needs to be addressed.
  • Background information : This component provides context for the problem by describing the current state of knowledge or practice related to the problem. It may include a review of relevant literature, data, or other sources of information.
  • Objectives : This component outlines the specific objectives that the project or research aims to achieve. It should explain what the project or research team hopes to accomplish by addressing the problem.
  • Scope : This component defines the boundaries of the problem by specifying what is included and excluded from the problem statement. It should clarify the limits of the project or research and ensure that the team remains focused on the core problem.
  • Methodology : This component outlines the approach or methodology that the project or research team will use to address the problem. It may include details about data collection, analysis, or other methods used to achieve the objectives.
  • Expected outcomes : This component describes the potential impact or outcomes that the project or research aims to achieve. It should explain how the solution or findings will address the problem and benefit the stakeholders.

How to write Problem Statement

Here are some general steps to follow when writing a problem statement:

  • Identify the problem : Clearly identify the problem that needs to be addressed. Consider the context, stakeholders, and potential consequences of the problem.
  • Research the problem: Conduct research to gather data and information about the problem. This may involve reviewing literature, analyzing data, or consulting with experts.
  • Define the problem: Define the problem clearly and concisely, using specific language and avoiding vague or ambiguous terms. Be sure to include the impact of the problem and the context in which it occurs.
  • State the objectives : Clearly state the objectives that the project or research aims to achieve. This should be specific and measurable, with clear outcomes that can be evaluated.
  • Identify the scope: Identify the boundaries of the problem, including what is included and excluded from the problem statement. This helps to ensure that the team remains focused on the core problem.
  • Outline the methodology : Outline the approach or methodology that the project or research team will use to address the problem. This should be based on research and best practices, and should be feasible and realistic.
  • Describe the expected outcomes : Describe the potential impact or outcomes that the project or research aims to achieve. Be specific about how the solution or findings will address the problem and benefit the stakeholders.
  • Revise and refine : Review the problem statement and revise it as needed to ensure clarity, accuracy, and completeness.

Applications of Problem Statement

Here are some of the applications of problem statements:

  • Research : In academic research, problem statements are used to clearly define the research problem, identify the research question, and justify the need for the study. A well-crafted problem statement is essential for the success of any research project.
  • Project management: In project management, problem statements are used to identify the issues or challenges that a project team needs to address. Problem statements help project managers to define project scope, set project goals, and develop project plans.
  • Business strategy: In business strategy, problem statements are used to identify business challenges and opportunities. Problem statements help businesses to define their strategic objectives, develop action plans, and allocate resources.
  • Product development : In product development, problem statements are used to identify customer needs and develop new products that address those needs. Problem statements help product developers to define product requirements, develop product features, and test product prototypes.
  • Policy-making: In public policy-making, problem statements are used to identify social, economic, and environmental issues that require government intervention. Problem statements help policymakers to define policy objectives, develop policy options, and evaluate policy outcomes.

Examples of Problem Statements

Examples of Problem Statements are as follows:

  • High student-to-teacher ratios are leading to decreased individualized attention and lower academic achievement.
  • Limited funding for extracurricular activities is limiting opportunities for student development and engagement.
  • The lack of diversity and inclusion in curriculum is limiting cultural understanding and perpetuating inequalities.
  • The need for continuous professional development for teachers is crucial to improving teaching quality and student outcomes.
  • Unequal access to education due to socio-economic status, geographical location, or other factors is contributing to disparities in academic achievement.
  • The shortage of healthcare professionals is leading to increased patient wait times and decreased quality of care.
  • Limited access to mental health services is contributing to the high prevalence of mental health issues and suicides.
  • The over-prescription of opioids is contributing to the current opioid epidemic and increasing rates of addiction and overdose.
  • Limited access to affordable and nutritious food is leading to poor nutrition and increased rates of chronic diseases.
  • The lack of standardized electronic health record systems is limiting coordination of care and leading to medical errors.

Environmental Science

  • Pollution from industrial and agricultural practices is contributing to climate change and increased health risks.
  • The overexploitation of natural resources is leading to decreased biodiversity and ecological imbalance.
  • Limited access to clean water is leading to health issues and affecting agriculture and economic development.
  • The destruction of natural habitats is leading to the extinction of many species and disrupting ecosystems.
  • Climate change is leading to more frequent and severe natural disasters, causing significant damage to infrastructure and displacement of populations.

Engineering

  • The inadequate design and maintenance of bridges and roads is leading to increased accidents and fatalities.
  • The lack of reliable and sustainable energy sources is contributing to environmental degradation and limiting economic growth.
  • The lack of cybersecurity measures in critical infrastructure is making it vulnerable to cyber attacks and compromising public safety.
  • The lack of efficient waste management systems is contributing to pollution and environmental degradation.
  • The need for developing technologies that are environmentally friendly and sustainable is crucial to addressing climate change.

Social Work

  • The lack of resources for mental health and social services is contributing to homelessness and the need for emergency assistance.
  • The high prevalence of child abuse and neglect is leading to long-term physical and emotional harm to children.
  • The lack of affordable and accessible childcare is limiting the opportunities for working parents, especially mothers.
  • The stigmatization of mental health issues is limiting access to mental health services and perpetuating discrimination.
  • The limited access to education, employment, and housing opportunities is contributing to poverty and social inequality.
  • The increasing use of ad-blocking software is limiting the effectiveness of traditional digital advertising.
  • The lack of transparency in digital advertising is leading to ad fraud and decreased trust in online marketing.
  • The need to adapt marketing strategies to changing consumer behaviors and preferences is crucial to reaching target audiences effectively.
  • The high competition in the marketplace is making it challenging for small businesses to compete with larger corporations.
  • The need to balance marketing goals with ethical considerations is crucial to maintaining consumer trust and avoiding negative publicity.
  • The high prevalence of anxiety and depression is leading to decreased productivity and increased healthcare costs.
  • The limited access to mental health services in certain geographic areas is limiting access to care and contributing to disparities in mental health outcomes.
  • The need for effective prevention and intervention programs for substance abuse and addiction is crucial to reducing rates of addiction and overdose.
  • The lack of awareness and understanding of mental health issues is perpetuating stigma and limiting access to care.
  • The need for culturally sensitive mental health services that are tailored to the needs of diverse populations is crucial to improving mental health outcomes.

Purpose of Problem Statement

The purpose of a problem statement is to clearly and concisely describe a specific problem or issue that needs to be addressed. It serves as a clear and succinct explanation of the problem, its context, and its importance, providing the necessary information to understand why the problem is worth solving. A well-crafted problem statement also helps to define the scope of the problem, which in turn helps to guide the research or problem-solving process. In essence, a problem statement sets the stage for identifying potential solutions and determining the best approach to solve the problem.

Characteristics of Problem Statement

The characteristics of a good problem statement include:

  • Clear and concise : A problem statement should be written in clear and concise language, free of technical jargon, and easily understandable to the intended audience.
  • Specific : The statement should clearly define the problem and its scope. It should identify the who, what, where, when, and why of the problem.
  • Measurable : A problem statement should be measurable in some way, whether through quantitative or qualitative methods. This allows for objective assessment of progress towards solving the problem.
  • Relevant : The problem statement should be relevant to the context in which it is presented. It should relate to the needs and concerns of stakeholders and the broader community.
  • Feasible : The problem statement should be realistic and achievable, given the available resources and constraints.
  • Innovative: A good problem statement should inspire creative and innovative solutions.
  • Actionable : The problem statement should lead to actionable steps that can be taken to address the problem. It should provide a roadmap for moving forward.

Advantages of Problem Statement

Advantages of Problem Statement are as follows:

  • Focus : A problem statement helps to clearly define the problem at hand and provides focus to the problem-solving process. It helps to avoid wasting time and resources on issues that are not relevant.
  • Alignment : A well-written problem statement ensures that everyone involved in the problem-solving process is on the same page and understands the issue at hand. This alignment helps to ensure that efforts are focused in the right direction and that everyone is working towards the same goal.
  • Clarity : A problem statement provides clarity about the nature of the problem and its impact. This clarity helps to facilitate communication and decision-making, making it easier to develop effective solutions.
  • Innovation : A well-crafted problem statement can inspire creativity and encourage innovative thinking. By clearly defining the problem, it can help to identify new approaches and solutions that may not have been considered before.
  • Measurability : A problem statement that is clear and specific can be used to measure progress and success. It helps to ensure that efforts are focused on addressing the root cause of the problem and that progress towards a solution can be tracked and evaluated.

Limitations of Problem Statement

While problem statements have many advantages, they also have some limitations, such as:

  • Limited Scope: A problem statement is usually focused on a specific issue or challenge. As a result, it may not capture the full complexity of a larger problem, which can limit the effectiveness of the solutions developed.
  • Lack of Detail : In some cases, problem statements may be too broad or lack sufficient detail, which can make it difficult to develop effective solutions. It’s important to ensure that the problem statement is specific enough to guide the problem-solving process.
  • Bias : The way in which a problem statement is written can sometimes reflect the biases or assumptions of the person or group writing it. This can lead to a narrow or incomplete understanding of the problem and limit the effectiveness of the solutions developed.
  • Inflexibility : A problem statement may be too rigid or inflexible, which can limit the exploration of alternative solutions. It’s important to keep an open mind and be willing to adapt the problem statement as new information or perspectives emerge.

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Unbalanced Assignment Problem: Definition, Formulation, and Solution Methods

Table of Contents

Are you familiar with the assignment problem in Operations Research (OR)? This problem deals with assigning tasks to workers in a way that minimizes the total cost or time needed to complete the tasks. But what if the number of tasks and workers is not equal? In this case, we face the Unbalanced Assignment Problem (UAP). This blog will help you understand what the UAP is, how to formulate it, and how to solve it.

What is the Unbalanced Assignment Problem?

The Unbalanced Assignment Problem is an extension of the Assignment Problem in OR, where the number of tasks and workers is not equal. In the UAP, some tasks may remain unassigned, while some workers may not be assigned any task. The objective is still to minimize the total cost or time required to complete the assigned tasks, but the UAP has additional constraints that make it more complex than the traditional assignment problem.

Formulation of the Unbalanced Assignment Problem

To formulate the UAP, we start with a matrix that represents the cost or time required to assign each task to each worker. If the matrix is square, we can use the Hungarian algorithm to solve the problem. But when the matrix is not square, we need to add dummy tasks or workers to balance the matrix. These dummy tasks or workers have zero costs and are used to make the matrix square.

Once we have a square matrix, we can apply the Hungarian algorithm to find the optimal assignment. However, we need to be careful in interpreting the results, as the assignment may include dummy tasks or workers that are not actually assigned to anything.

Solutions for the Unbalanced Assignment Problem

Besides the Hungarian algorithm, there are other methods to solve the UAP, such as the transportation algorithm and the auction algorithm. The transportation algorithm is based on transforming the UAP into a transportation problem, which can be solved with the transportation simplex method. The auction algorithm is an iterative method that simulates a bidding process between the tasks and workers to find the optimal assignment.

In summary, the Unbalanced Assignment Problem is a variant of the traditional Assignment Problem in OR that deals with assigning tasks to workers when the number of tasks and workers is not equal. To solve the UAP, we need to balance the matrix by adding dummy tasks or workers and then apply algorithms such as the Hungarian algorithm, the transportation algorithm, or the auction algorithm. Understanding the UAP can help businesses and organizations optimize their resource allocation and improve their operational efficiency.

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Operations Research

1 Operations Research-An Overview

  • History of O.R.
  • Approach, Techniques and Tools
  • Phases and Processes of O.R. Study
  • Typical Applications of O.R
  • Limitations of Operations Research
  • Models in Operations Research
  • O.R. in real world

2 Linear Programming: Formulation and Graphical Method

  • General formulation of Linear Programming Problem
  • Optimisation Models
  • Basics of Graphic Method
  • Important steps to draw graph
  • Multiple, Unbounded Solution and Infeasible Problems
  • Solving Linear Programming Graphically Using Computer
  • Application of Linear Programming in Business and Industry

3 Linear Programming-Simplex Method

  • Principle of Simplex Method
  • Computational aspect of Simplex Method
  • Simplex Method with several Decision Variables
  • Two Phase and M-method
  • Multiple Solution, Unbounded Solution and Infeasible Problem
  • Sensitivity Analysis
  • Dual Linear Programming Problem

4 Transportation Problem

  • Basic Feasible Solution of a Transportation Problem
  • Modified Distribution Method
  • Stepping Stone Method
  • Unbalanced Transportation Problem
  • Degenerate Transportation Problem
  • Transhipment Problem
  • Maximisation in a Transportation Problem

5 Assignment Problem

  • Solution of the Assignment Problem
  • Unbalanced Assignment Problem
  • Problem with some Infeasible Assignments
  • Maximisation in an Assignment Problem
  • Crew Assignment Problem

6 Application of Excel Solver to Solve LPP

  • Building Excel model for solving LP: An Illustrative Example

7 Goal Programming

  • Concepts of goal programming
  • Goal programming model formulation
  • Graphical method of goal programming
  • The simplex method of goal programming
  • Using Excel Solver to Solve Goal Programming Models
  • Application areas of goal programming

8 Integer Programming

  • Some Integer Programming Formulation Techniques
  • Binary Representation of General Integer Variables
  • Unimodularity
  • Cutting Plane Method
  • Branch and Bound Method
  • Solver Solution

9 Dynamic Programming

  • Dynamic Programming Methodology: An Example
  • Definitions and Notations
  • Dynamic Programming Applications

10 Non-Linear Programming

  • Solution of a Non-linear Programming Problem
  • Convex and Concave Functions
  • Kuhn-Tucker Conditions for Constrained Optimisation
  • Quadratic Programming
  • Separable Programming
  • NLP Models with Solver

11 Introduction to game theory and its Applications

  • Important terms in Game Theory
  • Saddle points
  • Mixed strategies: Games without saddle points
  • 2 x n games
  • Exploiting an opponent’s mistakes

12 Monte Carlo Simulation

  • Reasons for using simulation
  • Monte Carlo simulation
  • Limitations of simulation
  • Steps in the simulation process
  • Some practical applications of simulation
  • Two typical examples of hand-computed simulation
  • Computer simulation

13 Queueing Models

  • Characteristics of a queueing model
  • Notations and Symbols
  • Statistical methods in queueing
  • The M/M/I System
  • The M/M/C System
  • The M/Ek/I System
  • Decision problems in queueing

Some results on an assignment problem variant

  • Technical Note
  • Published: 06 August 2020
  • Volume 58 , pages 144–147, ( 2021 )

Cite this article

  • Pritibhushan Sinha   ORCID: orcid.org/0000-0002-4973-1635 1  

We consider a model of an assignment problem, in which an operator can do one job, multiple jobs, or no job at all. There is a job changeover cost, for any extra assignment in excess of one. The changeover costs depend only on the operator, but can be negative. We give a nonlinear integer programming formulation of the problem. We show that, the problem is NP-hard.

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Sinha, P. Some results on an assignment problem variant. OPSEARCH 58 , 144–147 (2021). https://doi.org/10.1007/s12597-020-00472-7

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  1. How to Define a Research Problem

    Step 1: Identify a broad problem area As you read about your topic, look for under-explored aspects or areas of concern, conflict, or controversy. Your goal is to find a gap that your research project can fill. Practical research problems

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    Step 1: Develop the Cost Table from the given Problem: ADVERTISEMENTS: If the no of rows are not equal to the no of columns and vice versa, a dummy row or dummy column must be added. The assignment cost for dummy cells are always zero. Step 2: Find the Opportunity Cost Table:

  3. An Assignment Problem and Its Application in Education Domain ...

    1. Introduction Problems related to assignment arise in a range of fields, for example, healthcare, transportation, education, and sports. In fact, this is a well-studied topic in combinatorial optimization problems under optimization or operations research branches.

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  5. The Research Problem/Question

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  6. Operations Research with R

    The assignment problem is a special case of linear programming problem; it is one of the fundamental combinational optimization problems in the branch of optimization or operations research in mathematics. Its goal consists in assigning m resources (usually workers) to n tasks (usually jobs) one a one to one basis while minimizing assignment costs.

  7. Assignment problems: A golden anniversary survey

    Assignment problems involve optimally matching the elements of two or more sets, where the dimension of the problem refers to the number of sets of elements to be matched. When there are only two sets, as will be the case for most of the variations we will consider, they may be referred to as "tasks" and "agents".

  8. How to Write a Research Problem Statement

    A research problem statement typically includes the following elements: 1. The research topic: The general area of interest or field of study that the research project addresses. 2. The specific problem or issue: A clear and concise statement of the problem or issue that the research project aims to address. 3.

  9. Chapter 5: Assignment Problem

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  12. A Target-Assignment Problem

    Abstract. This paper is concerned with a target assignment model of a probabilistic and nonlinear nature, but nevertheless one which is closely related to the "personnel-assignment" problem. It is shown here that, despite the apparent nonlinearities, it is possible to devise a linear programming formulation that will ordinarily provide a ...

  13. Problem Statement

    Example of a proper, specific, evidence-based, real-life dissertation research problem: "Only 6% of CEOs in Fortune 500 companies are women" (Center for Leadership Studies, 2019). Specific refers to the scope of the problem, which should be sufficiently manageable and focused to address with dissertation research. For example, the problem ...

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    Here are some general steps to follow when writing a problem statement: Identify the problem: Clearly identify the problem that needs to be addressed. Consider the context, stakeholders, and potential consequences of the problem. Research the problem: Conduct research to gather data and information about the problem.

  15. How to Solve the Assignment Problem: A Complete Guide

    Solving the Assignment Problem. There are various methods for solving the assignment problem, including the Hungarian method, the brute force method, and the auction algorithm. Here, we will focus on the steps involved in solving the assignment problem using the Hungarian method, which is the most commonly used and efficient method. Step 1: Set ...

  16. Unbalanced Assignment Problem: Definition, Formulation, and Solution

    Are you familiar with the assignment problem in Operations Research (OR)? This problem deals with assigning tasks to workers in a way that minimizes the total cost or time needed to complete the tasks. But what if the number of tasks and workers is not equal? In this case, we face the Unbalanced Assignment Problem (UAP).

  17. Assignment problems: A golden anniversary survey

    Abstract. Having reached the 50th (golden) anniversary of the publication of Kuhn's seminal article on the solution of the classic assignment problem, it seems useful to take a look at the variety of models to which it has given birth. This paper is a limited survey of what appear to be the most useful of the variations of the assignment ...

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  19. Some results on an assignment problem variant

    1 Introduction. The assignment problem is a well-known optimization problem. Many variations of the problem have been discussed in the literature (we may see, for instance, [ 1, 2 ]). Sinha [ 3] has discussed some such variants, in which jobs changeover costs are included. In such models, an operator can do multiple jobs or no job at all.

  20. PDF Introduction to Operations Research

    as the transportation problem, the assignment problem, the shortest path problem, the maximum flow problem, and the minimum cost flow problem. Very efficient algorithms exist which are many times more efficient than linear programming in the utilization of computer time and space resources. Introduction to Operations Research - p.6

  21. A Target-Assignment Problem

    Abstract. This paper is concerned with a target assignment model of a probabilistic and nonlinear nature, but nevertheless one which is closely related to the "personnel-assignment" problem. It is shown here that, despite the apparent nonlinearities, it is possible to devise a linear programming formulation that will ordinarily provide a ...

  22. PDF Unit 4: ASSIGNMENT PROBLEM

    Problem 5 A typical assignment problem, presented in the classic manner, is shown in Fig. Here there are five machines to be assigned to five jobs. The numbers in the matrix indicate the cost of doing each job with each machine. Jobs with costs of M are disallowed assignments. The problem is to find the minimum cost matching of machines to jobs.

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    ASSIGNMENT PROBLEM Consider an assignment problem of assigning n jobs to n machines (one job to one machine). Let c ij be the unit cost of assigning ith machine to the jth job and,ith machine to jth job. Let x ij = 1 , if jth job is assigned to ith machine. x ij = 0 , if jth job is not assigned to ith machine. K.BHARATHI,SCSVMV. ASSIGNMENT ...

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