how to solve the assignment problem

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:

ADVERTISEMENTS:

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:

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.

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

Stay tuned to BYJU’S – The Learning App and download the app to explore all Maths-related topics.

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.

Leave a Comment Cancel reply

Your Mobile number and Email id will not be published. Required fields are marked *

Request OTP on Voice Call

Post My Comment

• Share Share

Register with BYJU'S & Download Free PDFs

Register with byju's & watch live videos.

• Data Structures
• Linked List
• Binary Tree
• Binary Search Tree
• Segment Tree
• Disjoint Set Union
• Fenwick Tree
• Red-Black Tree
• Advanced Data Structures
• Hungarian Algorithm for Assignment Problem | Set 2 (Implementation)
• Count of nodes with maximum connection in an undirected graph
• Erdos Renyl Model (for generating Random Graphs)
• Types of Graphs with Examples
• Clustering Coefficient in Graph Theory
• Maximum number of edges in Bipartite graph
• Find node having maximum number of common nodes with a given node K
• Convert the undirected graph into directed graph such that there is no path of length greater than 1
• Count of Disjoint Groups by grouping points that are at most K distance apart
• Maximize count of nodes disconnected from all other nodes in a Graph
• Program to find the number of region in Planar Graph
• Cost of painting n * m grid
• Ways to Remove Edges from a Complete Graph to make Odd Edges
• Number of Simple Graph with N Vertices and M Edges
• Balance pans using given weights that are powers of a number
• Chiliagon Number
• Sum of all the numbers in the Nth parenthesis
• Shortest path in a graph from a source S to destination D with exactly K edges for multiple Queries
• Find if two given Quadratic equations have common roots or not

Hungarian Algorithm for Assignment Problem | Set 1 (Introduction)

• For each row of the matrix, find the smallest element and subtract it from every element in its row.
• Do the same (as step 1) for all columns.
• Cover all zeros in the matrix using minimum number of horizontal and vertical lines.
• Test for Optimality: If the minimum number of covering lines is n, an optimal assignment is possible and we are finished. Else if lines are lesser than n, we haven’t found the optimal assignment, and must proceed to step 5.
• Determine the smallest entry not covered by any line. Subtract this entry from each uncovered row, and then add it to each covered column. Return to step 3.

Try it before moving to see the solution

Explanation for above simple example:

  An example that doesn’t lead to optimal value in first attempt: In the above example, the first check for optimality did give us solution. What if we the number covering lines is less than n.

Time complexity : O(n^3), where n is the number of workers and jobs. This is because the algorithm implements the Hungarian algorithm, which is known to have a time complexity of O(n^3).

Space complexity :   O(n^2), where n is the number of workers and jobs. This is because the algorithm uses a 2D cost matrix of size n x n to store the costs of assigning each worker to a job, and additional arrays of size n to store the labels, matches, and auxiliary information needed for the algorithm.

In the next post, we will be discussing implementation of the above algorithm. The implementation requires more steps as we need to find minimum number of lines to cover all 0’s using a program. References: http://www.math.harvard.edu/archive/20_spring_05/handouts/assignment_overheads.pdf https://www.youtube.com/watch?v=dQDZNHwuuOY

Please Login to comment...

• Mathematical
• 10 Best Free Code Learning Apps for Android in 2024
• 5 Best AI Tools for Plagiarism Detection 2024
• 10 Best iMovie Alternatives in 2024
• 10 Best AI Tools for Sentiment Analysis
• 30 OOPs Interview Questions and Answers (2024)

Improve your Coding Skills with Practice

What kind of Experience do you want to share?

• Google OR-Tools
• Español – América Latina
• Português – Brasil
• Tiếng Việt

Solving an Assignment Problem

This section presents an example that shows how to solve an assignment problem using both the MIP solver and the CP-SAT solver.

In the example there are five workers (numbered 0-4) and four tasks (numbered 0-3). Note that there is one more worker than in the example in the Overview .

The costs of assigning workers to tasks are shown in the following table.

The problem is to assign each worker to at most one task, with no two workers performing the same task, while minimizing the total cost. Since there are more workers than tasks, one worker will not be assigned a task.

MIP solution

The following sections describe how to solve the problem using the MPSolver wrapper .

Import the libraries

The following code imports the required libraries.

Create the data

The following code creates the data for the problem.

The costs array corresponds to the table of costs for assigning workers to tasks, shown above.

Declare the MIP solver

The following code declares the MIP solver.

Create the variables

The following code creates binary integer variables for the problem.

Create the constraints

Create the objective function.

The following code creates the objective function for the problem.

The value of the objective function is the total cost over all variables that are assigned the value 1 by the solver.

Invoke the solver

The following code invokes the solver.

Print the solution

The following code prints the solution to the problem.

Here is the output of the program.

Complete programs

Here are the complete programs for the MIP solution.

CP SAT solution

The following sections describe how to solve the problem using the CP-SAT solver.

Declare the model

The following code declares the CP-SAT model.

The following code sets up the data for the problem.

The following code creates the constraints for the problem.

Here are the complete programs for the CP-SAT solution.

Except as otherwise noted, the content of this page is licensed under the Creative Commons Attribution 4.0 License , and code samples are licensed under the Apache 2.0 License . For details, see the Google Developers Site Policies . Java is a registered trademark of Oracle and/or its affiliates.

Last updated 2023-01-02 UTC.

Assignment problem: Hungarian method 3

Assignment problem: Hungarian Method Nui Ruppert (Mtk_Nr.: 373224) David Lenh (Mtk_Nr.: 368343) Amir Farshchi Tabrizi (Mtk-Nr.: 372894)

In this OR-Wiki entry we're going to explain the Hungarian method with 3 examples. In the first example you'll find the optimal solution after a few steps with the help of the reduced matrix. The second example illustrates a complex case where you need to proceed all the steps of the algorithm to get to an optimal solution. Finally in the third example we will show how to solve a maximization problem with the Hungarian method.

Inhaltsverzeichnis

• 1 Introduction
• 2 Example 1 – Minimization problem
• 3 Example 2 – Minimazation problem
• 4 Example 3 – Maximization problem
• 6 References

Introduction

The Hungarian method is a combinatorial optimization algorithm which was developed and published by Harold Kuhn in 1955. This method was originally invented for the best assignment of a set of persons to a set of jobs. It is a special case of the transportation problem. The algorithm finds an optimal assignment for a given “n x n” cost matrix. “Assignment problems deal with the question how to assign n items (e.g. jobs) to n machines (or workers) in the best possible way. […] Mathematically an assignment is nothing else than a bijective mapping of a finite set into itself […]” [1]

The assignment constraints are mathematically defined as:

To make clear how to solve an assignment problem with the Hungarian algorithm we will show you the different cases with several examples which can occur .

Example 1 – Minimization problem

In this example we have to assign 4 workers to 4 machines. Each worker causes different costs for the machines. Your goal is to minimize the total cost to the condition that each machine goes to exactly 1 person and each person works at exactly 1 machine. For comprehension: Worker 1 causes a cost of 6 for machine 1 and so on …

To solve the problem we have to perform the following steps:

Step 1 – Subtract the row minimum from each row.

Step 2 – Subtract the column minimum from each column from the reduced matrix.

The idea behind these 2 steps is to simplify the matrix since the solution of the reduced matrix will be exactly the same as of the original matrix.

Step 3 – Assign one “0” to each row & column.

Now that we have simplified the matrix we can assign each worker with the minimal cost to each machine which is represented by a “0”.

- In the first row we have one assignable “0” therefore we assign it to worker 3 .

- In the second row we also only have one assignable “0” therefore we assign it to worker 4 .

- In the third row we have two assignable “0”. We leave it as it is for now.

- In the fourth row we have one assignable “0” therefore we assign it. Consider that we can only assign each worker to each machine hence we can’t allocate any other “0” in the first column.

- Now we go back to the third row which now only has one assignable “0” for worker 2 .

As soon as we can assign each worker to one machine, we have the optimal solution . In this case there is no need to proceed any further steps. Remember also, if we decide on an arbitrary order in which we start allocating the “0”s then we may get into a situation where we have 3 assignments as against the possible 4. If we assign a “0” in the third row to worker 1 we wouldn’t be able to allocate any “0”s in column one and row two.

The rule to assign the “0”:

- If there is an assignable “0”, only 1 assignable “0” in any row or any column, assign it.

- If there are more than 1, leave it and proceed.

This rule would try to give us as many assignments as possible.

Now there are also cases where you won’t get an optimal solution for a reduced matrix after one iteration. The following example will explain it.

Example 2 – Minimazation problem

In this example we have the fastest taxi company that has to assign each taxi to each passenger as fast as possible. The numbers in the matrix represent the time to reach the passenger.

We proceed as in the first example.

Iteration 1:

Now we have to assign the “0”s for every row respectively to the rule that we described earlier in example 1.

- In the first row we have one assignable “0” therefore we assign it and no other allocation in column 2 is possible.

- In the second row we have one assignable “0” therefore we assign it.

- In the third row we have several assignable “0”s. We leave it as it is for now and proceed.

- In the fourth and fifth row we have no assignable “0”s.

Now we proceed with the allocations of the “0”s for each column .

- In the first column we have one assignable “0” therefore we assign it. No other “0”s in row 3 are assignable anymore.

Now we are unable to proceed because all the “0”s either been assigned or crossed. The crosses indicate that they are not fit for assignments because assignments are already made.

We realize that we have 3 assignments for this 5x5 matrix. In the earlier example we were able to get 4 assignments for a 4x4 matrix. Now we have to follow another procedure to get the remaining 2 assignments (“0”).

Step 4 – Tick all unassigned rows.

Step 5 – If a row is ticked and has a “0”, then tick the corresponding column (if the column is not yet ticked).

Step 6 – If a column is ticked and has an assignment, then tick the corresponding row (if the row is not yet ticked).

Step 7 - Repeat step 5 and 6 till no more ticking is possible.

In this case there is no more ticking possible and we proceed with the next step.

Step 8 – Draw lines through unticked rows and ticked columns. The number of lines represents the maximum number of assignments possible.

Step 9 – Find out the smallest number which does not have any line passing through it. We call it Theta. Subtract theta from all the numbers that do not have any lines passing through them and add theta to all those numbers that have two lines passing through them. Keep the rest of them the same.

(With this step we create a new “0”)

With the new assignment matrix we start to assign the “0”s after the explained rules. Nevertheless we have 4 assignments against the required 5 for an optimal solution. Therefore we have to repeat step 4 – 9.

Iteration 2:

Step 4 – Tick all unassigned row.

Note: The indices of the ticks show you the order we added them.

Iteration 3:

Iteration 4:

After the fourth iteration we assign the “0”s again and now we have an optimal solution with 5 assignments.

The solution:

- Taxi1 => Passenger1 - duration 12

- Taxi2 => Passenger4 - duration 11

- Taxi3 => Passenger2 - duration 8

- Taxi4 => Passenger3 - duration 14

- Taxi5 => Passenger5 - duration 11

If we define the needed duration as costs, the minimal cost for this problem is 56.

Example 3 – Maximization problem

Furthermore the Hungarian algorithm can also be used for a maximization problem in which case we first have to transform the matrix. For example a company wants to assign different workers to different machines. Each worker is more or less efficient with each machine. The efficiency can be defined as profit. The higher the number, the higher the profit.

As you can see, the maximal profit of the matrix is 13. The simple twist that we do is rather than try to maximize the profit, we’re going to try to minimize the profit that you don’t get. If every value is taken away from 13, then we can minimize the amount of profit lost. We receive the following matrix:

From now on we proceed as usual with the steps to get to an optimal solution.

With the determined optimal solution we can compute the maximal profit:

- Worker1 => Machine2 - 9

- Worker2 => Machine4 - 11

- Worker3 => Machine3 - 13

- Worker4 => Machine1 - 7

Maximal profit is 40.

The optimal solution is found if there is one assigned “0” for each row and each column.

[1] Linear Assignment Problems and Extensions, Rainer E. Burkard, Eranda Cela

[2] Operations Research Skript TU Kaiserslautern, Prof. Dr. Oliver Wendt

[3] The Hungarian method for the assignment problem, H. W. Kuhn, Bryn Mawr College

Fundamental of Operations Research, Lec. 16, Prof. G. Srinivasan

Navigationsmenü

• Quelltext anzeigen
• Versionsgeschichte

Meine Werkzeuge

• Gemeinschaftsportal
• Operations Research
• Studentenbeiträge zum Thema Operations Research
• Wirtschaftsinformatik
• Aktuelle Ereignisse
• Letzte Änderungen
• Zufällige Seite
• Links auf diese Seite
• Änderungen an verlinkten Seiten
• Spezialseiten
• Druckversion
• Permanenter Link
• Seiten­informationen

• Diese Seite wurde zuletzt am 1. Juli 2013 um 10:03 Uhr geändert.
• Datenschutz
• Über Operations-Research-Wiki

• Linear Programming using Pyomo
• Networking and Professional Development for Machine Learning Careers in the USA
• Predicting Employee Churn in Python
• Airflow Operators
• MLOps Tutorial

Solving Assignment Problem using Linear Programming in Python

Learn how to use Python PuLP to solve Assignment problems using Linear Programming.

In earlier articles, we have seen various applications of Linear programming such as transportation, transshipment problem, Cargo Loading problem, and shift-scheduling problem. Now In this tutorial, we will focus on another model that comes under the class of linear programming model known as the Assignment problem. Its objective function is similar to transportation problems. Here we minimize the objective function time or cost of manufacturing the products by allocating one job to one machine.

If we want to solve the maximization problem assignment problem then we subtract all the elements of the matrix from the highest element in the matrix or multiply the entire matrix by –1 and continue with the procedure. For solving the assignment problem, we use the Assignment technique or Hungarian method, or Flood’s technique.

The transportation problem is a special case of the linear programming model and the assignment problem is a special case of transportation problem, therefore it is also a special case of the linear programming problem.

In this tutorial, we are going to cover the following topics:

Assignment Problem

A problem that requires pairing two sets of items given a set of paired costs or profit in such a way that the total cost of the pairings is minimized or maximized. The assignment problem is a special case of linear programming.

For example, an operation manager needs to assign four jobs to four machines. The project manager needs to assign four projects to four staff members. Similarly, the marketing manager needs to assign the 4 salespersons to 4 territories. The manager’s goal is to minimize the total time or cost.

Problem Formulation

A manager has prepared a table that shows the cost of performing each of four jobs by each of four employees. The manager has stated his goal is to develop a set of job assignments that will minimize the total cost of getting all 4 jobs.  

Initialize LP Model

In this step, we will import all the classes and functions of pulp module and create a Minimization LP problem using LpProblem class.

Define Decision Variable

In this step, we will define the decision variables. In our problem, we have two variable lists: workers and jobs. Let’s create them using  LpVariable.dicts()  class.  LpVariable.dicts()  used with Python’s list comprehension.  LpVariable.dicts()  will take the following four values:

• First, prefix name of what this variable represents.
• Second is the list of all the variables.
• Third is the lower bound on this variable.
• Fourth variable is the upper bound.
• Fourth is essentially the type of data (discrete or continuous). The options for the fourth parameter are  LpContinuous  or  LpInteger .

Let’s first create a list route for the route between warehouse and project site and create the decision variables using LpVariable.dicts() the method.

Define Objective Function

In this step, we will define the minimum objective function by adding it to the LpProblem  object. lpSum(vector)is used here to define multiple linear expressions. It also used list comprehension to add multiple variables.

Define the Constraints

Here, we are adding two types of constraints: Each job can be assigned to only one employee constraint and Each employee can be assigned to only one job. We have added the 2 constraints defined in the problem by adding them to the LpProblem  object.

Solve Model

In this step, we will solve the LP problem by calling solve() method. We can print the final value by using the following for loop.

From the above results, we can infer that Worker-1 will be assigned to Job-1, Worker-2 will be assigned to job-3, Worker-3 will be assigned to Job-2, and Worker-4 will assign with job-4.

In this article, we have learned about Assignment problems, Problem Formulation, and implementation using the python PuLp library. We have solved the Assignment problem using a Linear programming problem in Python. Of course, this is just a simple case study, we can add more constraints to it and make it more complicated. You can also run other case studies on Cargo Loading problems , Staff scheduling problems . In upcoming articles, we will write more on different optimization problems such as transshipment problem, balanced diet problem. You can revise the basics of mathematical concepts in  this article  and learn about Linear Programming  in this article .

• Solving Blending Problem in Python using Gurobi
• Transshipment Problem in Python Using PuLP

You May Also Like

Sensitivity Analysis in Python

Solving Transportation Problem using Linear Programming in Python

Pandas DataFrame

OPERATIONS RESEARCH

Lesson 9. solution of assignment problem.

Current course

The assignment problem revisited

• Original Paper
• Published: 16 August 2021
• Volume 16 , pages 1531–1548, ( 2022 )

Cite this article

• Carlos A. Alfaro   ORCID: orcid.org/0000-0001-9783-8587 1 ,
• Sergio L. Perez 2 ,
• Carlos E. Valencia 3 &
• Marcos C. Vargas 1  

937 Accesses

4 Citations

4 Altmetric

Explore all metrics

First, we give a detailed review of two algorithms that solve the minimization case of the assignment problem, the Bertsekas auction algorithm and the Goldberg & Kennedy algorithm. It was previously alluded that both algorithms are equivalent. We give a detailed proof that these algorithms are equivalent. Also, we perform experimental results comparing the performance of three algorithms for the assignment problem: the \(\epsilon \) - scaling auction algorithm , the Hungarian algorithm and the FlowAssign algorithm . The experiment shows that the auction algorithm still performs and scales better in practice than the other algorithms which are harder to implement and have better theoretical time complexity.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price includes VAT (Russian Federation)

Instant access to the full article PDF.

Rent this article via DeepDyve

Institutional subscriptions

Similar content being viewed by others

Some results on an assignment problem variant

Pritibhushan Sinha

Integer Programming

A Full Description of Polytopes Related to the Index of the Lowest Nonzero Row of an Assignment Matrix

Bertsekas, D.P.: The auction algorithm: a distributed relaxation method for the assignment problem. Annal Op. Res. 14 , 105–123 (1988)

Article   MathSciNet   Google Scholar  

Bertsekas, D.P., Castañon, D.A.: Parallel synchronous and asynchronous implementations of the auction algorithm. Parallel Comput. 17 , 707–732 (1991)

Article   Google Scholar  

Bertsekas, D.P.: Linear network optimization: algorithms and codes. MIT Press, Cambridge, MA (1991)

MATH   Google Scholar  

Bertsekas, D.P.: The auction algorithm for shortest paths. SIAM J. Optim. 1 , 425–477 (1991)

Bertsekas, D.P.: Auction algorithms for network flow problems: a tutorial introduction. Comput. Optim. Appl. 1 , 7–66 (1992)

Bertsekas, D.P., Castañon, D.A., Tsaknakis, H.: Reverse auction and the solution of inequality constrained assignment problems. SIAM J. Optim. 3 , 268–299 (1993)

Bertsekas, D.P., Eckstein, J.: Dual coordinate step methods for linear network flow problems. Math. Progr., Ser. B 42 , 203–243 (1988)

Bertsimas, D., Tsitsiklis, J.N.: Introduction to linear optimization. Athena Scientific, Belmont, MA (1997)

Google Scholar  

Burkard, R., Dell’Amico, M., Martello, S.: Assignment Problems. Revised reprint. SIAM, Philadelphia, PA (2011)

Gabow, H.N., Tarjan, R.E.: Faster scaling algorithms for network problems. SIAM J. Comput. 18 (5), 1013–1036 (1989)

Goldberg, A.V., Tarjan, R.E.: A new approach to the maximum flow problem. J. Assoc. Comput. Mach. 35 , 921–940 (1988)

Goldberg, A.V., Tarjan, R.E.: Finding minimum-cost circulations by successive approximation. Math. Op. Res. 15 , 430–466 (1990)

Goldberg, A.V., Kennedy, R.: An efficient cost scaling algorithm for the assignment problem. Math. Programm. 71 , 153–177 (1995)

MathSciNet   MATH   Google Scholar  

Goldberg, A.V., Kennedy, R.: Global price updates help. SIAM J. Discr. Math. 10 (4), 551–572 (1997)

Kuhn, H.W.: The Hungarian method for the assignment problem. Naval Res. Logist. Quart. 2 , 83–97 (1955)

Kuhn, H.W.: Variants of the Hungarian method for the assignment problem. Naval Res. Logist. Quart. 2 , 253–258 (1956)

Lawler, E.L.: Combinatorial optimization: networks and matroids, Holt. Rinehart & Winston, New York (1976)

Orlin, J.B., Ahuja, R.K.: New scaling algorithms for the assignment ad minimum mean cycle problems. Math. Programm. 54 , 41–56 (1992)

Ramshaw, L., Tarjan, R.E., Weight-Scaling Algorithm, A., for Min-Cost Imperfect Matchings in Bipartite Graphs, : IEEE 53rd Annual Symposium on Foundations of Computer Science. New Brunswick, NJ 2012 , 581–590 (2012)

Zaki, H.: A comparison of two algorithms for the assignment problem. Comput. Optim. Appl. 4 , 23–45 (1995)

Download references

Acknowledgements

This research was partially supported by SNI and CONACyT.

Author information

Authors and affiliations.

Banco de México, Mexico City, Mexico

Carlos A. Alfaro & Marcos C. Vargas

Mountain View, CA, 94043, USA

Sergio L. Perez

Departamento de Matemáticas, CINVESTAV del IPN, Apartado postal 14-740, 07000, Mexico City, Mexico

Carlos E. Valencia

You can also search for this author in PubMed   Google Scholar

Corresponding author

Correspondence to Carlos A. Alfaro .

Ethics declarations

Conflict of interest.

There is no conflict of interest.

Additional information

Publisher's note.

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

The authors were partially supported by SNI and CONACyT.

Rights and permissions

Reprints and permissions

About this article

Alfaro, C.A., Perez, S.L., Valencia, C.E. et al. The assignment problem revisited. Optim Lett 16 , 1531–1548 (2022). https://doi.org/10.1007/s11590-021-01791-4

Download citation

Received : 26 March 2020

Accepted : 03 August 2021

Published : 16 August 2021

Issue Date : June 2022

DOI : https://doi.org/10.1007/s11590-021-01791-4

Share this article

Anyone you share the following link with will be able to read this content:

Sorry, a shareable link is not currently available for this article.

Provided by the Springer Nature SharedIt content-sharing initiative

• Assignment problem
• Bertsekas auction algorithm
• Combinatorial optimization and matching
• Find a journal
• Publish with us
• Track your research

Procedure, Example Solved Problem | Operations Research - Solution of assignment problems (Hungarian Method) | 12th Business Maths and Statistics : Chapter 10 : Operations Research

Chapter: 12th business maths and statistics : chapter 10 : operations research.

Solution of assignment problems (Hungarian Method)

First check whether the number of rows is equal to the numbers of columns, if it is so, the assignment problem is said to be balanced.

Step :1 Choose the least element in each row and subtract it from all the elements of that row.

Step :2 Choose the least element in each column and subtract it from all the elements of that column. Step 2 has to be performed from the table obtained in step 1.

Step:3 Check whether there is atleast one zero in each row and each column and make an assignment as follows.

Step :4 If each row and each column contains exactly one assignment, then the solution is optimal.

Example 10.7

Solve the following assignment problem. Cell values represent cost of assigning job A, B, C and D to the machines I, II, III and IV.

Here the number of rows and columns are equal.

∴ The given assignment problem is balanced. Now let us find the solution.

Step 1: Select a smallest element in each row and subtract this from all the elements in its row.

Look for atleast one zero in each row and each column.Otherwise go to step 2.

Step 2: Select the smallest element in each column and subtract this from all the elements in its column.

Since each row and column contains atleast one zero, assignments can be made.

Step 3 (Assignment):

Thus all the four assignments have been made. The optimal assignment schedule and total cost is

The optimal assignment (minimum) cost

Example 10.8

Consider the problem of assigning five jobs to five persons. The assignment costs are given as follows. Determine the optimum assignment schedule.

∴ The given assignment problem is balanced.

Now let us find the solution.

The cost matrix of the given assignment problem is

Column 3 contains no zero. Go to Step 2.

Thus all the five assignments have been made. The Optimal assignment schedule and total cost is

The optimal assignment (minimum) cost = ` 9

Example 10.9

Solve the following assignment problem.

Since the number of columns is less than the number of rows, given assignment problem is unbalanced one. To balance it , introduce a dummy column with all the entries zero. The revised assignment problem is

Here only 3 tasks can be assigned to 3 men.

Step 1: is not necessary, since each row contains zero entry. Go to Step 2.

Step 3 (Assignment) :

Since each row and each columncontains exactly one assignment,all the three men have been assigned a task. But task S is not assigned to any Man. The optimal assignment schedule and total cost is

The optimal assignment (minimum) cost = ₹ 35

Related Topics

Privacy Policy , Terms and Conditions , DMCA Policy and Compliant

Copyright © 2018-2024 BrainKart.com; All Rights Reserved. Developed by Therithal info, Chennai.

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.

How useful was this post?

Click on a star to rate it!

Average rating 1 / 5. Vote count: 1

No votes so far! Be the first to rate this post.

We are sorry that this post was not useful for you! 😔

Let us improve this post!

Tell us how we can improve this post?

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

7 Most Effective Ways For How To Solve Assignment Problems

Here in this blog, CodeAvail experts will explain to you 7 most effective ways for how to solve assignment problems step by step in detail.

How To Solve Assignment Problems

Table of Contents

The most common question asked by many students is how to solve assignment problems. There are many students who are having a hard time with their assignments thats why they are looking for proper guidelines to solve those problems. The assignment is one of the most critical parts of the students’ academic journey, and one always states that I have a lot of assignments to do. Besides this, there is not a single student in the world who has never done any assignment in their academic life. But the students always want to find the best and most effective ways for how to solve assignment problems . In this blog, we have given all the necessary information to help you solve your assignment problems.

How To Solve Assignment Problems-Stepwise Guide

To solve assignment problems, you need to understand the question carefully first. Because if you don’t understand the question, you will not know the information you need to complete your assignments. Follow these steps to know How To Solve assignment Problems :

1) Proper Planning Is Required 

This is the first step when you start solving your assignment, you’ll most likely jump directly into the main thing. The primary thing you will do is pull out of your beg, at that point work your way through the remainder of your assignment. There’s a superior way. Know how much time you need to do an assignment. At that point list down all the various chores that you need to do. Check to what extent it will take you to finish every task to check whether you have to permit yourself additional time. Be practical. When your note down everything then the next step is to find the best place for work.

2) Collect All the required Data Before You Start  

This is the biggest problem of many students, they don’t really follow this step. Make sure you have all the required information to solve assignment problems. Don’t start your assignment without the proper information. Because after starting your assignment when you come back it may be hard to get once again and write with the same flow. It will just destroy your assignment writing flow. If you have planned efficiently, you should know what exactly you want to complete your assignment and set up everything in your study table you’ll require.

3) Set A Timetable For Certain Assignment

Set a proper timetable to achieve each part of your assignment based on how long you think each part of your assignment will take and how much time you have. Give yourself enough time to complete each part and do other nightly routines. Set a proper time and be honest with it. The less time you waste on checking your laptop or mobile, the more quickly you can complete your assignment. If you believe you can complete everything in a half-hour, set a timer and work honestly to complete it.

4) Stay Away From Distractions

You need a quiet place when you are working on your assignment problems. Problems like Maths assignment problems, Computer science problems needs a quiet place to complete. Keep your telephone away from you, stay away from your PC, and make your surroundings as peaceful as possible. Because to solve assignment problems it requires a lot of focus. Giving work your full focus will really make it simpler, in light of the fact that your brain won’t balance various tasks simultaneously. 

Usually, students will attempt to perform multiple tasks, sitting in front of the TV or tuning in to the radio or proceeding to visit on Facebook or Instagram while additionally attempting to do assignments. It will be a lot more enjoyable to do those things after you are done completing your assignment.

5) Taking Breaks is Necessary

If your professor assigns you a lot of assignments to complete, then You want to work straight through hours and hours of assignment if you have a lot to do. But it would probably end up slowing you down and prolonging the whole session.

Get the work done in short periods. Go hard on an assignment, then take a short break to stretch and walk. To keep going, it will re-energize your mind and your body. This strategy will help you solve your assignment problems quickly and help you maintain your assignment’s quality. Try to do your assignment for 1 hour and then take a 10 minutes break.

6) Isolate Yourself

It is one of the best ways to do assignment problems. Because when we isolate ourselves from the outside world, we can do a better concentration on our assignment. The reason is, many outside elements distract our mind from our assignment. When we are going to do our assignment, we should isolate ourselves from our family, social media, and other social activities. 

7) Take Help From Online Service Providers

There are many Excel problems that are hard to solve at that time you can take help from online service providers. The reason for taking help from these online service providers because they have years of experience in their respective field. Plus if you need any help you can contact them because they are always available to deal with your problems. They are well aware of the guidelines provided by universities and colleges and know how to solve assignment problems .

Follow all the steps we mentioned above will help in solving your assignment problems. In this article, we have given all the required information that will help you find the answer on how to solve assignment problems . The assignment problems like Maths and Computer science required a lot of focus and proper time management. Time is everything if you manage your time effectively then you will not find any problem solving your assignment problems before the allotted time. Just put away the thing which you think can distract your mind. And give yourself a break after you complete every task because if you give your rain rest then it will be helpful for you to focus on your next task.

If you are facing a problem with completing your assignment or any other assignment, you can take help from us. Our Assignment providers have helped students across the world in completing their assignments on time, get good grades, and at the same time. There’s no doubt that many teachers are handing out assignments that are hard to complete on time. Some assignments can be about an unknown subject. But the truth is, often, the students need assignment help. It is your best decision when you have a lot of tasks to complete but still want to have free time.

As a result, Our computer science assignment help and programming assignment help experts are available for you to 24*7.

Related Posts

How to Hire someone to do my Statistics Homework for Me?

Students ask to do my statistics homework for me. Although there are many online tutors or statistics homework service providing websites available to help you…

How to Get Good Grades in Exams Tips by Experts

Here in this blog, Codeavail professional experts will help you to understand how to get good grades in Exams. Notice that not all the material…

Quadratic assignment problem

Author: Thomas Kueny, Eric Miller, Natasha Rice, Joseph Szczerba, David Wittmann (SysEn 5800 Fall 2020)

• 1 Introduction
• 2.1 Koopmans-Beckman Mathematical Formulation
• 2.2.1 Parameters
• 2.3.1 Optimization Problem
• 2.4 Computational Complexity
• 2.5 Algorithmic Discussions
• 2.6 Branch and Bound Procedures
• 2.7 Linearizations
• 3.1 QAP with 3 Facilities
• 4.1 Inter-plant Transportation Problem
• 4.2 The Backboard Wiring Problem
• 4.3 Hospital Layout
• 4.4 Exam Scheduling System
• 5 Conclusion
• 6 References

Introduction

The Quadratic Assignment Problem (QAP), discovered by Koopmans and Beckmann in 1957 [1] , is a mathematical optimization module created to describe the location of invisible economic activities. An NP-Complete problem, this model can be applied to many other optimization problems outside of the field of economics. It has been used to optimize backboards, inter-plant transportation, hospital transportation, exam scheduling, along with many other applications not described within this page.

Theory, Methodology, and/or Algorithmic Discussions

Koopmans-beckman mathematical formulation.

Economists Koopmans and Beckman began their investigation of the QAP to ascertain the optimal method of locating important economic resources in a given area. The Koopmans-Beckman formulation of the QAP aims to achieve the objective of assigning facilities to locations in order to minimize the overall cost. Below is the Koopmans-Beckman formulation of the QAP as described by neos-guide.org.

Quadratic Assignment Problem Formulation

Inner Product

Note: The true objective cost function only requires summing entries above the diagonal in the matrix comprised of elements

Since this matrix is symmetric with zeroes on the diagonal, dividing by 2 removes the double count of each element to give the correct cost value. See the Numerical Example section for an example of this note.

Optimization Problem

With all of this information, the QAP can be summarized as:

Computational Complexity

QAP belongs to the classification of problems known as NP-complete, thus being a computationally complex problem. QAP’s NP-completeness was proven by Sahni and Gonzalez in 1976, who states that of all combinatorial optimization problems, QAP is the “hardest of the hard”. [2]

Algorithmic Discussions

While an algorithm that can solve QAP in polynomial time is unlikely to exist, there are three primary methods for acquiring the optimal solution to a QAP problem:

• Dynamic Program
• Cutting Plane

Branch and Bound Procedures

The third method has been proven to be the most effective in solving QAP, although when n > 15, QAP begins to become virtually unsolvable.

The Branch and Bound method was first proposed by Ailsa Land and Alison Doig in 1960 and is the most commonly used tool for solving NP-hard optimization problems.

A branch-and-bound algorithm consists of a systematic enumeration of candidate solutions by means of state space search: the set of candidate solutions is thought of as forming a rooted tree with the full set at the root. The algorithm explores branches of this tree, which represent subsets of the solution set. Before one lists all of the candidate solutions of a branch, the branch is checked against upper and lower estimated bounds on the optimal solution, and the branch is eliminated if it cannot produce a better solution than the best one found so far by the algorithm.

Linearizations

The first attempts to solve the QAP eliminated the quadratic term in the objective function of

in order to transform the problem into a (mixed) 0-1 linear program. The objective function is usually linearized by introducing new variables and new linear (and binary) constraints. Then existing methods for (mixed) linear integer programming (MILP) can be applied. The very large number of new variables and constraints, however, usually poses an obstacle for efficiently solving the resulting linear integer programs. MILP formulations provide LP relaxations of the problem which can be used to compute lower bounds.

Numerical Example

Qap with 3 facilities.

Applications

Inter-plant transportation problem.

The QAP was first introduced by Koopmans and Beckmann to address how economic decisions could be made to optimize the transportation costs of goods between both manufacturing plants and locations. [1] Factoring in the location of each of the manufacturing plants as well as the volume of goods between locations to maximize revenue is what distinguishes this from other linear programming assignment problems like the Knapsack Problem.

The Backboard Wiring Problem

As the QAP is focused on minimizing the cost of traveling from one location to another, it is an ideal approach to determining the placement of components in many modern electronics. Leon Steinberg proposed a QAP solution to optimize the layout of elements on a blackboard by minimizing the total amount of wiring required. [4]

When defining the problem Steinberg states that we have a set of n elements

as well as a set of r points

In his paper he derives the below formula:

In his paper Steinberg a backboard with a 9 by 4 array, allowing for 36 potential positions for the 34 components that needed to be placed on the backboard. For the calculation, he selected a random initial placement of s1 and chose a random family of 25 unconnected sets.

The initial placement of components is shown below:

After the initial placement of elements, it took an additional 35 iterations to get us to our final optimized backboard layout. Leading to a total of 59 iterations and a final wire length of 4,969.440.

Hospital Layout

Building new hospitals was a common event in 1977 when Alealid N Elshafei wrote his paper on "Hospital Layouts as a Quadratic Assignment Problem". [5] With the high initial cost to construct the hospital and to staff it, it is important to ensure that it is operating as efficiently as possible. Elshafei's paper was commissioned to create an optimization formula to locate clinics within a building in such a way that minimizes the total distance that a patient travels within the hospital throughout the year. When doing a study of a major hospital in Cairo he determined that the Outpatient ward was acting as a bottleneck in the hospital and focused his efforts on optimizing the 17 departments there.

Elshafei identified the following QAP to determine where clinics should be placed:

For the Cairo hospital with 17 clinics, and one receiving and recording room bringing us to a total of 18 facilities. By running the above optimization Elshafei was able to get the total distance per year down to 11,281,887 from a distance of 13,973,298 based on the original hospital layout.

Exam Scheduling System

The scheduling system uses matrices for Exams, Time Slots, and Rooms with the goal of reducing the rate of schedule conflicts. To accomplish this goal, the “examination with the highest cross faculty student is been prioritized in the schedule after which the examination with the highest number of cross-program is considered and finally with the highest number of repeating student, at each stage group with the highest number of student are prioritized.” [6]

• ↑ 1.0 1.1 1.2 Koopmans, T., & Beckmann, M. (1957). Assignment Problems and the Location of Economic Activities. Econometrica, 25(1), 53-76. doi:10.2307/1907742
• ↑ 2.0 2.1 Quadratic Assignment Problem. (2020). Retrieved December 14, 2020, from https://neos-guide.org/content/quadratic-assignment-problem
• ↑ 3.0 3.1 3.2 Burkard, R. E., Çela, E., Pardalos, P. M., & Pitsoulis, L. S. (2013). The Quadratic Assignment Problem. https://www.opt.math.tugraz.at/~cela/papers/qap_bericht.pdf .
• ↑ 4.0 4.1 Leon Steinberg. The Backboard Wiring Problem: A Placement Algorithm. SIAM Review . 1961;3(1):37.
• ↑ 5.0 5.1 Alwalid N. Elshafei. Hospital Layout as a Quadratic Assignment Problem. Operational Research Quarterly (1970-1977) . 1977;28(1):167. doi:10.2307/300878
• ↑ 6.0 6.1 Muktar, D., & Ahmad, Z.M. (2014). Examination Scheduling System Based On Quadratic Assignment.

Navigation menu

Excel Tutorial: How To Solve Assignment Problem In Excel

Introduction.

Have you ever faced the challenge of assigning a set of tasks to a group of resources in Excel? This is what we call the assignment problem in Excel. It is a common issue faced by many professionals, and finding an efficient solution can greatly improve productivity and resource utilization. In this tutorial, we will guide you through the process of solving the assignment problem in Excel, and explain why it is important to master this skill.

Key Takeaways

• Solving the assignment problem in Excel can greatly improve productivity and resource utilization.
• Understanding the assignment problem and its real-life applications is important for professionals.
• Organizing and managing data accurately is crucial for solving the assignment problem in Excel.
• Using the Solver tool effectively can help find optimal solutions for the assignment problem.
• Efficiency tips and avoiding common mistakes can streamline the problem-solving process in Excel.

Understanding the Assignment Problem

The assignment problem is a fundamental optimization problem that involves finding the most efficient assignment of tasks to resources. In other words, it is the process of finding the best possible way to allocate a set of resources to a set of tasks in such a way that the overall cost or time is minimized.

The assignment problem can be defined as a special case of the transportation problem, where the objective is to minimize the cost of assigning a set of tasks to a set of resources, given certain constraints and limitations.

There are different types of assignment problems, including the balanced assignment problem, unbalanced assignment problem, and the generalized assignment problem. The balanced assignment problem occurs when the number of resources is equal to the number of tasks, while the unbalanced assignment problem occurs when the number of resources is not equal to the number of tasks. The generalized assignment problem allows for assigning a task to multiple resources, but with different costs associated with each assignment.

The assignment problem has numerous real-life applications, such as in workforce scheduling, project management, and supply chain optimization. In Excel, the assignment problem can be solved using various optimization techniques and algorithms, such as the Hungarian method, the auction algorithm, and the shortest path algorithm. These techniques can be implemented using Excel's built-in solver tool, which allows users to find the optimal solution to assignment problems by minimizing a given objective function, subject to certain constraints.

Setting up the Data in Excel

When it comes to solving the assignment problem in Excel, setting up the data properly is crucial for accurate and efficient analysis. In this chapter, we will discuss how to organize the data, use Excel tables for better data management, and ensure data accuracy and completeness.

• Identify the assignment problem variables and constraints
• Create a separate section in Excel for each variable and constraint
• Ensure the data is organized in a clear and logical manner for easy analysis
• Create an Excel table for each section of the assignment problem
• Use table features such as filtering and sorting to easily manipulate and analyze the data
• Utilize the structured format of tables for improved data organization and readability
• Double-check all data entries for accuracy
• Verify that all variables and constraints are accounted for in the data
• Use validation and error-checking features in Excel to minimize data errors

Using Solver Tool in Excel

Excel’s Solver tool is a powerful feature that allows users to find the optimal solution to complex problems, such as the assignment problem. By utilizing the Solver tool, you can efficiently allocate resources and optimize various aspects of your business or project.

Accessing the Solver tool in Excel

To access the Solver tool in Excel, you first need to ensure that it is installed as an add-in. You can do this by navigating to the “File” tab, selecting “Options,” and then clicking on “Add-Ins.” From there, you can enable the Solver add-in, which will then appear in the “Data” tab under the “Analysis” group.

Defining the objective and constraints

Once the Solver tool is accessible, you can begin defining the objective and constraints of your assignment problem. The objective is the goal you want to achieve, such as maximizing profits or minimizing costs. Constraints are the limitations or restrictions that must be considered, such as resource availability or capacity.

Running the Solver to find the optimal solution

After defining the objective and constraints, you can then run the Solver to find the optimal solution to your assignment problem. The Solver tool will utilize algorithms to analyze various combinations and iterations to determine the best possible outcome based on the defined parameters.

Interpreting the Results

After using Excel to solve the assignment problem, it is important to understand and interpret the results to ensure accuracy and make any necessary adjustments.

• Objective Function: The Solver provides the optimal value of the objective function, which represents the minimum cost or maximum profit.
• Variable Values: It also provides the optimal values for the decision variables, indicating the allocation of resources to tasks.
• Check Constraints: Ensure that all constraints are satisfied by the solution, such as resource limits and task requirements.
• Sensitivity Analysis: Conduct sensitivity analysis to understand how changes in inputs or constraints affect the solution.
• Scenario Analysis: Explore different scenarios by adjusting input values or constraints to evaluate alternative solutions.
• Iterative Process: If the initial solution is not optimal, iterate by making adjustments and re-solving the problem using Solver.

Tips for Efficiency

Efficiency is key when solving assignment problems in Excel. By utilizing shortcuts, functions, and avoiding common mistakes, you can streamline the process and save valuable time.

• Keyboard shortcuts: Familiarize yourself with common keyboard shortcuts in Excel to quickly perform functions such as copying, pasting, and formatting.
• Use of built-in functions: Take advantage of Excel's built-in functions such as VLOOKUP, INDEX, and MATCH to streamline the assignment problem-solving process.
• Organize data: Before starting to solve the assignment problem, ensure that your data is properly organized and formatted to avoid confusion and errors.
• Utilize templates: Consider creating templates or using pre-existing ones to simplify the process and avoid starting from scratch each time.
• Double-check formulas: Always double-check your formulas to avoid errors that can lead to incorrect solutions.
• Use of absolute references: When working with formulas, use absolute references to ensure that cell references do not change unintentionally.

Recap: Solving assignment problems in Excel is crucial for efficient project management and decision-making. It allows for optimal allocation of resources and time, leading to streamlined workflows and increased productivity.

Encouragement: Practice makes perfect, and the same goes for mastering Excel. I encourage you to continue practicing and applying the tutorial steps to become proficient in solving assignment problems in Excel.

Reiteration: Mastering Excel for problem-solving offers numerous benefits, including improved data analysis, better decision-making, and enhanced project management skills. By honing your Excel skills, you can excel in your professional and academic endeavors.

Immediate Download

MAC & PC Compatible

Free Email Support

Related aticles

The Benefits of Excel Dashboards for Data Analysts

Unlock the Power of Real-Time Data Visualization with Excel Dashboards

Unlocking the Potential of Excel's Data Dashboard

Unleashing the Benefits of a Dashboard with Maximum Impact in Excel

Exploring Data Easily and Securely: Essential Features for Excel Dashboards

Unlock the Benefits of Real-Time Dashboard Updates in Excel

Unleashing the Power of Excel Dashboards

Understanding the Benefits and Challenges of Excel Dashboard Design and Development

Leverage Your Data with Excel Dashboards

Crafting the Perfect Dashboard for Excel

An Introduction to Excel Dashboards

How to Create an Effective Excel Dashboard

• Choosing a selection results in a full page refresh.