## 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

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## Assignment Problem: Meaning, Methods and Variations | Operations Research

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

## Meaning of Assignment Problem:

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

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

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

## Definition of Assignment Problem:

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

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

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- Raúl Poler 0 ,
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- Manuel Díaz-Madroñero 2

## Research Centre on Production Management and Engineering, Polytechnic University of Valencia, Alcoy, Spain

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## Escuela Politécnica Superior de Alcoy, Universidad Politécnica de Valencia, Alcoy, Spain

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- Provides a valuable compendium of problems as a reference for undergraduate and graduate students, faculty, researchers and practitioners of operations research and management science
- Identifies different operations management problems in order to improve the decision making process concerning readers
- Addresses the following topics: Linear programming, integer programming, non-linear programming, network modeling, inventory theory, queue theory, tree decision, game theory, dynamic programming and markov processes

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## Applications and Mathematical Modeling in Operations Research

## From Operations Research to Dynamic Data Mining and Beyond

## Introduction to Stochastic Optimisation and Game Theory

Dynamic programming.

- Game Theory

## Integer Programming

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## Markov Processes

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## Table of contents (10 chapters)

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- Raúl Poler, Josefa Mula, Manuel Díaz-Madroñero

## Non-Linear Programming

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Find step-by-step solutions and answers to Operations Research - 9781337798211, as well as thousands of textbooks so you can move forward with confidence. ... Assignment Problems. Section 7-6: Transshipment Problems. Page 408: Review Problems. Exercise 1. Exercise 2. Exercise 3. Exercise 4. Exercise 5. Exercise 6. Exercise 7. Exercise 8 ...

Problem 4. Job shop needs to assign 4 jobs to 4 workers. The cost of performing a job is a function of the skills of the workers. Table summarizes the cost of the assignments. Worker1 cannot do job3, and worker 3 cannot do job 4. Determine the optimal assignment using the Hungarian method. Job.

Determine the optimum assignment schedule. Solution: 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. The cost matrix of the given assignment problem is. Column 3 contains no ...

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 ...

Remember, consistent practice is key to mastering the art of operations research! Solution with PuLP: ... 11. Assignment Problem: A company needs to assign n workers to n tasks. Each worker has ...

Resulting optimal solution: 13 = 0, = , = , = , 41 = 0, 42 = 1, 43 = 0. Machine 1 to location 4. Machine 2 to location 3. Machine 3 to location 1. We can see a lot of degenerate basic variables (. = 0) and the assignment to a dummy location. Transportation problem has generally. − 1 basic variables (.

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 ...

'Assignment Problem' published in 'Encyclopedia of Operations Research and Management Science ... The problem is a special form of the transportation problem and, as such, has an optimal solution in which each variable is either zero or one. ... H. W. (1995). The Hungarian method for the assignment problem. Naval Research Logistics Quarterly, 2 ...

The objective of this book is to provide a valuable compendium of problems as a reference for undergraduate and graduate students, faculty, researchers and practitioners of operations research and management science. These problems can serve as a basis for the development or study of assignments and exams. Also, they can be useful as a guide ...

The assignment network also has the bipartite structure. Figure 13. Network model of the assignment problem. The solution to the assignment problem as shown in Fig. 14 has a total flow of 1 in every column and row, and is the assignment that minimizes total cost. Figure 14.

Title: "Cracking the Balanced Assignment Problem in Operations Research!"🔍 Uncover the secrets of the Balanced Assignment Problem in this quick guide to Ope...

Economic Interpretation of the dual; Dual Simplex algorithm. Stepping stone method and Modified Distribution method. MODI method; Dual of the transportation problem and the optimality of the MODI method. Unequal number of rows and columns; Dual of the assignment problem. Setting up the problem and solving simple LP problems.

The objective of this book is to provide a valuable compendium of problems as a reference for undergraduate and graduate students, faculty, researchers and practitioners of operations research and management science. These problems can serve as a basis for the development or study of assignments and exams. Also, they can be useful as a guide for the first stage of the model formulation, i.e ...

Solutions. 56:171 Operations Research Final Exam '98 page 11 of 14 For $20,000, Sue can hire a consultant who will predict the outcome of the trial, i.e., either he predicts a loss of the suit (event PL), or he predicts a win (event PW). The consultant predicts the correct outcome 80% of the time. 2.

OPERATIONS RESEARCH Chapter 2 Transportation and Assignment Problems Prof. Bibhas C. Giri Professor of Mathematics Jadavpur University ... The Hungarian method is an eﬃcient method for ﬁnding the optimal solution of an assignment problem. The method works on the principle of reducing the given cost matrix to a matrix of opportunity costs ...

Operations Research Problems. pp.87-113. This chapter begins by introducing non-linear programming. Next, it proposes the formulation of a series of non-linear programming problems with their ...

Algorithm & Example-1. Algorithm. Hungarian Method Steps (Rule) Step-1: If number of rows is not equal to number of columns, then add dummy rows or columns with cost 0, to make it a square matrix. Step-2: a. Identify the minimum element in each row and subtract it from each element of that row.

OPERATIONS RESEARCH (UE18IE301) UNIT-3 TRANSPORTATION AND ASSIGNMENT PROBLEMS CONTENTS Sl. No. Name of the Topic 1. Formulation of Transportation model, Definition of Basic feasible solution

The transportation problem is a classic problem in operations research that involves finding the optimal way to move goods from one place to another. ... and transportation costs must be considered when choosing a solution method. 2.5. The assignment problem This problem is a combinatorial optimization problem that deals with allocating a set ...

chapter 01: graphical solutions to linear operations research problems. chapter 02: linear programming(lp) - introduction. chapter 03: linear programming - the simplex method. chapter 04: linear programming-advanced methods. chapter 05: the transportation and assignment problems

Operation Research Calculators ( examples ) 1.Assignment problem 1.1 Assignment problem (Using Hungarian method-2) 1.2 Assignment problem (Using Hungarian method-1) 2.1 Travelling salesman problem using hungarian method 2.2 Travelling salesman problem using branch and bound (penalty) method 2.3 Travelling salesman problem using branch and bound ...

There are 6 modules in this course. Operations Research (OR) is a field in which people use mathematical and engineering methods to study optimization problems in Business and Management, Economics, Computer Science, Civil Engineering, Industrial Engineering, etc. This course introduces frameworks and ideas about various types of optimization ...

Abstract. This note is concerned with two target assignment models. An optimum assignment is one which maximizes the expected value of targets destroyed. The first model, which admits an explicit solution, associates values only with the number of targets destroyed. An algorithm which enjoys a computational nicety is established when the values ...