MBA Notes

How to Solve the Assignment Problem: A Complete Guide

Table of Contents

Assignment problem is a special type of linear programming problem that deals with assigning a number of resources to an equal number of tasks in the most efficient way. The goal is to minimize the total cost of assignments while ensuring that each task is assigned to only one resource and each resource is assigned to only one task. In this blog, we will discuss the solution of the assignment problem using the Hungarian method, which is a popular algorithm for solving the problem.

Understanding the Assignment Problem

Before we dive into the solution, it is important to understand the problem itself. In the assignment problem, we have a matrix of costs, where each row represents a resource and each column represents a task. The objective is to assign each resource to a task in such a way that the total cost of assignments is minimized. However, there are certain constraints that need to be satisfied – each resource can be assigned to only one task and each task can be assigned to only one resource.

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 up the cost matrix

The first step in solving the assignment problem is to set up the cost matrix, which represents the cost of assigning a task to an agent. The matrix should be square and have the same number of rows and columns as the number of tasks and agents, respectively.

Step 2: Subtract the smallest element from each row and column

To simplify the calculations, we need to reduce the size of the cost matrix by subtracting the smallest element from each row and column. This step is called matrix reduction.

Step 3: Cover all zeros with the minimum number of lines

The next step is to cover all zeros in the matrix with the minimum number of horizontal and vertical lines. This step is called matrix covering.

Step 4: Test for optimality and adjust the matrix

To test for optimality, we need to calculate the minimum number of lines required to cover all zeros in the matrix. If the number of lines equals the number of rows or columns, the solution is optimal. If not, we need to adjust the matrix and repeat steps 3 and 4 until we get an optimal solution.

Step 5: Assign the tasks to the agents

The final step is to assign the tasks to the agents based on the optimal solution obtained in step 4. This will give us the most cost-effective or profit-maximizing assignment.

Solution of the Assignment Problem using the Hungarian Method

The Hungarian method is an algorithm that uses a step-by-step approach to find the optimal assignment. The algorithm consists of the following steps:

  • Subtract the smallest entry in each row from all the entries of the row.
  • Subtract the smallest entry in each column from all the entries of the column.
  • Draw the minimum number of lines to cover all zeros in the matrix. If the number of lines drawn is equal to the number of rows, we have an optimal solution. If not, go to step 4.
  • Determine the smallest entry not covered by any line. Subtract it from all uncovered entries and add it to all entries covered by two lines. Go to step 3.

The above steps are repeated until an optimal solution is obtained. The optimal solution will have all zeros covered by the minimum number of lines. The assignments can be made by selecting the rows and columns with a single zero in the final matrix.

Applications of the Assignment Problem

The assignment problem has various applications in different fields, including computer science, economics, logistics, and management. In this section, we will provide some examples of how the assignment problem is used in real-life situations.

Applications in Computer Science

The assignment problem can be used in computer science to allocate resources to different tasks, such as allocating memory to processes or assigning threads to processors.

Applications in Economics

The assignment problem can be used in economics to allocate resources to different agents, such as allocating workers to jobs or assigning projects to contractors.

Applications in Logistics

The assignment problem can be used in logistics to allocate resources to different activities, such as allocating vehicles to routes or assigning warehouses to customers.

Applications in Management

The assignment problem can be used in management to allocate resources to different projects, such as allocating employees to tasks or assigning budgets to departments.

Let’s consider the following scenario: a manager needs to assign three employees to three different tasks. Each employee has different skills, and each task requires specific skills. The manager wants to minimize the total time it takes to complete all the tasks. The skills and the time required for each task are given in the table below:

Task 1 Task 2 Task 3
Emp 1 5 7 6
Emp 2 6 4 5
Emp 3 8 5 3

The assignment problem is to determine which employee should be assigned to which task to minimize the total time required. To solve this problem, we can use the Hungarian method, which we discussed in the previous blog.

Using the Hungarian method, we first subtract the smallest entry in each row from all the entries of the row:

Task 1 Task 2 Task 3
Emp 1 0 2 1
Emp 2 2 0 1
Emp 3 5 2 0

Next, we subtract the smallest entry in each column from all the entries of the column:

Task 1 Task 2 Task 3
Emp 1 0 2 1
Emp 2 2 0 1
Emp 3 5 2 0
0 0 0

We draw the minimum number of lines to cover all the zeros in the matrix, which in this case is three:

Since the number of lines is equal to the number of rows, we have an optimal solution. The assignments can be made by selecting the rows and columns with a single zero in the final matrix. In this case, the optimal assignments are:

  • Emp 1 to Task 3
  • Emp 2 to Task 2
  • Emp 3 to Task 1

This assignment results in a total time of 9 units.

I hope this example helps you better understand the assignment problem and how to solve it using the Hungarian method.

Solving the assignment problem may seem daunting, but with the right approach, it can be a straightforward process. By following the steps outlined in this guide, you can confidently tackle any assignment problem that comes your way.

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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

Assignment Problem: Meaning, Methods and Variations | Operations Research

operations research assignment problems and solutions

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:

operations research assignment problems and solutions

OPERATIONS RESEARCH

Lesson 9. solution of assignment problem.

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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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operations research assignment problems and solutions

operations research assignment problems and solutions

  • Operations Research Problems

Statements and Solutions

  • © 2014
  • Raúl Poler 0 ,
  • Josefa Mula 1 ,
  • 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

Universitat politècnica de valència, alcoy, spain.

  • Provides a valuable compendium of problems as a reference for undergraduate and graduate students, faculty, researchers and practitioners of operations research and management science
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  • 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

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From Operations Research to Dynamic Data Mining and Beyond

operations research assignment problems and solutions

Introduction to Stochastic Optimisation and Game Theory

Dynamic programming.

  • Game Theory

Integer Programming

Inventory theory.

  • Linear and Non-Linear Programming

Markov Processes

  • Network Modeling
  • Queue Theory

Table of contents (10 chapters)

Front matter, linear programming.

  • Raúl Poler, Josefa Mula, Manuel Díaz-Madroñero

Non-Linear Programming

Network modelling, queueing theory, decision theory, games theory, back matter.

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Bibliographic Information

Book Title : Operations Research Problems

Book Subtitle : Statements and Solutions

Authors : Raúl Poler, Josefa Mula, Manuel Díaz-Madroñero

DOI : https://doi.org/10.1007/978-1-4471-5577-5

Publisher : Springer London

eBook Packages : Engineering , Engineering (R0)

Copyright Information : Springer-Verlag London Ltd., part of Springer Nature 2014

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eBook ISBN : 978-1-4471-5577-5 Published: 08 November 2013

Edition Number : 1

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operations research assignment problems and solutions



> Operation Research calculators
AtoZmath.com - Homework help (with all solution steps)
Secondary school, High school and College
Provide step by step solutions of your problems using online calculators (online solvers)
Your textbook, etc
Operation Research Calculators ( )

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1. Processing n Jobs Through 2 Machines Problem
2. Processing n Jobs Through 3 Machines Problem
3. Processing n Jobs Through m Machines Problem
4. Processing 2 Jobs Through m Machines Problem

1. Model-1 : Replacement policy for items whose running cost increases with time and value of money remains constant during a period
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2. : Replacement policy for items whose running cost increases with time but value of money changes constant rate during a period
3. : Group replacement policy
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Operation Research with example
Assignment Problem
1. A department has five employess with five jobs to be permormed. The time (in hours) each men will take to perform each job is given in the effectiveness matrix.
Employees
I II III IV V
Jobs A 10 5 113 15 16
B 3 9 18 13 6
C 10 7 2 2 2
D 7 11 9 7 12
E 7 9 10 4 12
2. In the modification of a plant layout of a factory four new machines M1, M2, M3 and M4 are to be installed in a machine shop. There are five vacant places A, B, C, D and E available. Because of limited space, machine M2 cannot be placed at C and M3 cannot be placed at A. The cost of locating a machine at a place (in hundred rupess) is as follows.
Location
A B C D E
Machine M1 9 11 15 10 11
M2 12 9 -- 10 9
M3 -- 11 14 11 7
M4 14 8 12 7 8





1. A travelling salesman has to visit five cities. He wishes to start from a particular city, visit each city only once and then return to his starting point. The travelling cost of each city from a particular city is given below.
To city
A B C D E
From city A x 2 5 7 1
B 6 x 3 8 2
C 8 7 x 4 7
D 12 4 6 x 5
E 1 3 2 8 x
1. Best-ride airlines that operates seven days a week has the following time-table.
Delhi - Mumbai Mumbai - Delhi
Flight No Departure Arrival
1 7.00 8.00
2 8.00 9.00
3 13.00 14.00
4 18.00 19.00
Flight No Departure Arrival
101 8.00 9.00
102 9.00 10.00
103 12.00 13.00
104 17.00 18.00
Simplex method
Solve the following LP problem by using









1. Use the simplex method to solve the following LP problem.
Maximize Z = 3x1 + 5x2 + 4x3
subject to the constraints
2x1 + 3x2 ≤ 8
2x2 + 5x3 ≤ 10
3x1 + 2x2 + 4x3 ≤ 15
and x1, x2, x3 ≥ 0

2. Use the simplex method to solve the following LP problem.
Maximize Z = 4x1 + 3x2
subject to the constraints
2x1 + x2 ≤ 1000
x1 + x2 ≤ 800
x1 ≤ 400
x2 ≤ 700
and x1, x2 ≥ 0
1. Use the penalty (Big - M) method to solve the following LP problem.
Minimize Z = 5x1 + 3x2
subject to the constraints
2x1 + 4x2 ≤ 12
2x1 + 2x2 = 10
5x1 + 2x2 ≥ 10
and x1, x2 ≥ 0

2. Use the penalty (Big - M) method to solve the following LP problem.
Minimize Z = x1 + 2x2 + 3x3 - x4
subject to the constraints
x1 + 2x2 + 3x3 = 15
2x1 + x2 + 5x3 = 20
x1 + 2x2 + x3 + x4 = 10
and x1, x2, x3, x4 ≥ 0
1. Solve the following LP problem by using the Two-Phase method.
Minimize Z = x1 + x2
subject to the constraints
2x1 + 4x2 ≥ 4
x1 + 7x2 ≥ 7
and x1, x2 ≥ 0

2. Solve the following LP problem by using the Two-Phase method.
Minimize Z = x1 - 2x2 - 3x3
subject to the constraints
-2x1 + 3x2 + 3x3 = 2
2x1 + 3x2 + 4x3 = 1
and x1, x2, x3 ≥ 0
1. Solve the following integer programming problem using Gomory's cutting plane algorithm.
Maximize Z = x1 + x2
subject to the constraints
3x1 + 2x2 ≤ 5
x2 ≤ 2
and x1, x2 ≥ 0 and are integers.

2. Solve the following integer programming problem using Gomory's cutting plane algorithm.
Maximize Z = 2x1 + 20x2 - 10x3
subject to the constraints
2x1 + 20x2 + 4x3 ≤ 15
6x1 + 20x2 + 4x3 ≤ 20
and x1, x2, x3 ≥ 0 and are integers.
1. Use graphical method to solve following LP problem.
Maximize Z = x1 + x2
subject to the constraints
3x1 + 2x2 ≤ 5
x2 ≤ 2
and x1, x2 ≥ 0

2. Use graphical method to solve following LP problem.
Maximize Z = 2x1 + x2
subject to the constraints
x1 + 2x2 ≤ 10
x1 + x2 ≤ 6
x1 - x2 ≤ 2
x1 - 2x2 ≤ 1
and x1, x2 ≥ 0
1. Write the dual to the following LP problem.
Maximize Z = x1 - x2 + 3x3
subject to the constraints
x1 + x2 + x3 ≤ 10
2x1 - x2 - x3 ≤ 2
2x1 - 2x2 - 3x3 ≤ 6
and x1, x2, x3 ≥ 0

2. Write the dual to the following LP problem.
Minimize Z = 3x1 - 2x2 + 4x3
subject to the constraints
3x1 + 5x2 + 4x3 ≥ 7
6x1 + x2 + 3x3 ≥ 4
7x1 - 2x2 - x3 ≤ 10
x1 - 2x2 + 5x3 ≥ 3
4x1 + 7x2 - 2x3 ≥ 2
and x1, x2, x3 ≥ 0
1. Solve the following LP problem by using Branch and Bound method
Max Z = 7x1 + 9x2
subject to
-x1 + 3x2 ≤ 6
7x1 + x2 ≤ 35
x2 ≤ 7
and x1,x2 ≥ 0

2. Solve the following LP problem by using Branch and Bound method
Max Z = 3x1 + 5x2
subject to
2x1 + 4x2 ≤ 25
x1 ≤ 8
2x2 ≤ 10
and x1,x2 ≥ 0

1. Solve LP using zero-one Integer programming problem method
Max Z = 300x1 + 90x2 + 400x3 + 150x4
subject to
35000x1 + 10000x2 + 25000x3 + 90000x4 ≤ 120000
4x1 + 2x2 + 7x3 + 3x4 ≤ 12
x1 + x2 ≤ 1
and x1,x2,x3,x4 ≥ 0

2. Solve LP using 0-1 Integer programming problem method
MAX Z = 650x1 + 700x2 + 225x3 + 250x4
subject to
700x1 + 850x2 + 300x3 + 350x4 ≤ 1200
550x1 + 550x2 + 150x3 + 200x4 ≤ 700
400x1 + 350x2 + 100x3 ≤ 400
x1 + x2 ≥ 1
-x3 + x4 ≤ 1
and x1,x2,x3,x4 ≥ 0
1. Solve the following LP problem by using Revised Simplex method
MAX Z = 3x1 + 5x2
subject to
x1 ≤ 4
x2 ≤ 6
3x1 + 2x2 ≤ 18
and x1,x2 ≥ 0

2. Solve the following LP problem by using Revised Simplex method
MAX Z = 2x1 + x2
subject to
3x1 + 4x2 ≤ 6
6x1 + x2 ≤ 3
and x1,x2 ≥ 0
Transportation Problem using









1. A Company has 3 production facilities S1, S2 and S3 with production capacity of 7, 9 and 18 units (in 100's) per week of a product, respectively. These units are tobe shipped to 4 warehouses D1, D2, D3 and D4 with requirement of 5,6,7 and 14 units (in 100's) per week, respectively. The transportation costs (in rupees) per unit between factories to warehouses are given in the table below.
D D D D Capacity
S 19 30 50 10 7
S 70 30 40 60 9
S 40 8 70 20 18
Demand 5 8 7 14 34
D D D D Supply
S 11 13 17 14 250
S 16 18 14 10 300
S 21 24 13 10 400
Demand 200 225 275 250
3. A company has factories at F1, F2 and F3 which supply to warehouses at W1, W2 and W3. Weekly factory capacities are 200, 160 and 90 units, respectively. Weekly warehouse requiremnet are 180, 120 and 150 units, respectively. Unit shipping costs (in rupess) are as follows:
W W W Supply
F 16 20 12 200
F 14 8 18 160
F 26 24 16 90
Demand 180 120 150 450
P Q R S Supply
A 6 3 5 4 22
B 5 9 2 7 15
C 5 7 8 6 8
Demand 7 12 17 9 45
4.
1. An assembly is to be made from two parts X and Y. Both parts must be turned on a lathe Y must be polished where as X need not be polished. The sequence of acitivities, together with their predecessors, is given below
Activity Description Predecessor Activity
A Open work order -
B Get material for X A
C Get material for Y A
D Turn X on lathe B
E Turn Y on lathe B,C
F Polish Y E
G Assemble X and Y D,F
H Pack G
2. An established company has decided to add a new product to its line. It will buy the product from a manufacturing concern, package it, and sell it to a number of distributors that have been selected on a geographical basis. Market research has already indicated the volume expected and the size of sales force required. The steps shown in the following table are to be planned.
Activity Description Predecessor Activity Duration (days)
A Organize sales office - 6
B Hire salesman A 4
C Train salesman B 7
D Select advertising agency A 2
E Plan advertising campaign D 4
F Conduct advertising campaign E 10
G Design package - 2
H Setup packaging campaign G 10
I Package initial stocks J,H 6
J Order stock from manufacturer - 13
K Select distributors A 9
L Sell to distributors C,K 3
M Ship stocks to distributors I,L 5
5.
1. There are seven jobs, each of which has to go through the machines A and B in the order AB. Processing times in hours are as follows.
Job 1 2 3 4 5 6 7
Machine A 3 12 15 6 10 11 9
Machine B 8 10 10 6 12 1 3
2. Find the sequence that minimizes the total time required in performing the following job on three machines in the order ABC. Processing times (in hours) are given in the following table.
Job 1 2 3 4 5
Machine A 8 10 6 7 11
Machine B 5 6 2 3 4
Machine C 4 9 8 6 5
6.
1. A firm is considering the replacement of a machine, whose cost price is Rs 12,200 and its scrap value is Rs 200. From experience the running (maintenance and operating) costs are found to be as follows:
Year12345678
Running Cost2005008001,2001,8002,5003,2004,000
1. The data collected in running a machine, the cost of which is Rs 60,000 are given below:
Year12345
Resale Value42,00030,00020,40014,4009,650
Cost of spares4,0004,2704,8805,7006,800
Cost of labour14,00016,00018,00021,00025,000
1. Machine A costs Rs 45,000 and its operating costs are estimated to be Rs 1,000 for the first year increasing by Rs 10,000 per year in the second and subsequent years. Machine B costs Rs 50,000 and operating costs are Rs 2,000 for the first year, increasing by Rs 4,000 in the second and subsequent years. If at present we have a machine of type A, should we replace it with B? if so when? Assume that both machines have no resale value and their future costs are not discounted.

Replacement policy for items whose running cost increases with time but value of money changes constant rate during a period
1. An engineering company is offered a material handling equipment A. It is priced at Rs 60,000 includeing cost of installation. The costs for operation and maintenance are estimated to be Rs 10,000 for each of the first five years, increasing every year by Rs 3,000 in the sixth and subsequent years. The company expects a return of 10 percent on all its investment. What is the optimal replacement period?
Year1234567
Running Cost10,00010,00010,00010,00010,00013,00016,000

Group replacement policy
1. A computer contains 10,000 resistors. When any resistor fails, it is replaced. The cost of replacing a resistor individually is Rs 1 only. If all the resistors are replaced at the same time, the cost per resistor would be reduced to 35 paise. The percentage of surviving resistors say S(t) at the end of month t and the probability of failure P(t) during the month t are as follows:
t0123456
P(t)00.030.070.200.400.150.15
t012345
P(t)00.050.100.200.400.25











1. For the game with payoff matrix
Player `B`
`B_1``B_2``B_3`
Player `A``A_1` -1  2  -2 
`A_2` 6  4  -6 
1. Dominance Example
Player `B`
`B_1``B_2``B_3``B_4`
Player `A``A_1` 3  5  4  2 
`A_2` 5  6  2  4 
`A_3` 2  1  4  0 
`A_4` 3  3  5  2 
1. Find the solution of game using algebraic method for the following pay-off matrix
Player `B`
`B_1``B_2`
Player `A``A_1` 1  7 
`A_2` 6  2 
1. Find the solution of game using calculus method for the following pay-off matrix
Player `B`
`B_1``B_2`
Player `A``A_1` 1  3 
`A_2` 5  2 
1. Find the solution of game using arithmetic method for the following pay-off matrix
Player `B`
`B_1``B_2``B_3`
Player `A``A_1` 10  5  -2 
`A_2` 13  12  15 
`A_3` 16  14  10 
1. Find the solution of game using matrix method for the following pay-off matrix
Player `B`
`B_1``B_2``B_3`
Player `A``A_1` 1  7  2 
`A_2` 6  2  7 
`A_3` 5  1  6 
1. Find the solution of game using 2Xn Games method for the following pay-off matrix
Player `B`
`B_1``B_2`
Player `A``A_1` -3  4 
`A_2` -1  1 
`A_3` 7  -2 
1. Find the solution of game using graphical method method for the following pay-off matrix
Player `B`
`B_1``B_2`
Player `A``A_1` 1  -3 
`A_2` 3  5 
`A_3` -1  6 
`A_4` 4  1 
`A_5` 2  2 
`A_6` -5  0 
1. Find the solution of game using linear programming method for the following pay-off matrix
Player `B`
`B_1``B_2``B_3`
Player `A``A_1` 3  -4  2 
`A_2` 1  -7  -3 
`A_3` -2  4  7 

operations research assignment problems and solutions

operations research assignment problems and solutions

Problem Questions with Answer, Solution | Operations Research - Exercise 10.1: Transportation Problem | 12th Business Maths and Statistics : Chapter 10 : Operations Research

Chapter: 12th business maths and statistics : chapter 10 : operations research, exercise 10.1: transportation problem.

Exercise 10.1

1. What is transportation problem?

2. Write mathematical form of transportation problem.

3. what is feasible solution and non degenerate solution in transportation problem?

4. What do you mean by balanced transportation problem?

5. Find an initial basic feasible solution of the following problem using north west corner rule.

operations research assignment problems and solutions

6. Determine an initial basic feasible solution of the following transportation problem by north west corner method

operations research assignment problems and solutions

7. Obtain an initial basic feasible solution to the following transportation problem by using least- cost method.

operations research assignment problems and solutions

8. Explain Vogel’s approximation method by obtaining initial feasible solution of the following transportation problem

operations research assignment problems and solutions

9. Consider the following transportation problem

operations research assignment problems and solutions

Determine initial basic feasible solution by VAM

10. Determine basic feasible solution to the following transportation problem using North west Corner rule.

operations research assignment problems and solutions

11. Find the initial basic feasible solution of the following transportation problem:

operations research assignment problems and solutions

Using (i) North West Corner rule

(ii) Least Cost method

(iii) Vogel’s approximation method

12. Obtain an initial basic feasible solution to the following transportation problem by north west corner method.

operations research assignment problems and solutions

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  2. Assignment problem || Production & operations management || MBS 2nd semester (part-1)

  3. Assignment problem Hungarian Method Part1

  4. Lecture 9 (part 1): The Transportation and Assignment Problems

  5. Assignment Problems Hungarian Method Operation Research

  6. ASSIGNMENT PROBLEMS

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  1. Solution of assignment problems (Hungarian Method)

    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 ...

  2. Operations Research

    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 ...

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

    Step 1: Set up the cost matrix. The first step in solving the assignment problem is to set up the cost matrix, which represents the cost of assigning a task to an agent. The matrix should be square and have the same number of rows and columns as the number of tasks and agents, respectively.

  4. Assignment Problem: Meaning, Methods and Variations

    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 ...

  5. PDF UNIT 5 ASSIGNMENT PROBLEMS

    5.2 ASSIGNMENT PROBLEM AND ITS SOLUTION An assignment problem may be considered as a special type of transportation problem in which the number of sources and destinations are equal. The capacity of each source as well as the requirement of each destination is taken as 1. In the case of an assignment problem, the given matrix must necessarily

  6. PDF Unit 4: ASSIGNMENT PROBLEM

    Step 2: next to examine the matrix for the best solutions to the assignment problem and first we try with value one (1) the cells having 1 are c12, c43, c45, using this cells we try for one sequence Let us try with assigning with c15 to c12 and c42 to c45. ∞. [1] 3. 6.

  7. ES-3: Lesson 9. SOLUTION OF ASSIGNMENT PROBLEM

    The assignment problem can be solved by the following four methods: a) Complete enumeration method. b) Simplex Method. c) Transportation method. d) Hungarian method. 9.2.1 Complete enumeration method. In this method, a list of all possible assignments among the given resources and activities is prepared.

  8. Sharpen Your Skills: 25 Operations Research Problems

    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 ...

  9. Chapter 5: 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 ...

  10. PDF Operations Research I

    Operations Research I. Assignment problems. Ing. Lenka Skanderová, Ph.D. Description and definition. • Assignees are assigned to do the tasks • Asignee: • Employee, machine, vehicle, etc. The assignment problem satisfies these assumptions: 1. The number of assignees equals to the number of tasks 2. Each assignee can be assigned to do ...

  11. Operations Research Problems: Statements and Solutions

    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 ...

  12. PDF 56:171 Operations Research Final Examination Solutions

    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.

  13. Operations Research with R

    The assignment problem represents a special case of linear programming problem used for allocating resources (mostly workforce) in an optimal way; it is a highly useful tool for operation and project managers for optimizing costs. The lpSolve R package allows us to solve LP assignment problems with just very few lines of code.

  14. Operation Research calculators

    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 ...

  15. PDF OPERATIONS RESEARCH

    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 ...

  16. Exercise 10.2: Assignment problems(Hungarian Method)

    Tags : Problem Questions with Answer, Solution , 12th Business Maths and Statistics : Chapter 10 : Operations Research Study Material, Lecturing Notes, Assignment, Reference, Wiki description explanation, brief detail

  17. Exercise 10.1: Transportation Problem

    Problem Questions with Answer, Solution | Operations Research - Exercise 10.1: Transportation Problem | 12th Business Maths and Statistics : Chapter 10 : Operations Research. ... Solution of assignment problems (Hungarian Method) - Procedure, Example Solved Problem | Operations Research.

  18. Operations Reseach Problems and Solutions

    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

  19. Transportation AND Assignment Problems

    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

  20. Transportation problems and their solutions: literature review

    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 ...

  21. Assignment problems

    Unit 8: Assignment Problem - Unbalanced. When an assignment problem has more than one solution, then it is Notes (a) Multiple Optimal solution (b) The problem is unbalanced (c) Maximization problem (d) Balanced problem. 8 Unbalanced Assignment Problem. If the given matrix is not a square matrix, the assignment problem is called an unbalanced ...

  22. Operation Research

    Ecole Polytechnique Problems and exercises in Operations Research Leo Liberti1 Last update: November 29, 2006 1 Some exercises have been proposed other authors, as detailed in the text. All the solutions, however, are the author, who takes full responsibility for their accuracy (or lack thereof).

  23. On Optimum Target Assignments

    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 ...