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Operations Research
Unit 6
Unit 6
Structure
Assignment Problem
6.1. 6.2. 6.3. 6.4.
Introduction Mathematical formulation of the problem Hungarian method algorithm Routing problem 6.4.1. Unbalanced A.P 6.4.2 Infeasible Assignments 6.4.3 Maximization in A.P
6.5. 6.6.
Traveling salesmen problem Summary Terminal Questions Answers to SAQs and TQs
6.1 Introduction The assignment problem is a special case of the transportation problem, where the objective is to minimize the cost or time of completing a number of jobs by a number of persons and Maximize efficiently Revenue, sales etc In other words, when the problem involves the allocation of n different facilities to n different tasks, it is often*…show more content…*

Repeat Step 3 and 4 till all zeros are either assigned or crossed. If the number of assignments made is equal to number of rows present, then it is the optimal solution otherwise proceed as follows. Step 5: Mark (P) the row which is not assigned. Look for crossed zero in that row. Mark the column containing the crossed zero. Look for assigned zero in that column. Mark the row containing assigned zero. Repeat this process till all makings are over. Step 6: Draw straight line through unmarked rows and marked column. The number of straight line drawn will be equal to number of assignments made. Step 7: Examine the uncovered elements. Select the minimum. Sikkim Manipal University 100 Operations Research Unit 6 a. Subtract it from uncovered elements. b. Add it at the point of intersection of lines. c. Leave the rest as it is. Prepare a New Table. Step 8: Repeat Steps 3 to 7 till number of allocations = Number of rows. Example 1: Find the optimum assignment so as to minimize the cost. Persons Jobs 1 2 3 4 5 A B C D E 8 4 2 6 1 0 9 5 5 4 3 8 9 2 6 4 3 1 0 3 9 5 8 9 5 Example: Consider the problem of assigning five jobs to five persons. The assignment costs are given as

Repeat Step 3 and 4 till all zeros are either assigned or crossed. If the number of assignments made is equal to number of rows present, then it is the optimal solution otherwise proceed as follows. Step 5: Mark (P) the row which is not assigned. Look for crossed zero in that row. Mark the column containing the crossed zero. Look for assigned zero in that column. Mark the row containing assigned zero. Repeat this process till all makings are over. Step 6: Draw straight line through unmarked rows and marked column. The number of straight line drawn will be equal to number of assignments made. Step 7: Examine the uncovered elements. Select the minimum. Sikkim Manipal University 100 Operations Research Unit 6 a. Subtract it from uncovered elements. b. Add it at the point of intersection of lines. c. Leave the rest as it is. Prepare a New Table. Step 8: Repeat Steps 3 to 7 till number of allocations = Number of rows. Example 1: Find the optimum assignment so as to minimize the cost. Persons Jobs 1 2 3 4 5 A B C D E 8 4 2 6 1 0 9 5 5 4 3 8 9 2 6 4 3 1 0 3 9 5 8 9 5 Example: Consider the problem of assigning five jobs to five persons. The assignment costs are given as

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