Assignment problem, Hungarian Method of Solution, Maximization Problems ,Unbalance Assignment problem, Multiple optimum Solution, Prohibited or Restricted Assignments

 

ASSIGNMENT PROBLEM

 

Introduction:

Assignment is a typical optimization technique practically useful in a situation where a certain number of tasks are required to be assigned to an equal number of facilities, on a one to one basis, so that the resultant effectiveness is optimized. eg. Jobs to be assigned to machines or workers, salesmen to the sales territories, vehicles to routes etc.

Note: Assignment problem is a case of transportation problems where the number of sources is equal to the number of destinations (i.e. m = n or number of rows = number of columns) and the supply and demand figures for each of the sources and destinations is one.

An Assignment Table or Matrix used in the Hungarian method consists of n rows (for say 1, 2, 3, 4 etc) and n columns (for machines A, B, C, D etc.) and its elements indicate the effectiveness (say time required for each machine to perform each of these four jobs) as -

Machines

Jobs

A

B

C

D

1

14

12

15

15

2

21

18

18

22

3

14

17

12

14

4

6

5

3

6

 

PDF for 

Hungarian Method of Solution 

https://drive.google.com/file/d/1xtnEHAGnH_cSczVSuO6Z1nj_u-zi5qX_/view?usp=sharing

Maximization Problems

https://drive.google.com/file/d/1VtXniBexQSqt2jXL8K30_ty0-ECw2P_M/view?usp=sharing

Multiple optimum Solution

https://drive.google.com/file/d/12OsKqgmOGMmqro5Oq2Pe4eufzdzZ0jUq/view?usp=sharing


Unbalance Assignment problem

https://drive.google.com/file/d/1t0-o-_8O8VvJDHBLjR8tzrV3fJNz0eSX/view?usp=sharing

Prohibited or Restricted Assignments

https://drive.google.com/file/d/14ihP5G1UwKNAOLrm5E_0Ei4yeoalHpny/view?usp=sharing

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