Assignment Problem

A plant manager has four subordinates and four tasks to perform. The subordinates differ in efficiency and task differ in their intrinsic difficulty. Estimates of the time subordinate would take to perform tasks are given in the following table:

Complete the following activity to allocate tasks to subordinates to minimize total time.

Solution:

Step I: Subtract the smallest element of each row from every element of that row:

Step II: Since all column minimums are zero, no need to subtract anything from columns.

Step III: Draw the minimum number of lines to cover all zeros.

Since minimum number of lines = order of matrix, optimal solution has been reached

Optimal assignment is A →`square`  B →`square`

C →IV  D →`square`

Total minimum time = `square` hours.

State whether the following is True or False :

It is not necessary to express an assignment problem into n x n matrix.

Solve the following maximal assignment problem :

Solve the following minimal assignment problem and hence find minimum time where  '- ' indicates that job cannot be assigned to the machine : 

A job production unit has four jobs A, B, C, D which can be manufactured on each of the four machines P, Q, R and S. The processing cost of each job for each machine is given in the following table:

Find the optimal assignment to minimize the total processing cost.

Fill in the blank :

When an assignment problem has more than one solution, then it is _______ optimal solution.

In a factory there are six jobs to be performed each of which should go through two machines A and B in the order A - B. The processing timing (in hours) for the jobs arc given here. You are required to determine the sequence for performing the jobs that would minimize the total elapsed time T. What is the value of T? Also find the idle time for machines · A and B.

What is the Assignment problem?