Numericals on Prohibited Assignment Problem

(Prohibited Assignment)

1.         There are 5 contractors and 4 projects. The objective is to find out which project is to be given to which contractor so that total cost is minimum. Also project 3 is not support to be given to contractor D. The following matrix shows the bids (1000’s). Which contractor remains idle ?

(Ans :  1 ® A, 2 ® E, 3 ® C, 4 ® D, Dummy ®B; Total Cost = 18 + 24 + 30 + 26 + 0 = 98; Total optimum Cost = Rs. 98000; Contractor B is assigned to dummy project, therefore B remains idle.)

2.         The following information is available regarding four different jobs to be performed and about the clerks capable of performing the jobs. Cost of each assignment is given in the table.

Clerk II cannot be assigned to job A and clerk III cannot be assigned to job B. You are required to find out the optimal assignment schedule and the total minimum cost of performing the jobs by using Hungarian method.

(Ans :  I ® C, II ® B, III ® A, IV ® D; Total Cost = 5 + 8 + 3 + 2 = 18; Optimal
Cost = Rs. 1800)

3.         A manager wants to assign 4 different jobs to 4 assistants. From his experience he knows that two assistants are not efficient enough to de two specific jobs. This is indicated by a x in the cost matrix. Determine the optimal assignment plan from the following matrix, which gives cost (in hundred rupees) of employing assistants on different jobs.

  (Ans :  A₁ ® 2, A₂ ® 4, A₃ ® 1, A₄ ® 3; Total Cost = 3 + 2 + 5 + 5 = 15 hundred    rupees)

This example also illustrates the possibilities of alternate optimal assignments for the same total cost is hundred rupees.

These assignments are

(i)         A₁ ® 2, A₂ ® 4, A₃ ® 3, A₄ ® 1

(ii)        A₁ ® 2, A₂ ® 3, A₃ ® 1, A₄ ® 4