Question

QUESTION 5     [10

A department has five employees and five jobs have been received which must be assigned to the employees for completion. The time (in hours) each person will take to complete each job is given in the table below. Assign the jobs so as to minimize the total number of man-hours required to complete the jobs. Identify the optimal assignments and compute the total minimum time required to complete

all jobs.                                                                                                                                  

	Sujay	Jane	Alex	Mary	Eric
Job 1	20	15	25	25	29
Job 2	13	19	30	13	19
Job 3	20	17	14	12	15
Job 4	14	20	20	16	24
Job 5	14	16	19	11	22

Answer 1

Optimal Assignment is

Job 1- Jane (15)

Job 2-Eric (19)

Job 3-Alex (14)

Job 4- Sujay (14)

Job 5-Mary (11)

Total Minimum time required is 15+19+14+14+11=73

Steps are as follows

Row Reduction

Reduce each rows by the minimum corresponding row element

Column Reduction

Reduce each columns by the minimum corresponding column element

Check for Optimal solution

Cross all the zeros using minimum number of vertical lines or horizontal lines.

Here the number of minimum line is not equal to the number of rows or columns,ie allocation is not optimum

Adjustment for Optimal Solution

So,Find out the minimum element out of the non striked elements and add that element to the intersection of two lines,subtract to the non striked elements and keep the other elements as such.

Again check for the optimal solution

Here number of minimum lines=number of rows or columns=5

So,Allocation is done to the row with only one zero. Once the row allocation are completed,do with column allocation.The final solution is as follows.

Optimal Assignment is

Job 1- Jane (15)

Job 2-Eric (19)

Job 3-Alex (14)

Job 4- Sujay (14)

Job 5-Mary (11)

Total Minimum time required is 15+19+14+14+11=73