Chapter 15, Problem 7P

a)

Summary Introduction

To solve: The given information by using the assignment method.

Introduction: The assignment method is one of the methods available in the process of optimization. Here, the jobs are assigned to every available resource.

Answer to Problem 7P

The problem has been solved by using the assignment method.

Explanation of Solution

Given information:

Squad	Case
	A	B	C	D	E
1	14	7	3	7	27
2	20	7	12	6	30
3	10	3	4	5	21
4	8	12	7	12	21
5	13	25	24	26	8

Assign cases to respective squads:

Row minimum:

Squad	Case					Row minimum
	A	B	C	D	E
1	14	7	3	7	27	3
2	20	7	12	6	30	6
3	10	3	4	5	21	3
4	8	12	7	12	21	7
5	13	25	24	26	8	8

Table after the row subtraction is given below:

The row minimum value mentioned in the above table should be subtracted from each value of the row.

Squad	Case
	A	B	C	D	E
1	11	4	0	4	24
2	14	1	6	0	24
3	7	0	1	2	18
4	1	5	0	5	14
5	5	17	16	18	0

Column minimum:

Squad	Case
	A	B	C	D	E
1	11	4	0	4	24
2	14	1	6	0	24
3	7	0	1	2	18
4	1	5	0	5	14
5	5	17	16	18	0
Column minimum	1	0	0	0	0

Table after the column subtraction is given below:

The column minimum value mentioned in the above table should be subtracted from each value of the column.

Squad	Case
	A	B	C	D	E
1	10	4	0	4	24
2	13	1	6	0	24
3	6	0	1	2	18
4	0	5	0	5	14
5	4	17	16	18	0

Assigning squads to the cases:

Step 1: The first row must be checked for the zero. As there is only one zero in the first row, it must be marked and the entire column should be striked out.

Step 2: As only one zero is available in the second row, it must be marked and the entire column should be striked out.

Step 3: As only one zero is available in the third row, it must be marked and the entire column should be striked out.

Step 4: As only one zero is available in the fourth row, it must be marked and the entire column should be striked out.

Step 5: As only one zero is available in the fourth row, it must be marked and the entire column should be striked out.

Step 5: All the zeroes in the table have been striked out. The marked zeroes help to assign the cases to the squads.

Calculate the total person-days that are projected by using the assignment method:

The value has been taken in the given information where, the zeroes have been marked in the final answer.

Squad	Case	Value
1	C	3
2	D	6
3	B	3
4	A	8
5	E	8
Total		28

Conclusion

According to the table, Squad 1 should be assigned to Case C, Squad 2 should be assigned to Case D, Squad 3 should be assigned to Case B, Squad 4 should be assigned to Case A, and Squad 5 should be assigned to Case E. The total person days are 28 days.

b)

Summary Introduction

To solve: The given information by using assignment method.

Introduction: The assignment method is one of the methods available in the process of optimization. Here, the jobs are assigned to every available resource.

Answer to Problem 7P

The problem has been solved by using the assignment method.

Explanation of Solution

Given information:

Squad	Case
	A	B	C	D	E
1	14	7	3	7	27
2	20	7	12	6	30
3	10	3	4	5	21
4	8	12	7	12	21
5	13	25	24	26	8

It is given that the squad 5 cannot work on Case 5 because of the conflict.

Modified given information:

It is given that the squad 5 cannot work on Case 5 because of the conflict. Thus, the value should be modified from 8 to any other higher values. It is taken as 50 here.

Squad	Case
	A	B	C	D	E
1	14	7	3	7	27
2	20	7	12	6	30
3	10	3	4	5	21
4	8	12	7	12	21
5	13	25	24	26	50

Assign cases to respective squads:

Row minimum:

Squad	Case					Row minimum
	A	B	C	D	E
1	14	7	3	7	27	3
2	20	7	12	6	30	6
3	10	3	4	5	21	3
4	8	12	7	12	21	7
5	13	25	24	26	50	13

Table after the row subtraction is given below:

The row minimum value mentioned in the above table should be subtracted from each value of the row.

Squad	Case
	A	B	C	D	E
1	11	4	0	4	24
2	14	1	6	0	24
3	7	0	1	2	18
4	1	5	0	5	14
5	0	12	11	13	37

Column minimum:

Squad	Case
	A	B	C	D	E
1	11	4	0	4	24
2	14	1	6	0	24
3	7	0	1	2	18
4	1	5	0	5	14
5	0	12	11	13	37
Column minimum	0	0	0	0	14

Table after the column subtraction is given below:

The column minimum value mentioned in the above table should be subtracted from each value of the column.

Squad	Case
	A	B	C	D	E
1	11	4	0	4	10
2	14	1	6	0	10
3	7	0	1	2	4
4	1	5	0	5	0
5	0	12	11	13	23

Assigning squads to the cases:

Step 1: The first row must be checked for the zero. As there is only one zero in the first row, it must be marked and the entire column should be striked out.

Step 2: As only one zero is available in the second row, it must be marked, and the entire column should be striked out.

Step 3: As only one zero is available in the third row, it must be marked, and the entire column should be striked out.

Step 4: As only one zero is available in the fourth row, it must be marked, and the entire column should be striked out.

Step 5: As only one zero is available in the fifth row, it must be marked, and the entire column should be striked out.

Step 5: All the zeroes in the table have been strikedout. The marked zeroes help to assign the cases to the squads.

Calculate the total person days that are projected by using the assignment method:

The value has been taken in the given information where, the zeroes have been marked in the final answer.

Squad	Case	Value
1	C	3
2	D	6
3	B	3
4	E	21
5	A	13
Total		46

Conclusion

According to the table, Squad 1should be assigned to Case C, Squad 2 should be assigned to Case D, Squad 3 should be assigned to Case B, Squad 4 should be assigned to Case E, and Squad 5 should be assigned to Case A. The total person days are 46 days.