Homework SourseAssigning Engineers A small engineering firm has 4 senior de
Assigning Engineers. A small engineering firm has 4 senior designers available to work on the firm’s 4 current projects over the next 2 weeks. The firm’s manager has developed the following table of quality scores, which show each designer’s quality on each type of project, on a scale of 100. Also shown is the estimate of the time(in hours) required for each project.
P1
P2
P3
P4
Designer 1
90
80
25
50
Designer 2
60
70
50
65
Designer 3
70
40
80
85
Designer 4
65
55
60
75
Time
70
50
85
35
a. Assume that one designed is assigned to each project. What assignment of designers to projects maximizes the sum of the quality scores assigned?
b. Suppose that each designer has 80 hours available over the next two weeks. Assuming that more than one designer can work on a project, what assignment schedule maximizes the sum of quality scores assigned?
| P1 | P2 | P3 | P4 | |
| Designer 1 | 90 | 80 | 25 | 50 |
| Designer 2 | 60 | 70 | 50 | 65 |
| Designer 3 | 70 | 40 | 80 | 85 |
| Designer 4 | 65 | 55 | 60 | 75 |
| Time | 70 | 50 | 85 | 35 |
Solution
Given Problem :
a. Assume that one designed is assigned to each project. What assignment of designers to projects maximizes the sum of the quality scores assigned?
Row Minimisation :
Column Minimisation
Optimization :
b. Suppose that each designer has 80 hours available over the next two weeks. Assuming that more than one designer can work on a project, what assignment schedule maximizes the sum of quality scores assigned?
Ans :
If each designer has 80 hrs availeble then there can be minimisation of Designers.
Total time required = 70 + 50 + 85 + 35 = 240
Total Designers = 240 / 80 = 3
Total designers = 3
3 Designers can work & complete the given task.
| P1 | P2 | P3 | P4 | |
| Designer 1 | 90 | 80 | 25 | 50 |
| Designer 2 | 60 | 70 | 50 | 65 |
| Designer 3 | 70 | 40 | 80 | 85 |
| Designer 4 | 65 | 55 | 60 | 75 |
| Time | 70 | 50 | 85 | 35 |
