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Question 3 The Operations Manager of a construction company wants to assign four contractors to four...

Question 3

The Operations Manager of a construction company wants to assign four contractors to four jobs in such a way as to minimize the time taken to complete four buildings of a special kind and size. Based on experience, the times taken (in months) for each contractor to complete each job are given in the table below.

.

Jobs Contractor
1 2 3 4
1 15 15 16 14
2 20 18 16 19
3 24 26 20 23
4 30 35 38 25

b. Write an LP formulation that could be used to solve this problem with the relevant LP software packages. [13 marks]

Solutions

Expert Solution

Let assune Xij reprsent the Jobs assignment to the contractor, where i = 1, 2, 3, 4 and j= 1,2,3,4.

Decision Variable - To find the value of Xij to minimize the time to complete the task.

Objective = Min. Z= 15X11+15X12+16X13+14X14+20X21+18X22+16X23+19X24+ 24X31+26X32+20X33+23X34+ 30X41+35X42+38X43+25X44

Constraints -

X11+X12+X13+X14=1

X21+X22+X23+X24=1

X31+X32+X33+X34=1

X41+X42+X43+X44=1

X11+X21+X31+X41=1

X12+X22+X32+X42=1

X13+X23+X33+X43=1

X14+X24+X34+X44=1

Xij = Binary (0 or 1)

Below is the screenshotof the LP table in excel -

Below is the screenshot of the formula applied -

Below is the screenshot of the solver -

Below is the screenshot of the result -

keosha answered 1 year ago
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