Question

Q4. CPM Consider the following list of activities and predecessors. Activity ProcessorsDuration (days) Build foundation Build walls&ceilin Build roof Complete electrical wirin Put in windows Put on sidin Paint house C,F a)Draw the network diagram. Write down the LP to determine the completion time. b)Suppose that by hiring additional workers, the duration of each activity can be reduced. The costs per day of reducing the duration of the activities are given in the following table. Write down the LP to complete the project within 20 days with minimum cost. Max Possible Reduction Cost per Day of Reducingin Duration of Activity Activity Duration of Activity Foundation Walls&ceilin Roof Electrical wirin Windows Sidin Paint S20 S30

Answer 1

(a)

5 0 E4 8 5

Let Tj be the start time for an activity j

Min Duration

s.t.

TB - TA >= 5
TD - TB >= 8
TC - TB >= 8
TE - TB >= 8
TF - TE >= 4
TG - TF >= 6
TG - TC >= 10

TD + 5 <= Duration
TG + 3 <= Duration

Tj >= 0

(b)

Let Cj be the days crash for an activity-j

Min Z = total crash cost = 30 CA + 15 CB + 20 CC + 40 CD + 20 CE + 30 CF + 40 CG

Subject to,

TB - TA + CA >= 5
TD - TB + CB >= 8
TC - TB + CB >= 8
TE - TB + CB >= 8
TF - TE + CE >= 4
TG - TF + CF >= 6
TG - TC + CC >= 10

CA <= 2, CB <= 3, CC <= 1, CD <= 2, CE <= 2, CF <= 3, CG <= 1

TD + 5 - CD <= 20
TG + 3 - CG <= 20

Tj, Cj >= 0