Question

The relevant project data are given as follows.

Activity	Predecessor(s)	Normal time (weeks)	Crash time	Normal cost	Crash cost	Possible number of weeks to crash	Cost/week to expedite
A	--	7	6	$7,000	$8,000
B	A	2	1	5,000	7,000
C	A	4	3	9,000	10,200
D	B,C	5	4	3,000	4,500
E	D	2	1	2,000	3,000
F	D	4	2	4,000	7,000
G	E,F	5	4	5,000	8,000

a)    Draw the AOA (Activity-On-Arc) diagram as shown in Chapter 13's Excel Worksheets.

b) Formulate the problem of finding project completion time as a LP problem. [You would only need the first 3 columns of the table and the diagram from a) to do the job!]

c)    Reformulate the problem when crashing the project completion time of 3 weeks is required. That is, reformulate the problem when the project completion time is required to be shorted by 3 weeks. Obviously, crashing is based on shortening the project completion time by 3 weeks with the minimal additional cost. In order to formulate the problem, you need to fill in the blank columns of the table.

NEED EXCEL ANSWERS! DO NOT COPY AND PASTE THE ANSWER FROM OTHER POSTS!

Answer 1

a)

AOA diagram is following:

b)

LP model to determine the completion time of the project time is as follows:

Let Xi be the finish time of activity i,

Minimize Xg   (activity G is the final activity, so its finish time is the project completion time)

s.t.

Xa >= 7

Xb-Xa >= 2

Xc-Xa >= 4

Xd-Xb >= 5

Xd-Xc >= 5

Xe-Xd >= 2

Xf-Xd >= 4

Xg-Xe >= 5

Xg-Xf >= 5

Xi >= 0

Solution of the LP model using Excel Solver:

Create Excel model as follows:

EXCEL FORMULA:

Enter Solver Parameters:

Click Solve to generate the solution:

Click Solve

Minimum project completion time = 25 weeks

c)

Draw the table listing Max crash time and Crash cost per week

Max Crash time = Normal time - Crash time

Crash cost per week = (Crash Cost - Normal Cost) / Max Crash time

Activity	Predecessor	Normal Time	Crash Time	Normal Cost	Crash Cost	Max Crash Time	Crash cost per week
A	-	7	6	7,000	8,000	1	1,000
B	A	2	1	5,000	7,000	1	2,000
C	A	4	3	9,000	10,200	1	1,200
D	B,C	5	4	3,000	4,500	1	1,500
E	D	2	1	2,000	3,000	1	1,000
F	D	4	2	4,000	7,000	2	1,500
G	E,F	5	4	5,000	8,000	1	3,000

After shortening the project completion time by 3 weeks, project completion time = 25-3 = 22 weeks

----------------------

Revised LP model to shorten the project by 3 weeks is following:

Let Xi be the finish time of activity i,

and, Yi be the time by which, activity i must be crashed to shorten the project

Minimize 1000Ya+2000Yb+1200Yc+1500Yd+1000Ye+1500Yf+3000Yg

s.t.

Xa+Ya >= 7

Xb-Xa+Yb >= 2

Xc-Xa+Yc >= 4

Xd-Xb+Yc >= 5

Xd-Xc+Yd >= 5

Xe-Xd+Ye >= 2

Xf-Xd+Yf >= 4

Xg-Xe+Yg >= 5

Xg-Xf+Yg >= 5

Ya <= 1

Yb <= 1

Yc <= 1

Yd <= 1

Ye <= 1

Yf <= 2

Yg <= 1

Xg = 22

Xi, Yi >= 0

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Solution of the LP model is as follows:

Total crash cost = $ 3,700