In: Operations Management
Consider the project described in the below Excel
a. Use Excel to find the critical path and the project duration using normal activity times.
b. What is the shortest duration the project can be crashed down to?
c. If you were to crash the project manually and your goal is to minimize crashing cost, which activity would you start with?
d. Find the cheapest way to crash the project to 33 weeks. What are the critical activities in the crashed network, and the cost of crashing?
Activity | Predecessor | Normal time (months) | Crashed time (months) | Normal Cost ($) | Crashed Cost ($) |
1 | -- | 8 | 5 | 700 | 1,200 |
2 | -- | 10 | 9 | 1,600 | 2,000 |
3 | -- | 9 | 7 | 900 | 1,500 |
4 | 1 | 4 | 2 | 500 | 700 |
5 | 1 | 6 | 3 | 500 | 900 |
6 | 2 | 5 | 4 | 500 | 800 |
7 | 3 | 7 | 5 | 700 | 1,000 |
8 | 3,5,6 | 15 | 12 | 1,400 | 2,000 |
9 | 3,5,6 | 12 | 10 | 1,800 | 2,300 |
10 | 4 | 18 | 14 | 1,400 | 3,200 |
11 | 7,9 | 4 | 3 | 500 | 800 |
12 | 12 | 7 | 6 | 800 | 1,400 |
Network diagram is following:
(a) Project duration is determined using Excel Solver as follows
Formulas:
E3 =C3
E4 =C4
E5 =C5
E6 =C6+D3
E7 =C7+D3
E8 =C8+D4
E9 =C9+D5
E10 =C10+D5
F10 =C10+D7
G10 =C10+D8
E11 =C11+D5
F11 =C11+D7
G11 =C11+D8
E12 =C12+D6
E13 =C13+D9
F13 =C13+D11
E14 =C14+D13
D19 =D17
Project duration = 38 weeks
Critical path is the longest path along the network
Critical path is: 2-6-9-11-12
(b) Minimum project duration is determined by crashing the project activities by maximum time.
K3 =C3-I3
K4 =C4-I4
K5 =C5-I5
K6 =C6-I6+K3
K7 =C7-I7+J3
K8 =C8-I8+J4
K9 =C9-I9+J5
K10 =C10-I10+J5
L10 =C10-I10+J7
M10 =C10-I10+J8
K11 =C11-I11+J5
L11 =C11-I11+J7
M11 =C11-I11+J8
K12 =C12-I12+J6
K13 =C13-I13+J9
L13 =C13-I13+J11
K14 =C14-I14+J13
J19 =J17
(c) The activity on critical path having the minimum crash cost slope is activity 9 with a crash cost slope of 250
(d) Cheapest way to crash the project is determined using Excel Solver as follows:
Formulas:
J19 =SUMPRODUCT(I3:I14,H3:H14) All other formulas are same as in part b
Minimum crashing cost = $ 1633.33