Question

2. Consider a project having the following seven activities:

                                                  Normal      Normal      Crash         Crash         Maximum

                        Immediate         Time        Cost         Time         Cost             Weeks

      Activity     Predecessors     (weeks)         ($)         (weeks)         ($)         Reduced

            A              none                  4            3,000            3            6,000               1

            B              none                  3            5,000            2            7,000               1

            C              A                    9            2,000            7            4,000               2

            D              A, B                  2            3,000            2            3,000               0

            E              B                     9            4,000            6            7,000               3

            F              C, D                  8            4,000            6            9,000               2

            G              E, F                   5            2,000            3            5,000               2

(a) What is the expected project completion time?   (3pts)

(b) What is the critical path?                                      (3pts

(c) What is the most economical way and how much will it cost to reduce the completion time of the project by three weeks?     (4pts)

Answer 1

activity	required time	cost	time available for crashing= normal duration-crashed duration	cost of crashing per period= (crashing cost-normal cost)/periods available for crashing
normal duration	crashed duration	normal cost	crashing cost
a	4	3	3,000	6,000	1	$3,000
b	3	2	5,000	7,000	1	$2,000
c	9	7	2,000	4,000	2	$1,000
d	2	2	3,000	3,000	0	-
e	9	6	4,000	7,000	3	$1,000
f	8	6	4,000	9,000	2	$2,500
g	5	3	2,000	5,000	2	$1,500

PATH	normal duration
bdfg	18
adfg	19
acfg	26
beg	17

a: Expect completion time through the critical path is 26 weeks

b: critical path is A-C-F-G

c:

	Steps for crashing a project
1	select the critical path and find the process with the least cost of crashing per week
2	If there are multiple critical paths, look for processes that are common, common processes may have low effective cost as common process crashes more than 1 path at once
3	you can only crash an activity depending on the time available for crashing. If an activity is only crashed that much time, choose another activity
4	add the cost of crashing later

Crashing

PATH	normal duration	crash C by 2 periods	crash G by 1 period
bdfg	18	18	17
adfg	19	19	18
acfg	26	24	23
beg	17	17	16
Cost	$23,000	$1,000	$1,500

it will cost $2500 to crash by 3 weeks.