Question

Consider a project having the following activities, time, and cost:

                                                  Normal      Normal      Crash         Crash         Maximum

                        Immediate         Time        Cost         Time         Cost             Time

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

            a               none                  4            3,000            2            5,000               2

            b               a                        5            5,000            3            8,000               2

            c               a                        4            7,000            4            7,000               0

            d               b                       4            6,000            2            8,000               2

            e               c,d                     8            4,000            6            8,000               2

            f               c                        3            4,000            2            9,000               1

            g               e,f                     4            2,000            2            7,000               2

Assume partial crashing (not all maximum crashing time has to be used) is available.

1. Draw the network diagram. How long does project take using normal time?
2. Which activities should be crashed to reduce the completion time of the project by two weeks? How much is the additional cost? Show all work.

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	2	3,000	5,000	2	$1,000
b	5	3	5,000	8,000	2	$1,500
c	4	4	7,000	7,000	0	-
d	4	2	6,000	8,000	2	$1,000
e	8	6	4,000	8,000	2	$2,000
f	3	2	4,000	9,000	1	$5,000
g	4	2	2,000	7,000	2	$2,500

network diagram

Normal cost is the sun at normal times=$31,000

PATH	normal duration
abdeg	25
aceg	20
acfg	15
Cost	$31,000

	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 A by 2 periods
abdeg	25	23
aceg	20	18
acfg	15	13
Cost	$31,000	$2,000

additional cost= $2000