Question

Consider a project having the following six activities:

                                                     Immediate                                                  Max        Crash cost

            Activity                           Predecessors           Time (weeks)             Crash*    per week

                  A                                none                                    6                          6                N/A

                  B                                none                                    5                          2               $500

                  C                                A                                       3                          2             $1000

                  D                                A, B                                    4                          2             $2000

                  E                                 C, D                                    5                          2             $1250

                  F                                D                                       6                          2             $1000

                                                                                                *Shortest possible time for the task

1. Draw the project network and list the earliest start (ES), earliest finish (EF), latest start (LS) and latest finish (LF) for each task

2. List the tasks on the critical path

3. What is the expected project duration in weeks?

4. What is the slack for each activity? A:___ B:___ C:___ D:___ E:___ F:____  

5. The project needs to be crashed by 2 weeks. What are the activities crashed to achieve the 2 week crash at lowest cost?

List the new duration of each task and any associated crash costs Activity Duration Crash Cost A B C D E F

6. Draw the NEW project network and list the earliest start (ES), earliest finish (EF), latest start (LS) and latest finish (LF) for each task

7. List the tasks on the critical path

Answer 1

CPM

ACTIVITY	DURATION	ES	EF	LS	LF	SLACK
A	6	0	6	0	6	0
B	5	0	5	1	6	1
C	3	6	9	8	11	2
D	4	6	10	6	10	0
E	5	10	15	11	16	1
F	6	10	16	10	16	0

FORWARD PASS: ES = MAXIMUM EF OF ALL PREDECESSOR ACTIVITIES; 0 IF NO PREDECESSORS ARE PRESENT. EF = ES + DURATION OF THE ACTIVITY.

BACKWARD PASS: LF = MINIMUM LS OF ALL SUCCESSOR ACTIVITIES; COMPLETION TIME OF THE PROJECT IF NO SUCCESSORS ARE PRESENT. LS = LF - DURATION OF THE ACTIVITY.

SLACK = LF - EF, OR, LS - ES

CRITICAL PATH = PATH WITH THE LONGEST COMBINED DURATION VALUE AND 0 SLACK.

CRITICAL PATH = A-D-F

DURATION OF PROJECT = 16

2. CRASHING

ACTIVITY	NORMAL TIME	CRASH TIME	COST / PERIOD	TIMES CRASHED	# CRASH	CRASH COST
A	6	6	0
B	5	2	500
C	3	2	1000
D	4	2	2000	1	2ND	2000
E	5	2	1250
F	6	2	1000	1	1ST	1000
TOTAL						3000

3. NEW CRITICAL PATH

ACTIVITY	DURATION	ES	EF	LS	LF	SLACK
A	6	0	6	0	6	0
B	5	0	5	1	6	1
C	3	6	9	6	9	0
D	3	6	9	6	9	0
E	5	9	14	9	14	0
F	5	9	14	9	14	0

ALL CRITICAL PATHS:

ACE = 14

ADE = 14

ADF = 14