Question

1. The managers of the Frigid Midget Widget (FMW) Company, makers of small frozen widgets, have listed the tasks that must be completed to assemble one midget frigid widget (see following table). The managers must decide how large a crew to assign to each task; the size of the crew will determine the duration of the task (generally, there is an inverse relationship between crew size and job duration). Each job can be assigned a crew of minimum size, normal size, or maximum size; no other choices are possible for technological reasons. In addition, union regulations require that an assigned crew cannot be changed for the duration of the task (e.g., they cannot assign a normal size crew for the first two days of a task and then increase the crew size for the remaining duration of the task). Task durations are merely equal to the total number of worker-days divided by the crew size assigned to the task. For example, if a normal crew is assigned to task A, then that task will require eight days to complete. The FMW Company has a contract to produce one frigid midget widget every twenty-four days. Assuming that all workers can perform all tasks, determine how the production tasks should be scheduled in order to minimize the workforce needed (hiring and firing costs are very high in this industry).

   Predecessor Total Worker Days Minimum Normal Maximum Task (1,1) Start A 32 48 B 40 Start Start A A D B,C E,F 12 30 54 F G End 24

Answer 1

Task	Predecessor	Total Worker Days	Crew			Duration (Worker Days/Crew)			Using Formula (TE=(To+4Tm+Tp)/6)	Duration	Manpower Required	Revised Duration	Crew Required	Nature
			Minimum	Normal	Maximum	Minimum (Optimistic)	Normal (Most Likely)	Maximum (Passimistic)
Start
A	Start	32	2	4	8	16	8	4	9	8	4	4	8	Critical
B	Start	48	4	6	8	12	8	6	8	8	6	8	6
C	A	40	4	5	8	10	8	5	8	8	5	5	8	Critical
D	A	12	2	3	4	6	4	3	4	4	3	4	3
E	D	30	3	5	6	10	6	5	7	6	5	6	5
F	B,C	54	3	6	9	18	9	6	10	9	6	9	6	Critical
G	E,F	24	3	4	6	8	6	4	6	6	4	6	4	Critical
End	G
Notes
Since Can be done only from Minimum or Normal or Maximum so if Duration is not from above same shall be adjusted among Three options
Critical Path Shall be A-C-F-G due to High Duration
	A-D-E-G	24
	A-C-F-G	31
	B-F-G	23
Since Project needs to be done with in 24 Days crashed duration to 24 Days by reducing duration of A and C by 4 and 3 Days Respectively
Revised Duration
	A-D-E-G	20
	A-C-F-G	24
	B-F-G	23
Since Critical Path Can not be postponed Max number of Crew required 8Mem and B needs be started with max 1Day Delay
Resource Aloocation as follows Max Crew Required 14Mem
Crew		4th		8th	9th	11th	12th	17th	18th	24th
1	A		C			F				G
2
3
4
5										Idle
6
7						Idle		E
8
9	B				D
10
11
12					Idle
13
14