QUESTION 28 (20 points) Critical Path Method (CPM) with Crashing

The film The Lord of the Rings: The Return of the King, the last installment of The Lord of the Rings trilogy, was released on December 17 2003 in the U.S. with huge success. Eventually, the film won 11 Oscars for all of its nominations. The film's box office was $1.12 billion. In the film, there are long sequences where the main characters split up in different directions. And, there are big scenes where all characters reunite. Reflecting on the film making, we can hypothetically break down the entire cinematic project into the following aggregate activities:

A Plan, screenplay, finance, cast, film crew, location B Construction of movie sets C Shooting sequence 1 D Shooting sequence 2

E Shooting sequence 3 F Big scene sequences G Postproduction & finalization before release

We have the following hypothetical data on time in months and costs in millions of dollars:

ID	IP	T	ES	EF	LS	LF	ST	NT	NC	CT	CC	CCR
A		5.0						5.0	15.0	5.0	15.0
B	A	8.0						8.0	12.0	7.0	14.0
C	B	6.0						6.0	11.0	5.0	12.5
D	B	7.0						7.0	14.0	5.0	16.4
E	B	5.0						5.0	13.0	4.0	19.0
F	C,D,E	3.0						3.0	18.0	3.0	18.0
G	F	6.0						6.0	11.0	5.0	12.8

Note: IP = Immediate Predecessor; T = Normal Time; ES = Earliest Start; EF = Earliest Finish; LS = Latest Start; LF = Latest Finish; ST = Slack Time; NT = Normal Time; NC = Normal Cost; CT = Crash Time; CC = Crash Cost; & CCR = Crash Cost Rate = crash cost per time unit.

Copy the table to your homework and complete the following parts: (a)[2] Based on the table, draw an AON project network: circles/nodes for activities and arrows/arcs for the precedence relationships between activities. Above each node, put a number to represent the activity's normal time. (b)[2] Draw a Gantt chart in Excel to represent the project schedule with earliest times, and make a printout. Refer to OM5Exhibit 18.9(P392) and the Gantt chart in Module 03. (c)[2] By looking at the chart in part (a), find all possible paths through the network with their corresponding path times. Based on these path times, determine the critical path and its length. (d)[2] Based on part (a), draw a boxed AON project network: nodes are boxes with data. Refer to the format in OM5Exhibit 18.6(P388) for your presentation. By using the forward and backward passes together with the four time determination rules, fill your calculations for ES, EF, LS, LF, and ST in the appropriate cells. (e)[2] Based on part (d), find the critical path by going through the activities with no slack time. Compare this result with the critical path found in part (c). (f)[2] Independently fill in the columns ES, EF, LS, LF, and SLK of the table. If you have difficulties, refer to part (d). Find the activity with the most slack time. Based on the table alone, find the critical path. Compare this result with the critical path found in part (c).

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(g)[2] Use appropriate data to compute crash cost per time unit and fill in the CCR column. Cross out any CCR cells where the corresponding activities cannot be crashed. (h)[2] Find the total normal cost of the film. Find the normal cost on the original critical path. Compute the cost proportion of the critical path in the film's budget.

The following considerations are for crashing the cinematic project month by month: (i)[1] Starting from the original critical path, the producers want to crash the cinematic project and reduce the completion time by one month. Propose the best solution to crashing. Identify the new critical path(s) if any change happens. Compute the new budget of the film. (j)[1] Following part (i), the producers consider options to crash the film by another month (a total of 2 months down from the original completion time). Propose the best solution to crashing. Identify the resulting critical path(s). Compute the new budget of the film. (k)[1] Following part (j), the producers consider options to crash the film by another month (a total of 3 months down from the original completion time). Propose the best solution to crashing. Identify the resulting critical path(s). Compute the new budget of the film. (l)[1] Following part (k), the producers want to crash the film by another month. Propose the best solution to crashing. Identify the resulting critical path(s). Compute the new budget of the film. After this, can they crash the project by one more month?