Solving a PERT problem with crashing - Ops. Management Help

Gadget Toy Company's head office was in Kitchener, Ontario, where it also operated a manufacturing plant and distribution center. Whenever possible, Gadget preferred to manufacture its products in-house.

Joe Huffman, a new project manager at Gadget Toy Company (Gadget), had just submitted a proposal for finding to the new product review committee. He recommended that Gadget introduce, through its retail distribution network. a new children's toy based on a popular cartoon character. Joe felt that if he could get the product out by Christmas, Gadget could take advantage of what he felt would be strong market demand. However, due to the volatility of the market for these types of toys, Joe could not be certain that the product would have the same level of market acceptance the following year. It was now May I u,2005, and Joe knew he would have to manage the timing of the project carefully to meet the delivery date of September 2114, just 18 weeks away.

Joe was confident of the approval of the project and expected feedback from the committee by the end of the week, at which time he would begin coordinating the launch of the project. At this point Joe had established a preliminary list of information about most activities in the project as shown in Exhibit 1. Based on his schedule, Joe felt he could start work on some activities immediately, such as finalizing the product design and placing an order for the equipment. However, many of the activities had to be performed sequentially. For example, he could not train the workers until the equipment was installed and the tools for the machine were built. Similarly, he could not order the raw material until the engineering work was complete and the advertising plan was completed, since the advertising plan would influence color selection.

Based on the information he collected in Exhibit 1, he has constructed the project schedule with task normal durations in the file Gadget Toy.mpp. Please help Joe to answer the following questions.

Questions:

1. According to the task normal duration information collected by Joe Huffman in Exhibit 1, what task should Joe watch closely In completing his project. i.e., which of the following is a critical task?

(a) Order new equipment

(b) Install equipment

(c) Train waters

(d) Order raw material

2. In order to meet the deadline of September 2nd, what is the minimum required crash cost according to Exhibit 1?

3. The minimum crash cost you find in question 2 is too high for Joe. So he looks closely at the logical dependencies in Exhibit 1, and thinks that he can change some of the precedence relationships as well as apply fast tracking techniques to shorten the project duration. He decides to let the task 'Order raw material' directly follow "Finalize engineering' and 'Finalize package and art work', but not follow 'Build dies/tools." In addition, he fast tracks the task 'Finalize production process' and let it start one week after the task 'Train workers' starts. Once you finish revising the precedence relationships for Joe, recalculate the minimum required crash cost that Joe needs to incur to meet the September 2nd deadline.

4. Joe just learns that the equipment delivery (task C) 1.1All likely take two weeks longer than he initially expects (i.e. task C normal duration becomes 10 weeks end them are still two weeks for possible crashing). What is the minimum crash cost in this situation if he still includes the revised precedence relationship and fast tracking mentioned in question 3?

Problem 1: Using The Management Scientist we get the following results:

This means that (A) Order new equipment, (B) Install new equipment, and (C) Order Raw material are critical tasks

• (G) Finalize production process, (L) Initialize production run, and (M) Pack and ship product are also critical tasks.

Problem 2: The projects need to be finished in 18 weeks, and without crashing mark is 23 weeks. Hence, there’s the need to crash some of the tasks. First, we have the following table with the crashing cost:

We need to crash first the critical task with the lowest cost, which means that we crash G. But the most we can get with G is 2 weeks (we need 5). So we also crash F in 1 week, and D in two weeks.

We get:

Here, we can only crash B, K, or L. Since K is cheaper, we crash K in 1 week. The results are shown below:

Finally, the project lasts 18 weeks, as needed. The cost of crashing is

\[C=2\times 2,200+1,600+2\times 2,500+2000=\$13,000\]

Problem 3: Adjusting the precedence relationships, we obtain:

We need to crash then 4 week in total:

The cheapest task is F, but there is no point in crashing F since we already allow G to start one week after F starts. Then, we crash G in two weeks, and D in two weeks:

This hits the required date. The cost is

\[C=2\times 2200+2\times 2500=\$9,400\]

Problem 4: If C gets delayed 2 weeks, we get:

We would need to crash 4 weeks. Since it would be pointless to crash F, we again crash G in two weeks, and D in two weeks. We get

We still need 2 weeks. Using the following table,

we should then crash E in 2 weeks:

We got the aimed project time. The cost is

\[C=2\times 2200+2\times 2500+2\times 3,200=\$15,800\]

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