Sprocket manufacturing. The manager of this production firm is faced with a potential problem: shortages in the supply of a vital gear sprocket. He is considering the development of an in-house capability to make the sprockets, knowing that the firm needs 35,000 such sprockets each year. If the firm elects to make the sprockets internally, then it must select one of the three possible production processes. Each has different costs, as shown in Table 10.17. Adopting a manual process may lead to union problems. The manager estimates the probability of these problems as 25%, and knows that if they do occur, then the variable cost will increase by $0.50 per sprocket. Further, if the semi-automatic or fully automatic option is selected, then additional training of personnel will be required. The amount and therefore the cost of training are uncertain. For the semi-automatic process, the fixed cost of basic training will add $15,000. However, there is a 20% chance the workers will need extra training at a cost of $5,000. For the fully automatic process, the fixed cost of basic training is $16,000, but there is a 30% chance they will need advanced training that will add $10,000 to the fixed cost. The firm has the option of purchasing the sprockets from their external supplier at a cost of $2.90 per sprocket; however, the manager estimates that there is a 40% chance that this supplier will fail to develop the process in a timely manner. If he does fail, then one of the three in-house processes must be developed; however, time pressure would increase the fixed cost of each process by 50%.

Table 10:17 Cost data for sprocket manufacturing case.

Production Process	Fixed costs/Year ($)	Variable cost/Unit ($)
Manual	20000	2.5
Semi automatic	50000	1.5
Fully automatic	80000	1

a. Construct the appropriate decision tree using PrecisionTree software.

b. What is the optimal strategy, and what is the final expected total payoff?

c. If the manager were to develop an in-house facility, which production process should he select and why?