Question

Book: Operations and Supply Chain Management Jacobs & Chase 14e

A manager is trying to decide whether to buy one machine or two. If only one is purchased and demand proves to be excessive, the second machine -can be pur­chased later. Some sales will be lost, however, because the lead time for producing this type of machine is 6 months. In addition, the cost per machine will be lower if both are purchased at the same time. The probability of low demand is estimated to be 0.20. The after-tax net present value of the benefits from purchasing the two machines together is $90,000 if demand is low and $180,000 if demand is high.

If one machine is purchased and demand is low, the net present value is $120,000. If demand is high, the man­ager has three options. Doing nothing has a net present value of $120,000; subcontracting, $160,000; and buying the second machine, $140,000.

1. Draw a decision tree for this problem.
2. How many machines should the company buy
   initially? What is the expected payoff for this
   alternative?

Answer 1

The decision tree is as follows:

From decision node 1, draw two decision branches “purchase 1 machine” and “Purchase 2 machine”.

From Event node 2 of “purchase 1 machine” decision, draw two event branches – Low demand (0.2) and High Demand (0.8).

After event node of “Purchase 2 machine” decision draw two evenet branches with Low and High demand

From decision node 5, draw three decision branches – do nothing, subcontract, purchase 2nd machine

EMV (all EMV’s are in $1000) is calculated by backward process.

EMV of decision node 5 = max (Payoff of three decisions) = max (120, 160, 140) = $160

EMV of event node 2 = (0.2 x $120) + (0.8 x $160) =$152

EMV of event node 3 = (0.2 x $90) + (0.8 x $180) =$162

EMV of decision node 1 = max (EMV of two decisions) = max (152, 162) = $160

The maximum EMV is for decision of purchasing two machines initially.

Optimal Decision is:

Decision- to purchase 2 machines initially

Expected payoff = $160,000