Exercise 1.1 Arthrodax Company has been approached by Ranger Sound with a rush order offer to purchase 100 units of a customized version of Arthrodax s SoundScreamer audio mixer at $5,000 per unit, and Arthrodax needs to decide how to respond. The electronic modifications of the standard SoundScreamer needed for this customized version are straightforward, but there will be a fixed cost of $100,000 to design the modifications and set up for assembly of the customized SoundScreamers, regardless of the number of units produced. It will cost $2,000 per unit to manufacture the circuit boards for the units. Since Arthrodax has some short term spare manufacturing capacity, the Ranger offer is potentially attractive. However, the circuit boards for the customized units will not fit into the standard SoundScreamer case, and Arthrodax must decide what to do about acquiring cases for the customized units as it decides whether to accept Ranger’s purchase offer. An appropriate case can be purchased at $500 per case, but Arthrodax could instead purchase an injection molder to make the cases. It will cost $20,000 to purchase the molder, and there is a 0.6 probability that it will be possible to successfully make the cases using the molder. If the molder does not work, then the purchase price for the molder will be totally lost and Arthrodax must still purchase the cases at $500 per case. If the molder works, then it will cost $60 per case to make the cases using the molder. Regardless of which case is used, the cost of assembling the SoundScreamer circuit boards into the case is $20 per unit. Unfortunately, there is no way to test the molder without purchasing it. Assume that there is no other use for the molder except to make the cases for the Ranger order.

1. Draw a decision tree for Arthrodax s decision about whether to accept the Ranger offer and how to acquire the cases for the customized SoundScreamers.
2. Using expected net profit as the decision criterion, determine the preferred course of action for Arthrodax.

Exercise 1.2 This is a continuation of Exercise 1.1. Assume that all information given in that exercise is still valid, except as discussed in this exercise. Ranger now tells Arthrodax that there is uncertainty about the number of customized SoundScreamers that will be needed. Specifically, there is a 0.35 probability that it will need 100 units, and a 0.65 probability that it will need 50 units. If Arthrodax will agree now to produce either number of units, then Ranger will pay $6,000 per unit if it ultimately orders 50 units, and will pay $5,000 per unit if it ultimately orders 100 units. The timing is such on this rush order that Arthrodax will have to make a decision about purchasing the injection molder before it knows how many units Ranger will take. However, Arthrodax will only need to purchase or manufacture the number of circuit boards and cases needed for the final order of either 50 or 100 units.

1. Draw a decision tree for Arthrodax s decision about whether to accept the Ranger offer and how to acquire the cases for the customized SoundScreamers. Note that this is a situation with dependent uncertainties, as discussed in Section 10.3.
2. Using expected net profit as the decision criterion, determine the preferred course of action for Arthrodax.

Exercise 1.3 This is a continuation of Exercise 1.2. Assume that all information given in that exercise is still valid, except as discussed in this exercise. Assume now that Arthrodax could delay the decision about purchasing the injection molder until after it knows how many units Ranger will take.

1. Draw a decision tree for Arthrodax s decision about whether to accept the Ranger offer and how to acquire the cases for the customized SoundScreamers. Note that this is a situation with sequential decisions, as discussed in Section 10.4.
2. Using expected net profit as the decision criterion, determine the preferred course of action for Arthrodax.

Exercise 1.4 Aba Manufacturing has contracted to provide Zyz Electronics with printed circuit ( PC ) boards under the following terms: (1) 100,000 PC boards will be delivered to Zyz in one month, and (2) Zyz has an option to take delivery of an additional 100,000 boards in three months by giving Aba 30 days notice. Zyz will pay $5.00 for each board that it purchases. Aba manufactures the PC boards using a batch process, and manufacturing costs are as follows: (1) there is a fixed setup cost of $250,000 for any manufacturing batch run, regardless of the size of the run, and (2) there is a marginal manufacturing cost of $2.00 per board regardless of the size of the batch run. Aba must decide whether to manufacture all 200,000 PC boards now or whether to only manufacture 100,000 now and manufacture the other 100,000 boards only if Zyz exercises its option to buy those boards. If Aba manufactures 200,000 now and Zyz does not exercise its option, then the manufacturing cost of the extra 100,000 boards will be totally lost. Aba believes there is a 50% chance Zyz will exercise its option to buy the additional 100,000 PC boards.

1. Explain why it might potentially be more profitable to manufacture all 200,000 boards now.
2. Draw a decision tree for the decision that Aba faces.
3. Determine the preferred course of action for Aba assuming it uses expected profit as its decision criterion.

Exercise 1.5 Kezo Systems has agreed to supply 500,000 PC FAX systems to Tarja Stores in 90 days at a fixed price. A key component in the FAX systems is a programmable array logic integrated circuit chip ( PAL chip ), one of which is required in each FAX system. Kezo has bought these chips in the past from an American chip manufacturer AM Chips. However, Kezo has been approached by a Korean manufacturer, KEC Electronics, which is offering a lower price on the chips. This offer is open for only 10 days, and Kezo must decide whether to buy some or all of the PAL chips from KEC. Any chips that Kezo does not buy from KEC will be bought from AM. AM Chips will sell PAL chips to Kezo for $3.00 per chip in any quantity. KEC will accept orders only in multiples of 250,000 PAL chips, and is offering to sell the chips for $2.00 per chip for 250,000 chips, and for $1.50 per chip in quantities of 500,000 or more chips. However, the situation is complicated by a dumping charge that has been filed by AM Chips against KEC. If this charge is upheld by the U. S. government, then the KEC chips will be subject to an antidumping tax. This case will not be resolved until after the point in time when Kezo must make the purchase decision. If Kezo buys the KEC chips, these will not be shipped until after the antidumping tax would go into effect and the chips would be subject to the tax. Under the terms offered by KEC, Kezo would have to pay any antidumping tax that is imposed. Kezo believes there is a 60% chance the antidumping tax will be imposed. If it is imposed, then it is equally likely that the tax will be 50%, 100%, or 200% of the sale price for each PAL chip.

1. Draw a decision tree for this decision.
2. Using expected value as the decision criterion, determine Kezo s preferred ordering alternative for the PAL chips.

Exercise 1.6 Intermodular Semiconductor Systems case. The Special Products Division of Intermodular Semiconductor Systems has received a Request for Quotation from Allied Intercontinental Corporation for 100 deep sea semiconductor electrotransponders, a specialized instrument used in testing undersea engineered structures. While Intermodular Semiconductor Systems has never produced deep sea electrotransponders, they have manufactured subsurface towed transponders, and it is clear that they could make an electrotransponder that meets Allied’s specifications. However, the production cost is uncertain due to their lack of experience with this particular type of transponder. Furthermore, Allied has also requested a quotation from the Undersea Systems Division of General Electrodevices. Intermodular Semiconductor Systems and General Electrodevices are the only companies capable of producing the electrotransponders within the time frame required to meet the construction schedule for Allied s new undersea habitat project. Mack Reynolds, the Manager of the Special Products Division, must decide whether to bid or not, and if Intermodular Semiconductor Systems does submit a bid, what the quoted price should be. He has assembled a project team consisting of Elizabeth Iron from manufacturing and John Traveler from marketing to assist with the analysis. Daniel A. Analyst, a consulting decision analyst, has also been called in to assist with the analysis.

Analyst: For this preliminary analysis, we have agreed to consider only a small number of different possible bids, production costs, and General Electrodevices bids.

Reynolds: That s correct. We will look at possible per-unit bids of $3,000, $5,000, and $7,000. We will look at possible production costs of $2,000, $4,000, and $6,000 per unit, and possible per-unit bids by General Electrodevices of $4,000, $6,000, and $8,000.

Iron: There is quite a bit of uncertainty about the cost of producing the electrotransponders. I’d say there is a 50% chance we can produce them in a volume of 100 units at $4,000 per unit. However, that still leaves a 50% chance that they will either be $2,000 or $6,000 per unit.

Analyst: Is one of these more likely than the other?

Iron: No. It s equally likely to be either $2,000 or $6,000. We don t have much experience with deep sea transponders. Our experience with subsurface towed transponders is relevant, but it may take some effort to make units that hold up to the pressure down deep. I’m sure we can do it, but it may be expensive.

Analyst: Could you do some type of cost-plus contract?

Reynolds: No way! This isn t the defense business. Once we commit, we have to produce at a fixed price. Allied would take us to court otherwise. They’re tough cookies, but they pay their bills on time.

Iron: I want to emphasize that there is no problem making the electrotransponders and meeting Allied s schedule. The real issue is what type of material we have to use to take the pressure. We may be able to use molyaluminum like we do in the subsurface towed units in which case the cost will be lower. If we have to go to molyzirconium, then it will be more expensive. Most likely, we will end up using some of each, which will put the price in the middle.

Analyst: What is General Electrodevices likely to bid?

Traveler: They have more experience than we do with this sort of product. They have never made deep sea electrotransponders, but they have done a variety of other deep sea products. I spent some time with Elizabeth discussing their experience, and also reviewed what they did on a couple of recent bids. I’d say there is a 50% chance they will bid $6,000 per unit. If not, they are more likely to bid low than high there is about a 35% percent chance they will bid $4,000 per unit.

Analyst: So that means there is 15% chance they will bid $8,000.

Traveler: Yes.

Reynolds: Suppose we had a better handle on our production costs. Would that give us more of an idea what General Electrodevices would bid?

Iron: No. They use graphite-based materials to reinforce their transponders. The cost structure for that type of production doesn’t have any relationship
to our system using moly alloys.

1. Draw a decision tree for the decision that Reynolds must make.
2. Determine the expected values for each of the alternatives, and specify which alternative Reynolds should select if he uses expected value as a decision criterion

Attribution

By Craig W. Kirkwood, Chapter 1 of Decision Tree Primer,  January 11, 2013, licensed under a Creative Commons Attribution License CC BY-NC-SA 4.0.