Decision Analysis Solutions

Managerial Decision Analysis Bus 260 Chapter 1 Homework Solutions Spring 2013

KENDALL CRAB AND LOBSTER, INC. (a) There are two main decisions that Jeff has to make. First, at noon he has three options: • Send lobsters by truck using EPD. • Pack lobsters and wait until 5 p.m. • Do not pack lobsters and send coupons. Second, if he decides to wait, the storm hits Boston, and Logan closes, then he will have to choose from: • Send lobsters through MAF. • Cancel orders and send coupons. The uncertainties involved in this problem are: • The incremental delivery cost per lobster if EPD is chosen. • The incremental delivery cost per lobster if MAF is chosen. • Whether or not the storm will hit Boston. • Whether or not Logan will close if the storm hits Boston. • The percentage of coupons that would generate incremental demand for lobster. To determine the revenues and costs in the tree, consider the following: • The unit variable contribution to earnings is $30 - $20 = $10. • With MAF, this is $10 - $13 = -$3 or $10 - $19 = -$9. • With EPD, this is $10 - $2 = $8, $10 - $3 = $7, or $10 - $4 = $6. • A coupon used by a recipient might create incremental demand. If that happens, the downstream effect on earnings will be $10 (extra contribution) $20 (coupon cost) = -$10. If the coupon does not create incremental demand, then the downstream effect on earnings is simply -$20. •

Let p be the probability that the coupon is used by a recipient and creates incremental demand, and q the probability that the coupon is used by a recipient and does not create incremental demand, then p + q = 0.70. The unit cost for a canceled lobster order is -$1 - $10p - $20q for lobsters not already packed and -$1.25 -$1.25 - $10p - $20q for lobsters lobsters already packed. packed. Since p + q = 0.70, the total cost of canceling unpacked lobsters ranges between between -$24,000 and -$45,000. The total cost of canceling packed lobsters ranges from $24,750 and -$45,750. To create a more realistic analysis of this case you may want to consider: • More detail if the orders are canceled. For instance, you may consider several uncertain scenarios for the number of coupons redeemed, ranging from 0 to 3000 or any other reasonable interval.


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Model demand uncertainty. For instance, assigning a probability distribution to the several uncertain demand scenarios: Probability Demand 0.1 2800 0.2 2900 0.5 3000 0.2 3200

To perform some sensitivity analysis, you may want to consider changing the probability that the storm would hit Boston or the probability that Logan would close if the storm hits Boston. (b) The optimal decision strategy for Jeff is to pack the lobsters and wait until 5 p.m. If the storm hits Boston and Logan Airport closes, then he should choose to transport the lobster by using MAF. The EMV for this strategy is $25,500.



1.2 (a) See decision tree above. (b) Once Monday's bid is made, Newtone's optimal strategy is to accept the bid if it is a $3,000,000 bid and reject it if the bid is for $2,000,000. If Monday's bid is rejected, then accept Tuesday's bid, regardless of the amount offered. The EMV of this strategy is $2,600,000.

1.3 (a) As shown in the table below, as p decreases James' optimal decision changes as to take Meditech's offer. A break-even analysis where we solve the equation 440p - 200(1-p) = 150 reveals that the break-even probability is p=0.55. In other words, if the probability of successful 3D software is below 0.55, then it is better for James to accept Meditech's offer, otherwise continue with the project.


Probability of Successful 3D Development p EMV Optimal Strategy 0.00 $150 Accept Medtech 's of fer 0.10 $150 Accept Medtech 's of fer 0.20 $150 Accept Medtech 's of fer 0.30 $150 Accept Medtech 's of fer 0.40 $150 Accept Medtech 's of fer 0.50 $150 Accept Medtech 's of fer 0.60 $184 Cont inue wit h pro ject 0.70 $248 Cont inue wit h pro ject 0.80 $312 Cont inue wit h pro ject 0.90 $376 Cont inue wit h pro ject 1.00 $440 Cont inue wit h pro ject

(b) In this case, the EMV at nodes E and H is $2,040,000, so that James' optimal decision is to continue the project and if the 3D software is successful, then he should either apply for SBIR or accept Nugrowth's offer. (c) We assume that we only change the high-profit probability under successful 3D software, the probability of medium-profit remains the same as the probability of low-profit, and all other probabilities, revenues, and costs remain the same. As shown in the table below, under these assumptions, we have that James' optimal strategy is to accept Meditech's offer if probability of high-profit is 10% or less. He should continue with the project, and then accept Nugrowth's offer is 3D software is successful, whenever the probability of high-profit is more than or equal to 20%, but less than or equal to 50%. Finally, he should continue with the project, and then apply for SBIR if the 3D software is successful, whenever the probability of high-profit is 60% or more.

1.6 (a) See decision tree on next page. (b) The missing probabilities are: • The tumor is benign given that the exploratory surgery indicated a benign tumor. • The tumor is benign given that the exploratory surgery indicated a malignant tumor. • The exploratory surgery will indicate a benign tumor.


(c) The corresponding probabilities are shown in the table below. James’ optimal decision strategy is to undergo exploratory surgery. If he survives and the surgery indicates a benign tumor, he should choose to leave the tumor. If he survives and the surgery indicates a malignant tumor, he should choose to remove the tumor. The EMV of this strategy is 5.15 years. Joint Probabilities Benign Malignant Total Test Benign 0.375 0.175 0.55 Test Malignant 0.125 0.325 0.45 Total 0.50 0.50 1 Conditional Probabilities Benign Malignant Total Test Benign 0.68 0.32 1 Test Malignant 0.28 0.72 1

(d) In this case we replace the remaining lifetime years at the l eaves in the tree by zeros and ones. If the tumor is left and is indeed malignant (1 year to live), we assign a value of 0 to the corresponding leaf node, and for all the other leaves, we assign a value of 1. By doing this, we find that James’ optimal decision strategy is to remove the tumor without undergoing exploratory surgery. (e) This problem poses the ethical question of how valid is to make life or death decisions based on a decision tree numerical analysis and in particular, based on the EMV. After all, it is necessary to remember that the EMV is a number that should be interpreted in a long run sense. For instance, suppose that you


buy a $1 lottery ticket with a probability of 1:10000000 of winning 100 million dollars, then your EMV is $9. This means that if you play this game many times, in the long run your average number of earnings is $9. Nevertheless, it is very likely that you will play for a lifetime and never win this lottery. Therefore, you should be very careful when making one-shot or life-death decisions based on decision trees and the EMV.

Decision Analysis Solutions

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