Quantitative and Qualitative Decision Making
yenomrah
AD715_Assignment2-BikeShop-Exampleforformatandstructure.pdf
CASE PROBLEM ‘BICYCLE SHOP’ 1
Assignment 2:
Case Problem – Bicycle Shop
Tom Grady
Boston University
AD715 Quantitative and Qualitative Decision-Making
Richard Maltzman, PMP
11 MARCH 2016
CASE PROBLEM ‘BICYCLE SHOP’ 2
Table of Contents
Executive Summary ................................................................................................................. 3
The Bicycle Shop Case Problem ............................................................................................. 4
Payoff Table and Decision Tree Analysis .......................................................................... 4
Should Jerry Conduct and Use Marketing Research? ..................................................... 6
Sensitivity Analysis .............................................................................................................. 7
Conclusion ............................................................................................................................ 7
References ................................................................................................................................. 8
APPENDIX A ........................................................................................................................... 9
APPENDIX B ......................................................................................................................... 10
CASE PROBLEM ‘BICYCLE SHOP’ 3
Executive Summary
This managerial report aims to analyze Jerry Smith’s problem as to whether he should
start a bicycle shop business either by opening a small shop, a large shop or no shop at all.
Further analysis was done on whether he should engage his old marketing professor to
conduct a marketing research study before starting his new business venture with a fee of
$5,000. As such, payoff table, decision tree analysis and sensitivity analysis were used in
analyzing Jerry’s problem and coming up with a decision on which alternative to be carried
out. The result from the analysis in this managerial report indicates that Jerry should engage
his old marketing professor to conduct a market research study with the fee of $5,000 with
the condition that the probability of a favorable market research is more than 0.3 as shown in
the sensitivity analysis. If the result of the market research study is favorable, Jerry should
open a large shop as the expected monetary value (EMV) is $45,000 and if the research result
is not favorable, Jerry should not open any shop at all as it has the best EMV of negative
$5,000.
CASE PROBLEM ‘BICYCLE SHOP’ 4
The Bicycle Shop Case Problem
Jerry Smith had been contemplating on whether to start a new business venture by
opening a bicycle shop in his hometown as he had found the right building at the perfect
location to operate his business. The profit from the new business venture will depend on the
size of the shop and whether there is a market for Jerry’s product. As such, Jerry has to make
a few key decisions which are listed below before he could move forward.
(1) Jerry has an alternative to either open a small shop, a big shop or no shop at all; and
(2) Jerry could engage his old marketing professor to conduct a marketing research study
with a fee of $5,000 before deciding the alternative stated in (1) above.
Payoff Table and Decision Tree Analysis
As Render et al. (2015) mentioned, a good decision is a decision that is based on
logic, considers all available data and possible alternatives as well as applying quantitative
approach. In order to make the best decision, Jerry has done some analysis on the profitability
of the bicycle shop. He determined that there are only two possible outcomes – the market for
bicycles could be favorable or it could be unfavorable, both the outcomes have a 0.5
probability. Jerry thinks that a large bicycle shop will earn $60,000 in a favorable market or
loses $40,000 if the market is unfavorable. A small bicycle shop will result in a $30,000
profit in a favorable market and a loss of $10,000 in an unfavorable market. Not opening a
shop would result in $0 profit/loss in either market. The payoff table for Jerry’s conditional
values is shown in table 1.
Alternatives State of Nature
Favorable Market ($) Unfavorable Market ($)
Small Shop 30,000 -10,000
Large Shop 60,000 -40,000
No Shop 0 0
Probability 0.5 0.5
Table 1: Payoff Table with Conditional Values for the Bicycle Shop
CASE PROBLEM ‘BICYCLE SHOP’ 5
Buckley and Dudley (1999) stated that in some cases where decisions have to be
made, certain alternative choices could be clear. However, the consequences of these choices
may not be readily apparent. As such, one possible tool that could be use in such a situation is
the decision tree analysis whereby the payoff table could be graphically illustrated. Figure 1
shows the payoffs and probabilities for Jerry’s decision situation.
Figure 1: Bicycle Shop’s Decision Tree
The most popular method of making decision under risk where a decision is made in
which several possible states of nature occurs and its possibilities are known is by selecting
the alternative with the highest expected monetary value (EMV) (Render et al. 2015). As
reflected in the decision tree in Figure 1, both the small shop and large shop has the same
highest EMV of $10,000 whereas the EMV for no shop is $0. The calculations are as follow:
EMV (small shop) = ($30,000)(0.5) + (-$10,000)(0.5) = $10,000
EMV (large shop) = ($60,000)(0.5) + (-$40,000)(0.5) = $10,000
EMV (no shop) = ($0)(0.5) + ($0)(0.5) = $0
Jerry’s initial analysis on the payoff for the alternatives and probability for the market
conditions yielded the same EMV for both small shop and large shop which is $10,000. If
0.5 TreePlan.com
Favorable Market
$30,000
Small Shop $30,000
$10,000 0.5
Unfavorable Market
-$10,000
-$10,000
0.5
Favorable Market
$60,000
1 Large Shop $60,000
$10,000
$10,000 0.5
Unfavorable Market
-$40,000
-$40,000
No Shop
$0
$0
1
2
CASE PROBLEM ‘BICYCLE SHOP’ 6
Jerry uses the information from the marketing research conducted by his old marketing
professor with a fee of $5,000, the expanded decision tree is as shown in Figure 2 in
Appendix A. Examining the decision tree in Figure 2, it is apparent that the best EMV is to
conduct the market research with a value of $25,000 as compared to an EMV of $10,000 if
market research was not conducted. So the best choice would be to conduct a market
research. If the market research result is favorable, Jerry should open a large shop as
indicated with an EMV of $45,000. However, if the research result is negative, Jerry should
not open any shop at all as it has the best EMV of negative $5,000.
Should Jerry Conduct and Use Marketing Research?
As reflected in the decision tree in Figure 2, the best choice is to conduct a marketing
research study. If Jerry were to engage his old marketing professor to conduct the marketing
research study, it could change his situation from one of decision making under risk to one of
decision making under certainty (Render et al. 2015). However, before engaging his old
professor, Jerry should calculate the maximum that he would pay for that information using
the expected value of perfect information (EVPI). The calculation is as follows,
EVPI = Expected Value with Perfect Information (EVwPI) – Best EMV
= [(best payoff in favorable market)(probability of favorable market) + (best
payoff in unfavorable market)(probability of unfavorable market)] - Best EMV
= [($60,000)(0.5) + ($0)(0.5)] - $10,000 = $20,000
Therefore, the maximum amount that Jerry should pay for the perfect information is $20,000.
Thus, the rate of $5,000 for the service that Jerry’s professor is charging to conduct a market
research study is reasonable and Jerry should take the opportunity to carry out and use the
marketing research.
CASE PROBLEM ‘BICYCLE SHOP’ 7
Sensitivity Analysis
Render et al. (2015) states that “sensitivity analysis investigates how our decision
might change given a change in the problem data”. As such, we could use the sensitivity
analysis to evaluate the impact that a change in the probability value of a favorable marketing
research would have on the decision facing Jerry since he is unsure that the 0.6 probability of
a favorable marketing research result is correct.
In order to compute the sensitivity of the data, let ‘p’ be the probability of the
favorable market research results and ‘1 – p’ is the probability for the unfavorable results.
The equation for EMV of conducting the market research which is node 1 is as follows,
EMV (node 1) = ($45,000)p + (-$5,000) (1 – p) = $50,000p – $5,000
Jerry will maintain indifferent with his decision to conduct the market research when
the EMV for node 1 (conducting market research) is the same as the EMV of not conducting
a market research with a value of $10,000. The indifference point is calculated as follows,
$50,000p – $5,000 = $10,000
p = $15,000 / $50,000 = 0.3
By referring to the sensitivity analysis, it indicates that the probability of the favorable market
research has to be less than 0.3 (as shown in point 1 in the graph of the EMV values in Figure
3 – Appendix B), in order for Jerry to change his decision to not conduct a market research.
Conclusion
With the above analysis, Jerry can finally decide to proceed with engaging his old
marketing professor to conduct a market research study with a fee of $5,000 as long as the
probability of the favorable market research is more than 0.3. If the result of the study is
favorable, than Jerry should open a large shop. However, if the research result is negative,
Jerry should not open any shop at all.
CASE PROBLEM ‘BICYCLE SHOP’ 8
References
Buckley, J. &. (1999). How Gerber Used a Decision Tree in Strategic Decision-Making.
Graziadio Business Review, 2(3). Retrieved from
https://gbr.pepperdine.edu/2010/08/how-gerber-used-a-decision-tree-in-strategic-
decision-making/
Render, Stair, Hanna & Hale (2015). Quantitative Analysis for Management, 12 Edition.
Pearson Education. Chapter 3: Decision Analysis, pages 65 - 95
CASE PROBLEM ‘BICYCLE SHOP’ 9
APPENDIX A
Figure 2: Bicycle Shop’s Decision Tree with Market Research
0.9 TreePlan.com
Favorable Market
$25,000
Small Shop $25,000
$21,000 0.1
Unfavorable Market
-$15,000
-$15,000
0.6 0.9
Favorable Market
$55,000
2 Large Shop $55,000
$45,000
$45,000 0.1
Unfavorable Market
-$45,000
-$45,000
No Shop
-$5,000
-$5,000
0.12
$25,000 Favorable Market
$25,000
Small Shop $25,000
-$10,200 0.88
Unfavorable Market
-$15,000
-$15,000
0.4 0.12
Favorable Market
$55,000
3 Large Shop $55,000
-$5,000
-$33,000 0.88
Unfavorable Market
-$45,000
-$45,000
1
$25,000
No Shop
-$5,000
-$5,000
0.5
Favorable Market
$30,000
Small Shop $30,000
$10,000 0.5
Unfavorable Market
-$10,000
-$10,000
0.5
Favorable Market
$60,000
1 Large Shop $60,000
$10,000
$10,000 0.5
Unfavorable Market
-$40,000
-$40,000
No Shop
$0
$0
Favorable
Survey Result
Unfavorable
Survey Result
Conduct
Market
Research
Do Not
Conduct
Market
Research
1
2
3
4
5
6
7
CASE PROBLEM ‘BICYCLE SHOP’ 10
APPENDIX B
Figure 3: Sensitivity Analysis for the Probability of Favorable Market Research for the Bicycle Shop
-$10,000
$0
$10,000
$20,000
$30,000
$40,000
$50,000
0 0.5 1
EX P
EC TE
D M
O N
ET A
R Y
V A
LU E
(E M
V )
PROBABILITY OF FAVORABLE MARKET RESEARCH (P)
SENSITIVITY ANALYSIS - BICYCLE SHOP
Conduct Market Research Do Not Conduct Market Research
point 1
0.3
