University of Illinois at Chicago
College of Business Administration

MBA 503:   Statistics
Instructor:   Prof. Stanley L. Sclove
Textbook:   Levine, Berenson Stephan (LBS), updated ed.

Notes to Accompany Ch. 14:   Decision Making
These notes Copyright © 1998 Stanley Louis Sclove

HyperTable of Contents

14.1 Introduction
14.2 The Payoff Table and Decision Trees
14.3 Criteria for Decision Making
14.4 Decision Making with Sample Information
14.5 Utility
14.6 Decision Making: a Review
Sections 14.5 and 14.6 are not required in this course.

14.1 Introduction

 The topic of this chapter is Decision Analysis, the science of quantifying alternative decisions and choosing from among them.

14.2. The Payoff Table and Decision Trees

The various alternatives and contingencies ("states of nature") are represented in a "decision tree." This gives "branches" of the tree. The cash flows ("gets" and "pays"), suitably discounted if necessary, along each branch are entered. This gives a net cash flow for that alternative.

Toy marketing example:  
STATES OF NATURE (EVENTS)
Successful Unsuccessful
ALTERNATIVE COURSES OF ACTIONA1: Market+$45,000-$36,000
A2: Do not market-$3,000-$3,000

14.3. Criteria for Decision Making

Expected Monetary Value

LBS Chapter 4 includes the basic definition of the mean of a random variable. The expected monetary value (EMV) of the net cash flows is computed by averaging over the different contingencies applying to each alternative.

In the toy marketing example, a probability of .40 is assigned to the event that the toy will be successful (so that a probability of .60 is assigned to the event that it will be unsuccessful).

Sensitivity Analysis consists of varying the inputs to find the range of values under which the current optimal decision remains best. The kind of "What if?" questions involved can be asked and answered using software.

Exercises. (i) Find the range of values of p, the probability that the toy is successful, for which the current optimal decision remains best. (ii) Find the range of values of x11, the profit if the toy is marketed and is successful (the current value is $45,000) for which the current optimal decision remains best.

Various Decision Criteria

More generally, the range of possibilities attendant upon each alternative decision is computed and brought into consideration as the probability distribution of Monetary Value or some other criterion or criteria. The distribution is summarized by its expected value (e.g., Expected Monetary Value or "EMV"), median, maximum, minimum and standard deviation. The return to risk ratio is the reciprocal of the coefficient of variation.

14.4 Decision Making with Sample Information

Suppose the market research department were asked to do a survey, the results of which would tend to indicate whether the market for the toy would be good or bad. How much would such a survey be worth? On what does its value depend?

Suppose the last 100 market surveys for similar items turned out like this.

TABLE. Results of the last 100 similar market surveys 


                                  MARKET WAS ACTUALLY
                                favorable     unfavorable     Total
                                                            
  SURVEY       favorable (F)     32 (.64)       18 (.36)    50 (1.00)
  PREDICTED  unfavorable (F')     8 (.16)       42 (.84)    50 (1.00)
                                 __             __         ___

                    Total        40 (.40)       60 (.60)   100 (1.00)
Now if a survey is done, a prediction will be obtained, and the probabilities pertinent to that prediction (F or F') can be used, rather than the original .40 and .60.

Sections 14.5 and 14.6 are not required in this course.

14.5. Utility

14.6. Decision Making: a Review

Software

Spreadsheets or specialized software can be used for decision trees and the accompanying calculations. One of the first software packages for decision trees was called "Arborist." One of the currently highest rated programs is DPL.

Bibliography

Clemen, Robert T. Making Hard Decisions: An Introduction to Decision Analysis. 2nd ed. Duxbury (Wadsworth/ITP), Belmont, CA, 1996.

APPENDIX: The Getz Case (not in LBS)

Getz Products Co. needs to decide whether to expand, and, if so, whether to build a large plant or a small plant. The large plant costs 900 K$; the small plant, 600 K$. Revenues depend upon whether the market will be favorable or not. The probabilities are assessed at .5 for favorable, .5 for unfavorable. The revenue from a large plant will be 1100 K$ in a favorable market, 720 K$ in an unfavorable market. The revenue from a small plant will be 700 K$ in a favorable market, 580 K$ in an unfavorable market.

Exercise: Calculate the expected net revenues based on these inputs.

Sensitivity Analysis consists of varying the inputs to find the range of values under which the current optimal decision remains best. The kind of "What if?" questions involved can be asked and answered using software.

Exercise: Find the range of values of p, the probability of a favorable market, for which the current optimal decision of building a small plant is best.

Decision Making with Sample Information

Suppose the market research department were asked to do a survey, the results of which would tend to indicate whether the market for Getz' sheds would be good or bad. How much would such a survey be worth? On what does its value depend?

References

Heizer & Render. Production and Operations Management. 4th ed. Prentice-Hall, 1996. (Supplement 2: Decision-Making Tools).

Render, Barry, and Heizer, Jay. Principles of Operations Management, with Tutorials. 2nd ed. Prentice-Hall, 1997. (Tutorial T1)

latest revision 6-Sept-1998