## Interesting Different Decision Problems

Conference

2009 Annual Conference & Exposition

Location

Austin, Texas

Publication Date

June 14, 2009

Start Date

June 14, 2009

End Date

June 17, 2009

ISSN

2153-5965

Conference Session

Tagged Division

Engineering Economy

Page Count

10

Page Numbers

14.782.1 - 14.782.10

DOI

10.18260/1-2--5598

Permanent URL

https://peer.asee.org/5598

166

#### Jane Fraser Colorado State University, Pueblo

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Jane M. Fraser is chair of the Department of Engineering at Colorado State University-Pueblo. She was formerly on the faculty at the Ohio State University and Purdue University. She has a BA in mathematics from Swarthmore College and MS and PhD in industrial engineering and operations research from the University of California-Berkeley.

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#### Ray Tsai Taiwan

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Ray Jui-Feng Tsai received a BS in Industrial Engineering & Engineering Management from National Tsing Hua University in Taiwan and MS in Industrial Engineering from Colorado State University-Pueblo.

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#### Abstract NOTE: The first page of text has been automatically extracted and included below in lieu of an abstract

Interesting Different Decision Problems

Introduction

Consider a choice among three used cars based upon three criteria, miles, price, and year. Year is used as a proxy for other features, such as an adjustable seat and so forth, that have been added to cars over time. The three cars have the following values on the criteria:

Criterion miles price year 1 45K $8K 2000 Car 2 100K$9K 1995 3 60K \$10K 1998 Figure 1: choice among three cars

Because Car 1 has the lowest miles, lowest price, and newest year, it is better than the other two cars on every criterion and the decision is easy. Car 1 dominates the other Cars. We call a decision problem containing a dominated alternative “not interesting.” We call a decision problem containing no dominated alternative “interesting.”

Assuming no ties in preferences among alternatives, we can represent a decision problem with 3 alternatives and 3 criteria in a 3 x 3 matrix; an example is shown in Figure 2, where B indicates the best value on that criterion, W the worst value, and M the middle value. Each column must have one B, one M, and one W.

Criterion C1 C2 C3 A1 B M M Alternative A2 W B M A3 M W B Figure 2: Representation of a decision problem

Now compare the matrices in Figures 2 and 3.

Criterion C1 C2 C3 A1 B M M Alternative A2 W M B A3 M B W Figure 3: Matrix equivalent to Figure 2

Each of these matrices contains no dominated alternative, so they are interesting, but the matrices can be obtained from each other by switching C2 and C3. We want to focus on the structure of the decision problems, not the labels for the criteria (or the alternatives), so we call these two

Fraser, J., & Tsai, R. (2009, June), Interesting Different Decision Problems Paper presented at 2009 Annual Conference & Exposition, Austin, Texas. 10.18260/1-2--5598

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