Introduction to Problem Solving with Multi-Attribute Decision Making

Objectives:

• (1) Know the types of multi-attribute decision techniques.
• (2) Understand the different weighting schemes and how to implement them.
• (3) Know which technique or techniques to use.
• (4) Know the importance of sensitivity analysis.
• (5) Recognize the importance of technology in the solution process.

The Department of Homeland Security (DHS) has a limited number of assets and a finite amount of time to conduct investigations, thus action priorities must be established. The Risk Assessment Office has collected the data shown in Table 8.1 for the morning Daily Briefing. Your Operations Research Team must analyze the information and provide a priority list to the Risk Assessment Team in time for the briefing.

TABLE 8.1: DHS Risk Assessment Data

 Threat Nature Reliability Assess. Approx. deaths (xlO3) Damage Estimate (xlO6) Pop. Density (x 106) Psych- Factor Number Intel. Tips Dirty Bomb 0.40 10 150 4.5 9 3 Bio-Terror 0.45 0.8 10 3.2 7.5 12 DC Roads or Bridges 0.35 0.005 300 0.85 6 8 NY Subway 0.73 12 200 6.3 7 5 DC Metro 0.69 11 200 2.5 7 5 Major Bank Robbery 0.81 0.0002 10 0.57 2 16 Air Traffic Control 0.70 0.001 5 0.15 4.5 15

TASK. Build a model that ranks the incidents in a priority order.

ASSUMPTIONS. The main suppositions are:

• • Past decisions will give insights into the decision maker’s process.
• • Table 8.1 holds the only data available: reliability, approximate number of deaths anticipated, approximate remediation costs, location of the action, destructive psychological influence on the citizenry, and the number of intelligence tips gathered.
• • The listed factors will form the criteria for the analysis.
• • The data is accurate and precise.

The problem will be solved with the SAW (exercise) and TOPSIS methods.

Introduction

Multiple-attribute decision making (MADM) concerns making decisions when there are multiple, but finite, alternatives and criteria. This topic is sometimes called multi-criteria decision analysis or MCDA. These problems differ from analysis where we have only one criteria such as cost with several alternatives. We address problems such as in the DHS scenario where there are six criteria with seven alternatives that impact the decision.

Consider a problem where management needs to prioritize or rank order alternative choices such as: identifing key nodes in a supply chain, choosing a contractor or sub-contractor, selecting airports, ranking recruiting efforts, ranking banking facilities, ranking schools or colleges, etc. How can setting relative priorities or choosing rank orders be accomplished analytically?

We will present four methodologies for prioritizing or rank ordering alternatives based upon multiple criteria. The methodologies are

• • Data Envelopment Analysis (DEA)
• • Simple Average Weighting (SAW)
• • Analytical Hierarchy Process (AHP) with Objective Data[1]
• • Technique of Order Preference by Similarity to Ideal Solution (TOPSIS)

For each technique, we describe its methodology, discuss strengths and limitations, offer tips for conducting sensitivity analysis, and present illustrative examples using Maple.

• [1] Our discussion of AHP will be restricted to data that is real, and not subjective. Forfurther study, see Saaty’s Fundamentals of Decision Making and Priority Theory With theAnalytic Hierarchy Process.