1. Data Analysis and Decision Making (Albrigth, Winston and Zappe)
Decision Making ADMI 6510
Decision Analysis Models
Key Sources:
Data Analysis and Decision Making (Albrigth, Winston and Zappe)
An Introduction to Management Science: Quantitative Approaches to Decision Making (Anderson, Sweeny, Williams, and Martin), Essentials of MIS (Laudon and Laudon), Slides from N. Yildrim at ITU, Slides from Jean Lacoste, Virginia Tech, ….

2. Outline Basic concepts Payoff table Decision making
Expected value DA models
Decision trees

3. Basics
Decision Support Systems (DSS) use a variety of mathematical approaches to analyze business processes/ problems/ decisions.
Generate alternatives.
Visualize environment, effect of the environment.
Estimate cost and benefit of the alternatives.
Use data from customers, sales, economic factors to forecast.

4. Decision Alternatives Model Decision Analysis Model
Basics
Data
Cost Analysis
Model
Data
Forecast Models
Decision Options
Decision Alternatives Model
Forecast and Probabilities
Decision Analysis Model

5. Basics Decision Analysis models have the following structure:
Decision alternatives (DA): different options related to a system/ product.
States of nature (SN): future events, not under the control of the decision maker, which may occur.
States of nature should be defined so that they are mutually exclusive and collectively exhaustive.
For each DA and SN combination there is an effect ($) called a payoff. Could be a profit or a cost.

6. Basics

7. Payoff tables Decisions have an associated sets of costs/profits.
States of nature have an effect on those costs, profits, … performance level.
State of nature 1
State of nature 2
State of nature 3
Decision option 1 $
Decision option 2
Decision option 3

8. Payoff table – Example 1
You are getting into the Xmas trees selling business.
Decision, how many containers to buy?
System characteristics/ constraints
Each container has 400 trees and costs $10,000 (delivered).
Other costs are “fixed” at $6,000 for the season (location, salaries, marketing).

9. Payoff table – Example 1 States of nature:
Low demand, low prices: Market for about 1,200 at an average of $35/each.
Medium demand/ medium prices: Market for about 1,500 at an average of $45/each.
High demand/ high prices: Market for about 2,100 at an average of $50/each.

10. Payoff table – Example 2
Select from 3 leasing options for a copy machine.
System characteristics/ options:
Lease 1: $5,000 per year; $0.035 per copy.
Lease 2: $8,000 per year; $0.015 per copy.
Lease 3: $10,000 per year; first 80,000 are “free”, after that $0.009 per copy.
States of nature:
5,000 copies per month.
7,000 copies per month.
15,000 copies per month.

11. Decision making
Rules that do not take into account the likelihood (probability) of each SN.
Optimistic: the best possible payoff.
Conservative: maximize the minimum payoff.
Minimize the maximum cost.
Maximize the minimum profit.
Minimize maximum regret: avoid the maximum mistake.

12. Decision making Costs Optimistic: d3 sn1 sn2 sn3 d1 190 120 130 d2 90
140
200 d3 70
150
300
Costs
Optimistic: d3

13. Decision making Conservative: d1
For each decision the worst result is listed.
Select the best of the worst results.
sn1
sn2
sn3
max cost d1
190
120
130 d2 90
140
200 d3 70
150
300
Conservative: d1

14. Decision making Minimize Maximum Regret MinMax: d2
sn1
sn2
sn3 d1
190
120
130 d2 90
140
200 d3 70
150
300
Build a Regret table
For each SN, ID the best payoff.
Table items:
Regret = difference between each payoff and best payoff.
Select the minimum of the maximum regrets.
sn1
sn2
sn3
Max. Regret d1
120 d2 20 70 d3 30
170
MinMax: d2

15. Expected value DA models
Expected value of a random variable is the weighted average of all possible values that this random variable can take on.
The weights used in computing this average correspond to the probabilities in case of a discrete random variable,
What is the expected value when rolling a 6 sided dice?
What if it was a rigged dice and the “one” side has a probability of 55%, the “six” side has a probability of 5%, and the other four sides have a probability of 10% each.

16. Expected value DA models
Example 1 Probabilities
Low demand/prices: 50%
Medium demand/prices: 30%
High demand/prices: 20%
Example 2 Probabilities
5,000 copies/mo: 15%
7,000 copies/mo: 60%
15,000 copies/mo: 25%

17. Sensitivity analysis
Sensitivity analysis (or post-optimality analysis) is used to determine how the optimal solution is affected by changes:
To the objectives
To the constraints
Sensitivity analysis is important to the manager who must operate in a dynamic environment with imprecise estimates.
Sensitivity analysis is about asking what-if questions about the problem.

18. Sensitivity analysis
Assume that the probability of high demand/prices is fixed at 20%.
And that pSN=low + pSN=medium = 80%.
What is the sensitivity of the optimal solution to changes in pSN=low ?

19. Decision trees Graphical representation of decisions
Could be used to represent multi-level/time decisions or states of nature.
Useful for models where decisions are based on expected values.
Each decision tree has two types of nodes; round nodes for SNs, square nodes correspond to DA.
The branches leaving each round node represent the different states of nature while the branches leaving each square node represent the different decision alternatives.
At the end of each limb of a tree are the payoffs attained from the series of branches making up that limb.

20. Decision trees – example
Sourcing of a critical component.
Considering two vendors.
DA1: all requirements to vendor A.
DA2: all requirements to vendor B.
DA3: split requirements; 50% vendor A, 50% vendor B.
States of nature based on the following events: vendor delivers or a vendor fails to deliver.

21. Decision trees – example
Vendor A delivers
Use A only
Vendor A fails to deliver
Vendor B delivers
Use B only
Vendor B fails to deliver
Use both
Vendor A delivers and Vendor B delivers
Vendor A delivers, Vendor B fails
Vendor A fails, Vendor B delivers
Both vendors fail
Requirement per cycle is 1,000 units. Loss costs = $400/unit not available.
Vendor A
Vendor B
Cost per unit
$100
$95
Delivery probability
96%
92%
Additional delivery capacity
150 units
0 units

22. Decision trees – example
Each decision has an expected value based on the applicable SNs.
EV =
96% ($100 x 1,000) +
4%($400 x 1,000)
A delivers
$112,000
Use A only
A fails to deliver
EV =
92% ($95 x 1,000)
+ 8%($400 x 1,000)
B delivers
$119,400
Use B only
B fails to deliver
Use both
A delivers & B delivers
EV =
(96%)(92%) ($100 x $95 x 500)
+ (96%)(8%) ($100 x $400 x 350)
+ (4%)(92%) ($400 x $95 x 500)
+ (4%)(8%) ($400 x 1,000)
A delivers, B fails
A fails, B delivers
Both vendors fail
$112,244

23. Decision trees – example
Sensitivity to Loss cost