1

Decision Making ADMI

6510Decision 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

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.

3

Basics

4

Data

Forecast and Probabilities

Forecast Models

Decision Alternatives

Model

Data

Cost AnalysisModel

Decision Options

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.

Basics

6 http://www.dilbert.com/

Payoff tables

• Decisions have an associated sets of costs/profits.

• States of nature have an effect on those costs, profits, … performance level.

7

State of nature 1

State of nature 2

State of nature 3

Decision option 1 $ $ $

Decision option 2 $ $ $

Decision option 3 $ $ $

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).

8

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.

9

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.

10

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.

11

Decision making

sn1 sn2 sn3

d1 190 120 130

d2 90 140 200

d3 70 150 300

12

Costs

Optimistic: d3

Decision making

13

sn1 sn2 sn3 max cost

d1 190 120 130 190

d2 90 140 200 200

d3 70 150 300 300

Conservative: d1

– For each decision the worst result is listed.– Select the best of the worst results.

Decision making

– 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.

14

sn1 sn2 sn3

d1 190 120 130

d2 90 140 200

d3 70 150 300

Minimize Maximum Regret

sn1 sn2 sn3 Max. Regret

d1 120 0 0 120

d2 20 20 70 70

d3 0 30 170 170

MinMax: d2

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.

15

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%

16

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.

17

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 ?

18

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.

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.

20

Decision trees – example

21

Use A only

Use B only

Use both

Vendor A deliversVendor A fails to deliverVendor B deliversVendor B fails to deliver

Vendor A delivers and Vendor B deliversVendor A delivers, Vendor B failsVendor A fails, Vendor B delivers

Both vendors fail

Vendor A Vendor B

Cost per unit $100 $95

Delivery probability 96% 92%

Additional delivery capacity 150 units 0 units

Requirement per cycle is 1,000 units.Loss costs = $400/unit not available.

Decision trees – example• Each decision has an expected value based on

the applicable SNs.

22

Use A only

Use B only

Use both

A delivers

A fails to deliver

B delivers

B fails to deliver

A delivers & B delivers

A delivers, B fails

A fails, B delivers

Both vendors fail

EV = 96% ($100 x 1,000) + 4%($400 x 1,000)

EV = 92% ($95 x 1,000) + 8%($400 x 1,000)

EV = (96%)(92%) ($100 x 500 + $95 x 500) + (96%)(8%) ($100 x 650 + $400 x 350)+ (4%)(92%) ($400 x 500 + $95 x 500) + (4%)(8%) ($400 x 1,000)

$112,000

$119,400

$112,244

Decision trees – example• Sensitivity to Loss cost

23

80,000

90,000

100,000

110,000

120,000

130,000

140,000

150,000

160,000

0 100 200 300 400 500 600 700 800Loss cost/ unit

A

B

A&B