What is decision theory? How it is used for businesses?, Study notes of Quantitative Techniques

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Lesson 9.

Decision Theory with

Unknown State Probabilities

Decision Theory

Most management decisions are

made in an environment of

uncertainty.

Decision theory provides a orderly

way of choosing among several

alternative strategies when decisions

are made under uncertainty or risk.

Payoff Matrix

States of Nature

j

s

1

s

2

s

3

s 4 a 1 a 2 a 3

Alternatives

i

States of Nature

j

s

1

s

2

s

3

s 4 a 1 a 2 a 3

Alternatives

i

c

11

c

12

c

13

c

14

c

21

c

22

c

23

c

24

c

31

c

32

c

33

c

34

Payoff Matrix

Home Health Example

Suppose a home health agency is considering adding

physical therapy (PT) services for its clients. There

are three ways to do this:

Option A : contract with an independent practitioner

at $60 per visit.

Option B : hire a staff PT at a monthly salary of $

plus $400/mo. for a leased car plus $7/visit for

supplies and travel.

Option C : independent practitioner at $35/visit but

pay for fringe benefits at $200/mo. and cover the car

and expenses as in Option B.

Source: Austin, CJ and Boxerman, SB, Quantitative Analysis for Health Services

Administration, AUPHA/Health Administration Press, Ann Arbor, Michigan, 1995

Payoff Matrix: Home Health Example

States of Nature

j

s

1

s

2

s

3

s

4

Demand of

Patient

Services:

Visits/ mo.

30 90 140 150

Assumption: Probabilities of States of Nature are

unknown.

Payoff Matrix: Home Health Example

Alternatives

i a 1 a 2 a 3

• Contract with independent Contractor at $60/visit.

Net Profit = (75 - 60) * D = 15*D

Assumption: Charge $75 per visit.

• Pay monthly salary of $4,
• Car allowance $
• Expenses @$7 a visit

Net Profit = - 4,000 - 400 + (75 - 7) * D = -4,400 + 68*D

Alternatives

i a 1 a 2 a 3

• Contract with independent Contractor at $60/visit.

Net Profit = (75 - 60) * D = 15*D

Assumption: Charge $75 per visit.

• Pay monthly salary of $4,
• Car allowance $
• Expenses @$7 a visit

Net Profit = - 4,000 - 400 + (75 - 7) * D = -4,400 + 68*D

• Contract @ $35 per visit
• Car allowance $
• Fringe benefits of $
• Expenses @$7 a visit

Net Profit = -400 -200+ (75 - 35 -7) * D = -600 + 33*D

Payoff Matrix: Home Health Example

s

1

s

2

s

3

s

4

450 1350 2100 2250

30 90 140 150

Total Profit (Alt 2) = -4,400 + 68D

-2360 1720 5120 5800

a

1

a

2

Payoff Matrix

s

1

s

2

s

3

s 4 a 1 a 2

450 1350 2100 2250

30 90 140 150

Total Profit (Alt 3) = -600 + 33D

-2360 1720 5120 5800

390 2370 4020 4350

Payoff Matrix

s

1

s

2

s

3

s 4 a 1 a 2

450 1350 2100 2250

30 90 140 150

-2360 1720 5120 5800

390 2370 4020 4350

No alternative dominates any other alternative

Payoff Matrix

Criteria for Decision Making

Maximin Criterion- criterion that

maximizes the minimum payoff for each

alternative.

Steps:

1. Identify the minimum payoff for each

alternative.

2. Pick the largest minimum payoff.

Maximin Decision Criterion

The maximin criterion is a

very conservative or risk

adverse criterion. It is a

pessimistic criterion. It

assumes nature will vote

against you.

Minimax Decision Criterion

If the values in the payoff

matrix were costs, the

equivalent conservative or

risk adverse criterion would

be the minimax criterion. It

is a pessimistic criterion.