Decision under uncertainty
DECISION UNDER
UNCERTAINTY
MZ510 ANALYTICAL METHODS
23 SEPTEMBER 2013
OUTLINE
Objectives
Introduction
Application (Example)
Decision Criteria
Summary
2
OBJECTIVES
Study situations where decisions are made in an uncertain environment
Introduce basic theory of decision making under uncertainty
Demonstrate how to calculate and select a decision when uncertainties regarding the future exist
Understand the method that will optimize the resulting payoff in terms of a decision criterion
3
WEDDING ANNIVERSARY?
Mr. Right is about to leave work for home. He looks at his calendar. It is August 24. This, he feels, is an important date.
Is it his wedding anniversary?
He better buy his wife some flowers (cost $25).
What if it is not their anniversary and he arrives home with the present?
She will become suspicious.
He would have to take her out to dinner to explain
(cost $125).
Worse still if he does not bring anything home and it is their anniversary there will be trouble; perhaps $500 would be needed to help patch things up. What should he do?
4
INTRODUCTION
State‐of‐the‐World Decision‐Making Model
Possible states Sj = {S1, S2…., Sk}
Assume that Sj happens with probability Pj P = {P1, P2…., Pk}
Decision maker chooses an action, ai A = {a1, ,a2…., ak}
If action, ai , is chosen and the state of the world is Sj then the reward is, rij
Mr. Right’s Wedding Anniversary?
S = {anniversary, no anniversary}, P is equally likely
A = {buy, don't buy}
Pay Off Table
Anniversary
No Anniversary
Buy
‐25
‐150
Don’t Buy
‐500
0
5
SCM APPLICATION: NEWSVENDOR EXAMPLE
Needs to decide on an order quantity Demand unknown
Possibility is equally likely,
P6 = p7 = p8 = p9 = p10 = 1/5
Possible values of daily demand
S = {6,7,8,9,10}
A = {6,7,8,9,10}
Cost = 20 cents
UNCERTAINTY
MZ510 ANALYTICAL METHODS
23 SEPTEMBER 2013
OUTLINE
Objectives
Introduction
Application (Example)
Decision Criteria
Summary
2
OBJECTIVES
Study situations where decisions are made in an uncertain environment
Introduce basic theory of decision making under uncertainty
Demonstrate how to calculate and select a decision when uncertainties regarding the future exist
Understand the method that will optimize the resulting payoff in terms of a decision criterion
3
WEDDING ANNIVERSARY?
Mr. Right is about to leave work for home. He looks at his calendar. It is August 24. This, he feels, is an important date.
Is it his wedding anniversary?
He better buy his wife some flowers (cost $25).
What if it is not their anniversary and he arrives home with the present?
She will become suspicious.
He would have to take her out to dinner to explain
(cost $125).
Worse still if he does not bring anything home and it is their anniversary there will be trouble; perhaps $500 would be needed to help patch things up. What should he do?
4
INTRODUCTION
State‐of‐the‐World Decision‐Making Model
Possible states Sj = {S1, S2…., Sk}
Assume that Sj happens with probability Pj P = {P1, P2…., Pk}
Decision maker chooses an action, ai A = {a1, ,a2…., ak}
If action, ai , is chosen and the state of the world is Sj then the reward is, rij
Mr. Right’s Wedding Anniversary?
S = {anniversary, no anniversary}, P is equally likely
A = {buy, don't buy}
Pay Off Table
Anniversary
No Anniversary
Buy
‐25
‐150
Don’t Buy
‐500
0
5
SCM APPLICATION: NEWSVENDOR EXAMPLE
Needs to decide on an order quantity Demand unknown
Possibility is equally likely,
P6 = p7 = p8 = p9 = p10 = 1/5
Possible values of daily demand
S = {6,7,8,9,10}
A = {6,7,8,9,10}
Cost = 20 cents