DDecision ecision MMaking aking

under under RRiskisk

for for CCapacity apacity PPlanninglanning

Certainty, Uncertainty, & Certainty, Uncertainty, & RiskRisk

• The gap under certainty and uncertainty is the Risky passage with probability.

• Certainty: Environment in which relevant parameters have known values.

• Definite payoff with definite demand• Uncertainty: Environment in which impossible to assess the

likely hood of various future elements.• Not definite payoff with no definite demand• Risk : Environment in which certain future events have

probable outcome.

• Contrary to certainty we have uncertainty at the opposite extreme.

• 50% chances are in between certainty and uncertainty that, a definite payoff will meet with preplanned demand.

• Certainty-------------50%---------------- uncertainty

• <-------------Probability------------>

• Probability of Moderate demand at middle• So first half is 30% at Low Demand• At second half 20% at high Demand

Types in Un CertaintyTypes in Un Certainty• Contrary to certainty we have uncertainty at the opposite

extreme. No information is available on how likely the various states of nature are. Lets assume following the scenarios as possible payoffs.

• Maximin Worst, Pessimistic• Maximax Best, Optimistic• Laplace Average• Minimax regret Approach seems to minimize the

difference between the payoff that is realized and the best

payoff for the each state of nature.• Gives “worst regret” for each alternative and choose the

alternative with the “best worst”

• Maxmin 10 Laplace 30/3 = 10• 07 31/3 = 10.33• -04 14/3 = 4.67• Maximax 10 Minmax Regret 6• 12 4• 16 14 see later

In millions dollars

Example of Un certainty components

Alternative Low Moderate High

Small Facility $10m $10m $10m

Medium Facility 7 12 12

Large Facility -4 2 16

Finding the Expected

Value

Using the Uncertainty

Finding the Expected Value

FFinding inding thethe EExpected xpected VValuealue

• The Expected value is computed for each alternatives e.g. small, med, Large facilities from where the highest Expected value is selected.

• The Expected value is sum of the pay offs for an alternative, where each pay off is weighted by the probability for the relevant state of nature.

In millions dollars

Future Demand in an example of Capacity Planning

Alternative Low Moderate High

Small Facility $10m $10m $10m

Medium Facility 7 12 12

Large Facility -4 2 16

DDecision ecision MMaking under aking under RRiskisk

• Expected Monetary Value Criterion

• EMV The best expected value

among the alternatives. The medium is highest so we select this $10.5m

Expected value or Expected payoff under Risk or

Best Expected value one and the same thing

In millions dollars

Expected Monetary Value Criterion  

Alternatives Low Moderate High Total

Small Facility 0.3x10 + 0.5x 10 + 0.2x10 = $10m

Medium Facility 0.3x 7 + 0.5x 12 + 0.2x12 = $10.5m

Large Facility 0.3x(4) + 0.5x 2 + 0.2x16 = $3m

EExpected xpected VValuealue of of PPerfect erfect

IInformation nformation (EVPI)(EVPI)• The difference between the Expected Payoff with perfect

information (EPPI ) and the Expected Payoff under Risk.• EVPI = Expected Payoff - Expected Payoff (under certainty) ( Under Risk)

EVPI = Expected Payoff - $ 10.5m ( perfect information)

EVPI = EPPI - $ 10.5m Max pay off in each alternatives below

In millions dollars

Maximum Future Demand in each Alternatives

Alternative Low Moderate High

Small Facility 10    

Medium Facility   12  

Large Facility     16

Max pay off multiplying with Probability Max Pay

off

Low Moderate High   EPPIEPPI

Small Facility 10 x 0.3 +      

Medium Facility   12 x 0.5 +   million $

Large Facility     16 x 0.2 = 12.2

In millions dollars

Maximum future demand in each Alternatives

Alternative Low Moderate High

Small Facility 10    

Medium Facility   12  

Large Facility     16

EPPI EPPI conted:conted:

EVPI EVPI conted:conted:

• EVPI = Expected Payoff - Expected Payoff ( perfect information) ( Under Risk)

EVPI = $12.2m - $ 10.5m

EVPI = $1.7m

Using the Uncertainty

Un CertaintyUn Certainty• Maximin Worst, Pessimistic• Maximax Best, Optimistic• Laplace Average• Minimax regret Approach seems to minimize

the difference between the payoff that is realized and

the best payoff for the each state of nature.

• Gives “worst regret” for each alternative and choose the alternative with the “best worst”

EVPI EVPI with with Minmax Minmax RegretRegret

With Minmax Regret Alternative Low Moderate HighSmall Facility 10-10= 0 12-10= 2  16-10= 6 Medium Facility 10-7 = 3  12-12= 0 16-12= 4 Large Facility 10-(4)= 14  12- 2= 10  16-16= 0

In millions dollars Future Demand

Alternative Low Moderate High

Small Facility 10 10 10

Medium Facility 7 12 12

Large Facility -4 2 16

CCalculating alculating EEVPI VPI with with MMinimaxinimax regretregret

• Select “worst regret” for each alternative and choose the alternative with the “best worst”.

 • Alternative Low Moderate High Worst• Small Facility 0 2 6 $6m• Medium Facility 3 0 4 $4m ---------- Best Worst• Large Facility 14 10 0 $14m

In millions dollars With Minmax Regret

Alternative Low Moderate High

Small Facility 10-10= 0 12-10= 2  16-10= 6 

Medium Facility 10-7= 3  12-12= 0 16-12= 4 

Large Facility 10-(4)= 14  12-2= 10  16-16= 0

Expected value Expected value throughthrough EVPI = EVPI = Expected value Expected value through through Minimax Minimax

regret (medium facility)regret (medium facility)• Minmax Regret  • Alternative Low Moderate High Worst• Small Facility 0 2 6 $6m• Medium Facility 3 0 4 $4m• Large Facility 14 10 0 $14m

In millions dollarsExpected Monetary Value

Criterion  

Alternative Low Moderate High TOTAL

Small Facility 0.3x0+ 0.5x2+ 0.2x6 2.2

Medium Facility 0.3x3+ 0.5x0+ 0.2x4 $1.7m Minimum

Large Facility 0.3x14+ 0.5x10+ 0.2x0 9.2