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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
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