copyright © 2011 lumina decision systems, inc. optimization with uncertainty analytica user group...
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Copyright © 2011 Lumina Decision Systems, Inc.
Optimization with Uncertainty
Analytica User Group14 April 2011
Lonnie Chrisman, Ph.D.Lumina Decision Systems
Copyright © 2011 Lumina Decision Systems, Inc.
Timing of Actionin optimal decision making
TimeNow
Take Action
Information becomesavailable
Acting oninformation:
Decision underuncertainty:
?Uncertain
information
Take Action Outcome
Copyright © 2011 Lumina Decision Systems, Inc.
Acting on Information
Examples:• Forecast next quarter’s factory
output.Uncertainties: Machine failures, Supply chain delays, Labor unrest, ...Bottlenecks: Determine maximal output (motivates use of optimization)
• Predict behavior of physical systemUncertainties: Component values, world stateSimultaneous equations (solved via optimizer)
Copyright © 2011 Lumina Decision Systems, Inc.
Decisions under Uncertainty
Examples:• How much product to stock in a store?
Uncertainties: Future demand, risk of loss
• R&D projects to invest in?Uncertainties: Research success, dev. costs, future market potential.
• Determine optimal carbon tax rateUncertainties: impact on economy, energy use elasticity, compliance rates, …
?
Copyright © 2011 Lumina Decision Systems, Inc.
Analytica Examples
• Two-mines (LP)
• Famine relief (NLP)
Copyright © 2011 Lumina Decision Systems, Inc.
Famine Relief
Disaster relief agency has $5M budget for famine relief across 5 regions.
• With (optimal) intervention, # of deaths from famine next year?
Actual famines to occur aren’t yet known.
• How to distribute resources amongst current famines?
Copyright © 2011 Lumina Decision Systems, Inc.
Modeling Famine Relief(Very simplistic)
• Famine Intensity?Fi = Deaths per 10,000 each day
• Famine Progression?
t = months elapsed = doublings per month
• Impact of aid
= halvings per $1M of aid
tFitFi 2*)0()(
tFitFi )(2*)0()(