Optimization with Uncertainty
Analytica User Group
14 April 2011
Lonnie Chrisman, Ph.D.
Lumina Decision Systems
Copyright © 2011 Lumina Decision Systems, Inc.
Timing of Action
in optimal decision making
Time
Now
Acting on
information:
?
Information
becomes
available
Take
Action
Uncertain
information
Decision under
uncertainty:
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 system
Uncertainties: Component values, world state
Simultaneous 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 rate
Uncertainties: 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?
Fi(t )  Fi(0) * 2t
t = months elapsed
 = doublings per month
• Impact of aid
Fi(t )  Fi(0) * 2(  )t
 = halvings per $1M of aid
Copyright © 2011 Lumina Decision Systems, Inc.