1. Copyright © 2011 Lumina Decision Systems, Inc. Optimization with Uncertainty Analytica User Group 14 April 2011 Lonnie Chrisman, Ph.D. Lumina Decision Systems

2. Copyright © 2011 Lumina Decision Systems, Inc. Timing of Action in optimal decision making Time Now Take Action Information becomes available Acting on information: Decision under uncertainty: ? Uncertain information Take Action Outcome

3. 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)

4. 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, … ?

5. Copyright © 2011 Lumina Decision Systems, Inc. Analytica Examples Two-mines (LP) Famine relief (NLP)

6. 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?

7. 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