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1CUSTOM Conference, December 20011Introduction to Stochastic ProgrammingJohn R. BirgeNorthwestern UniversityCUSTOM Conference, December 20012Outline Overview Examples Vehicle Allocation Financial planning Manufacturing Methods View ahead2CUSTOM Conference, December 20013Overview Stochastic optimization Traditional Small problems Impractical Current Integrate with large-scale optimization ( Stochastic Programming ) Practical examples Expanding rapidlyCUSTOM Conference, December 20014Vehicle Allocation Decision: How to position empty freight cars?NOW:AB5 cars0 carsDAY 1:DAY 2:ABABDEMAND:DAY 1: B to A:Mean Value=2DAY 1: A to B:Mean Value=2??223CUSTOM Conference, December 20015 Maximize:Revenue-Cost MOVE TWO EMPTY CARS FROM A to BNOW:AB5 cars0 carsDAY 1:DAY 2:ABABRESULT:Net 2: A to B; Net 2: B to ATOTAL(MV) = 43122Parameters: COST: per empty car from A to BREVENUE: per full car from A to B222Vehicle Allocation: Mean Value SolutionCUSTOM Conference, December 20016 Find: Expected(Revenue-Cost) MOVE TwoEMPTY CARS FROM A to BNOW:AB5 cars0 carsDAY 1:DAY 2:ABABExpected Value:Net 2: A to B; Net 2: B to A ( 2/3)-1: B to A ( 1/3)TOTAL (EMV): 323 ( )2Suppose: Demand is Random (Expectationfrom A to B=2) 0 from A to B with prob.

Introduction to Stochastic Programming John R. Birge Northwestern University CUSTOM Conference, December 2001 2 Outline •Overview •Examples • Vehicle Allocation • Financial planning • Manufacturing • Methods • View ahead. 2 CUSTOM Conference, December 2001 3 Overview • Stochastic optimization

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