# lec10 - Outline Probabilistic Dynamic Programming Dealing...

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1 Outline Probabilistic Dynamic Programming Dealing with U N C E R T A I N T Y ! Current stage costs uncertain, but next period’s state is certain: ! RESOURCE ALLOCATION EXAMPLE ! Next period’s state is uncertain: ! INVENTORY EXAMPLE 2 Resource Allocation Example ! 6 gallons of milk available, \$1 each ! Selling price is \$2 per gallon ! Salvage cost is \$0.50 per gallon ! 3 stores, uncertain demand ! Want to maximize expected net profit 0.4 3 0 2 0.6 1 PROB DAILY DEM STORE 1 0.4 3 0.1 2 0.5 1 PROB DAILY DEM STORE 2 0.3 3 0.3 2 0.4 1 PROB DAILY DEM STORE 3

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3 Inventory Example ! At Period 1, firm has 1 unit. ! Production cost for x units is c(x)=3+2x, c(0)=0, x<5. ! Demand is random and equal to 1 w.p. 0.5, 2 w.p. 0.5. ! Holding cost \$1/unit, inventory at end cannot exceed 3. ! Salvage cost \$2/unit. 4 Example: Sunco Oil ! D dollars to allocate ! Sites 1,2,…,T ! q t (x) = probability that oil will be found on site t | x dollars allocated ! r t = worth of oil found at site t ! Goal: maximize E(value) of oil found on all sites.
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lec10 - Outline Probabilistic Dynamic Programming Dealing...

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