Unformatted text preview: n } ]I Â· E [( xD n ) + ]W Â· d nK Â· 1 { d n 6 = d n1 } + Î± Â· E [ V n +1 (( xD n ) + + d n ,d n )] } The boundary condition is: V 13 ( x,d 12 ) = W Â· x We want to calculate V 1 ( x ), then: V 1 ( x ) = max d 1 â‰¥ { R Â· E [min { x,D 1 } ]I Â· E [( xD 1 ) + ]W Â· d 1 + Î± Â· E [ V 2 (( xD 1 ) + + d 1 ,d 1 )] } Based on the above dynamic optimality formulation, we can calculate d 1 ,d 2 ,...,d 11 and d 12 is always 0. Problem 3 Let V n ( i ) denote the minimum expected total discounted cost from period n to period N given that the state at the beginning of period n is i. Then the dynamic optimality formulation is: V n ( i ) = min { C R + Î± Â· K X j =1 P 1 j V n +1 ( j ) ,C ( i ) + Î± Â· K X j = i P ij V n +1 ( j ) } i = 1 , 2 ,...,K1 V n ( K ) = C R + Î± Â· K X j =1 P 1 j V n +1 ( j ) The boundary condition is: V N +1 ( i ) = 0 1...
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This note was uploaded on 03/16/2012 for the course IEOR 466 taught by Professor Richard during the Spring '12 term at Columbia.
 Spring '12
 Richard

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