Bayes Markovian Decision Models for a Multistage Reject Allowance Problem

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Bayes Markovian Decision Models for a Multistage Reject Allowance Problem
Leon S Leon Seligsberger White
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If i e T or x = 0, then c(i, x) also includes the cost of excess if i > I or shortage if i < I, and the remaining storage costs until the date of shipments The description of the fixed capacity problem is now complete. Using the results of Derman [2], we can formulate the problem as a linear programs - 9 - The solution to the linear program is then used to find the optimal decision rule. (As pointed out in [U], [8], the problem could also be formulated as a dynamic programs ) The linear program to be solved is given by: Minimize: Z = E I z(i, x)c(i, x) i X ^ ^ Subject to: z(j, x) - 0, j^ e S, x = O, l, „o, k-s; s s z(''0 - l E z(j^. X) - z(*) = 1 X s I z(j^, x) - i: z(i^, s-r) q^ (r, s-r) = 0, j - i» s - r, j^ e S-O^; I z(0, x) - E E z(i, x) = X i eT X ^ r T. Z(0^, x) = 1, X 0* The elements of the optimal decision rule are computed as d(i, x) =, . . , . , '^ T. Z(i, x) - 10 - If the denominator is zero then the value of d may be set arbitrarily without changing the expected minimum costo It might be assumed that prior to the start of production several different production capacities are available rather than just one» In this case, let K denote the set of capacities and C(K), Ke K » the costs related to operating at capacity Ko Then the optimal capacity K* could be determined by sowing the equation C(K''0 = Min {c(K) + Z(K)} KeK.

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