Multistage Production for Stochastic Seasonal Demand

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Multistage Production for Stochastic Seasonal Demand
Wallace B S Crowston
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This relationship can be applied to find an upper bound on expected profit for the multistage, multiperiod problem. We will apply the newsboy bound to each stage, n, of the multistage problem, considering only those costs prior to and including the production of stage n, and using as a measure of uncertainty in demand that uncertainty remaining in the last period at which stage n can begin production, T-Z^.
We now compute the upper bound, B, as (23) ^n = (Pr - ^N^^ where i2^) ^n = (OC^ , T-Zj (
...C + I C - V ) f(q 7 ) ^ jea(n) J J "'^-^n and G(n) is the set of all stages (in} such that Z - Z . Then B* = mln {B } is an overall bound on expected profit, but a bound which does not include losses that may arise from underage or overage in later production stages, nor does it in- clude potential losses from demand prior to the production of ^See [li|], p. 302, 22.
the final batch for the bounding stage.
The bound was applied to the sample problem reported in Table 3 for which H4 gave expected profits of $68, 862, $66, 167, and $66, 579.


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