Two-Stage Serial System under Centralized Control

4 Two-Stage Serial System under Centralized Control 

To find the optimal centralized control policy for the 2-stage serial system we considered in the previous section, we must find inventory cycle lengths Xi and X2 that minimize 

To simplify this expression, we use echelon holding costs, defined as follows The echelon holding cost at echelon j is Hj = hj - hj y where, consistent with the earlier sections of the chapter, hj is per-unit cost of holding inventory per period. (Since ho = 0, = hi.) Thus, echelon stock at echelon j is valued at 

The first-order condition on expression (3.38) with respect to T2 is 

Rather than using the first difference on expression (3.38) to find m as in the previous section, we employ the approach suggested by Axsater (2006). First, substitute expression (3.39) into expression (3.38), to obtain 

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