Continuous Review Policies for a Multi Echelon Inventory Problem With Stochastic
Continuous Review Policies for a Multi Echelon Inventory Problem With Stochastic
Marc De Bodt
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^, and Q. = n. N. , ... N^O-, . 1 11-1 ^1 1 1-1 2^1 For convenience, we define r. = n. N. , ... N„ so that Q. = r. Q, and r. -, /r. Is 1 1 1-1 2 ^1 1^1 1+1 1 an integer. We assume, as in the two-stage example, that the reordering policy is a "nested" policy. That is, for any two successive stages, say k and k+1, the lower stage orders exactly n, times for each order by the higher stage. Furthermore, whenever stage k+1 orders, there is a joint replenishment with stage k and all lower stages. We ...now express the expected annual cost as a function of the policy parameters. To do this we will again consider separately the three types of costs: setup or ordering, inventory holding and backorder. The expected annual ordering cost is now given by (11) f • (a^ +^ + ^+ ... +^). ^1 ^ ^2 ^3 ^M To express the expected holding cost we consider each stage separately. For stage one (end item) the derivation is analogous to that for the two-stage example, but more complex. There are now M types of replenishment at stage one.
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