Abstract
Consider an inventory system with one supplier, two retailers, Poisson demand, and constant lead times. One retailer has a higher demand rate and can ship items to the other retailer when facing a stock out, for example. Arriving demands to any retailer are lost if it is out of stock, and it is not possible to initiate a transshipment. Retailers apply one-for-one-period ordering, (1, T), policy. We derive the long-run average cost, prove its convexity, and show that it is independent of the lead time. We present an algorithm to find the optimal solution and minimize the system cost. We show that for long lead times, applying one-for-one-period ordering policy results in a lower cost than the base stock, (S-1, S), policy, so it is preferred in long lead time condition.
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