On the Convexity of the Backorder Function for an E.O.Q. Policy

by Robin B. S. Brooks, John Y. Lu

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The backorder function for an economic order policy as derived by Hadley and Whitin, while convex in [r] (the reorder point) and convex in [Q] (the order quantity), is unfortunately not generally convex in both [r] and [Q]. It has been pointed out previously that such nonconvexity can lead to a failure of the optimization technique suggested by Hadley and Whitin. This study shows that if [r] is restricted to be suitably large, then [B(r, Q)] is convex within such a region.

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