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Existence and Properties of Optimal Production and Inventory Policies

Department of Computing and Decision Sciences, Lingnan University, Tuen Mun, Hong Kong and Faculty of Commerce, University of British Columbia, Vancouver, British Columbia, Canada V6T 1Z2
dsun{at}ln.edu.hk

It is an important and fundamental question whether an optimal inventory policy exists for a general deterministic multi-item, multistage (GDMM) production and inventory model. We show that an inventory model with a nonsubadditive ordering cost function could have no optimal policy over a finite horizon. However, when the ordering cost is a subadditive function an optimal policy exists for a GDMM production and inventory model over both a finite horizon and an infinite horizon. Properties of optimal inventory policies are crucial to investigating an inventory problem. We present four properties of optimal policies: (1) nonpositive inventory ordering, (2) last-minute ordering, (3) extended last-minute ordering, and (4) nonnegative filling properties. They have been explicitly or implicitly used in analyzing many different inventory models. The last two properties have been used but not proved before.

Key Words: production and inventory policy; optimal policy; existence theory; property of optimal policy
History: Received: June 8, 2000; revision received: June 2, 2003;revision received: November 13, 2003;

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