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Optimal Inventory Policy with Two Suppliers

Edwin L. Cox School of Business, Southern Methodist University, P.O. Box 750333, Dallas, Texas 75275-0333
Goizueta Business School, Emory University, Atlanta, Georgia 30322-2710
Edwin L. Cox School of Business, Southern Methodist University, P.O. Box 750333, Dallas, Texas 75275-0333
efox{at}mail.cox.smu.edu
richard_metters{at}bus.emory.edu
jsemple{at}mail.cox.smu.edu

We analyze a periodic-review inventory model where the decision maker can buy from either of two suppliers. With the first supplier, the buyer incurs a high variable cost but negligible fixed cost; with the second supplier, the buyer incurs a lower variable cost but a substantial fixed cost. Consequently, ordering costs are piecewise linear and concave. We show that a reduced form of generalized (s, S) policy is optimal for both finite and (discounted) infinite-horizon problems, provided that the demand density is log-concave. This condition on the distribution is much less restrictive than in previous models. In particular, it applies to the normal, truncated normal, gamma, and beta distributions, which were previously excluded. We concentrate on the situation in which sales are lost, but explain how the policy, cost assumptions, and proofs can be altered for the case where excess demand is backordered. In the lost sales case, the optimal policy will have one of three possible forms: a base stock policy for purchasing exclusively at the high variable cost (HVC) supplier; an (s_LVC, S_LVC) policy for buying exclusively from the low variable cost (LVC) supplier; or a hybrid (s, S_HVC, S_LVC) policy for buying from both suppliers.

Subject classifications: inventory/production; dynamic programming.
History: Received August 2003; revision received March 2004; accepted November 2004.

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