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Coordinating Production and Delivery Under a (z, Z)-Type Vendor-Managed Inventory Contract

Department of Industrial and Operations Engineering, 2811 IOE Building, 1205 Beal Avenue, University of Michigan, Ann Arbor, Michigan 48109-2117
University of Michigan Business School, 701 Tappan Street, Ann Arbor, Michigan 48109-1234
John M. Olin School of Business, Campus Box 1133, Washington University in St. Louis, St. Louis, Missouri 63130-4899
mjfry{at}umich.edu
roman.kapuscinski{at}umich.edu
olsen{at}olin.wustl.edu

This paper models a type of vendor-managed inventory (VMI) agreement that occurs in practice called a (z, Z) contract. We investigate the savings due to better coordination of production and delivery facilitated by such an agreement. The optimal behavior of both the supplier and the retailer are characterized. The optimal replenishment and production policies for a supplier are found to be up-to policies, which are shown to be easily computed by decoupling the periods when the supplier outsources from those when the supplier does not outsource. A simple application of the newsvendor relation is used to define the retailer's optimal policy. Numerical analysis is conducted to compare the performance of a single supplier and a single retailer operating under a (z, Z) VMI contract with the performance of those operating under traditional retailer-managed inventory (RMI) with information sharing. Our results verify some observations made in industry about VMI and show that the (z, Z) type of VMI agreement performs significantly better than RMI in many settings, but can perform worse in others.

Key Words: Vendor-Managed Inventory; Supply Chain; Contract; Markov Decision Process; Multi-Echelon
History: Received: August 16, 1999;

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