Optimal capacity in a coordinated supply chain

Abstract

Abstract:We consider a supply chain in which a retailer faces a stochastic demand, incurs backorder and inventory holding costs and uses a periodic review system to place orders from a manufacturer. The manufacturer must fill the entire order. The manufacturer incurs costs of overtime and undertime if the order deviates from the planned production capacity. We determine the optimal capacity for the manufacturer in case there is no coordination with the retailer as well as in case there is full coordination with the retailer. When there is no coordination the optimal capacity for the manufacturer is found by solving a newsvendor problem. When there is coordination, we present a dynamic programming formulation and establish that the optimal ordering policy for the retailer is characterized by two parameters. The optimal coordinated capacity for the manufacturer can then be obtained by solving a nonlinear programming problem. We present an efficient exact algorithm and a heuristic algorithm for computing the manufacturer's capacity. We discuss the impact of coordination on the supply chain cost as well as on the manufacturer's capacity. We also identify the situations in which coordination is most beneficial.

Aligning Capacity Decisions in Supply Chains When Demand Forecasts Are Private Information: Theory and Experiment

“…From a modeling perspective, the paper most closely related to ours is Tomlin (2003) (but see also Shapiro 1977, Lee and Whang 1999, Chao et al 2008). Tomlin (2003) studies coordination when both firms have identical beliefs about demand.…”