Inventory Control for Supply Chains with Service Level Constraints: A Synergy between Large Deviations and Perturbation Analysis

We consider a model of a supply chain consisting of n production facilities in tandem and producing a single product class. External demand is met from the finished goods inventory maintained in front of the most downstream facility (stage 1); unsatisfied demand is backlogged. We adopt a base-stock production policy at each stage of the supply chain, according to which the facility at stage i produces if inventory falls below a certain level wi and idles otherwise. We seek to optimize the hedging vector w = (w1, . . . , wn) to minimize expected inventory costs at all stages subject to maintaining the stockout probability at stage 1 below a prescribed level (service level constraint). We make rather general modeling assumptions on demand and production processes that include autocorrelated stochastic processes. We solve this stochastic optimization problem by combining analytical (large deviations) and sample path-based (perturbation analysis) techniques. We demonstrate that there is a natural synergy between these two approaches.