Coordinating Lead-Time and Safety Stock Decisions in a Two-Echelon Supply Chain with Autocorrelated Consumer Demand

Abstract

In this paper we study a two-echelon supply chain with a retailer serving a consumer who is sensitive to marketing and pricing promotions. This results in either positively or negatively autocorrelated demand. Based on the observed consumer demand, the retailer replenishes with an adaptive order-up-to inventory policy satisfying a pre-specified fill rate. We assume the manufacturer produces the retailer’s orders on a make-to-order basis and he decides on the lead time based on the retailer’s order pattern. We analyze the interaction between the consumer demand process, the retailer’s replenishment decision (and corresponding safety stock decision), and the manufacturer’s production lead time. We encounter a lead time/safety stock dependency problem – the retailer’s replenishment decision depends on the expected manufacturer’s lead time, whereas the actual manufacturing lead time depends on the replenishment decision (order size) – and develop an exact iterative procedure to solve this interaction effect. Surprisingly, given equal variability, a negatively autocorrelated, period-to-period oscillatory consumer demand provides shorter lead times and lower safety stocks as opposed to a positively autocorrelated, meandering consumer demand.