Coping with Demand Uncertainty: The Interplay between Dual Sourcing and Endogenous Partial Backordering

Yanyi Xu, Doğan A. Serel, Arnab Bisi, Maqbool Dada

Production and Operations Management · 2022 · Volume 31 · Issue 4

Abstract

In some stockout situations, a retailer may be better off declining to fulfill some demand even though it could have been backordered. We study the conditions under which endogenous (retailer-driven) partial backordering is the cost-minimizing strategy in an infinite horizon periodic review inventory system with dual sourcing. At the beginning of each period, the retailer can place two orders. The first order (with higher unit purchase cost) is delivered immediately from the fast supplier and brings the inventory level up to a target levelZ. The second order (with lower unit purchase cost) is delivered one period later from the slow supplier (or the same supplier using a slower delivery mode) and brings the inventory position up to the base-stockR. In each period, the realized demand can be accepted up to the maximum of inventory on-hand andR–k, implying that some excess demand requests may be backordered while the rest is rejected. The on-order quantitykdenotes the reservation quantity held back for use in subsequent periods. Each ofk,Z, andRis a decision variable in our model with dual sourcing. The casek=R–Zyields the full lost sales model while the casek= –∞ yields the full backorder model. We determine structural properties of the optimal (k,Z,R) policy and discuss how to find the optimal base-stock and reservation quantities. In a complementary numerical investigation, we find that a suitably designed single supplier partial backorder policy can be nearly as cost-effective as the optimal dual source policy.

Keywords

stochastic demand, periodic review, base-stock system, endogenous partial backorders and lost sales, (k,Z,R) policy, (k,R) policy

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