The Effect of Supply Uncertainty on Dynamic Procurement and Pricing Strategies Under Lost Sales

Abstract

The uncertainty in the supplier’s material flows has become a norm rather than an exception in supply chains. The supply uncertainty can result in unexpected inventory shortfall, amplifying lost sales. However, the design of inventory replenishment and product pricing policy to mitigate both supply uncertainty and demand loss remains unexplored. This is because the resulting dynamic planning problem is highly nonconcave and thus intractable. To address this challenge, we propose an approach that focuses on a class of intuitively appealing and practically plausible policies. Specifically, as the level of on-hand inventory increases, we expect an increased amount of demand fulfillment and a decreased product price. Applying the notions of stochastic functions, we show that, under general conditions of the stochastic supply and demand functions, the dynamic planning problem becomes a concave optimization problem over the restricted policy class. We further reduce the set of candidate policies to a refined class by excluding the dominated policies. A refined policy can be easily computed, and appropriately selected refined policies produce close-to-optimal profits. These developments allow us to evaluate the consequences of demand loss. In particular, demand retention through backordering can be beneficial when overstocking is costly in relation to understocking, but the benefit is insensitive to supply and demand uncertainties. Moreover, inventory-based dynamic pricing is more valuable in mitigating supply risk under lost sales than under backordering.