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

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 non-concave and thus intractable. To address this challenge, we propose an approach that focuses on a class of intuitively appealing and practically plausible policies that require the amount of stock allocated for meeting the demand to be increasing and the product price to be decreasing in the available inventory level. Applying the notion of stochastic functions, we show that, under general conditions for 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. A refined policy can be easily computed, and an appropriately selected refined policy produces 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 the supply and demand uncertainties. Moreover, the inventory-based dynamic pricing is more valuable under lost sales than under backordering