Dynamic Pricing and Inventory Control in a Continuous Review System with Batch Ordering and Random Leadtimes

Most of the dynamic pricing and inventory-control literature assumes zero leadtimes, due to the challenges intrinsic to problems with dynamically controllable prices. In standard inventory models with full backlogging and exogenous prices (and hence demand distributions), it is easy to handle leadtimes by using inventory positions (= inventory levels + outstanding orders) and a standard accounting device, by which each period is charged with the expected inventory costs of one leadtime later. However, with dynamically controllable prices, these future costs depend on the price decisions of future periods, and they are therefore unspecified in the current period.This proposed project will attempt to take a major step forward fulfilling the above gap in the literature. Specifically, we will begin with a single-item continuous-review inventory/production system with batch ordering/production and Poisson demand whose arrival rate is price-sensitive. The order leadtime will be modeled by an Erlang or mixed-Erlang distribution. The objective is to find an optimal dynamic pricing and inventory control policy to maximize the expected discounted profit or the long-run average profit in an infinite horizon. The Erlang (mixed-Erlang) distribution represents a convenient family of distributions with coefficients of variation between the zero variation of the constant leadtime case and the large variation of the exponentially distributed leadtime case (can approximate any leadtime distribution to any pre-specified level of accuracy). Hence, it offers great flexibility in modeling replenishment leadtimes.We will consider both lost-sales and backlogging cases. Our preliminary research into the lost-sales case has achieved promising results: under the assumptions that the batch size is exogenously determined and there is at most one order outstanding, the optimal inventory replenishment is characterized by a critical inventory (on-hand) level at or below which an order is placed if there is no outstanding order, and the optimal pricing decision is characterized by state-dependent price-switch levels. Such a structural property allows us to compute the optimal prices and inventory control parameters efficiently. We will extend this analysis to cases with backorders, compound Poisson demand, and multiple outstanding orders. Moreover, we will also develop heuristic methods that can be evaluated exactly in special cases and assessed using bounds, in addition to being easy to compute and implement.The PI have been working on pricing and inventory control problems for the past several years. Equally importantly, the PI and Co-I have recently been engaged in developing related models, which offers a fresh direction for taking up the challenges proposed here.