Joint dynamic pricing decisions and operations planning

Alejandro Llamas, Neoma Business School, Rouen

We consider a firm whose goal is to set the price of a product for a specific period while organizing the day-to-day activities. In this context, we focus on two problems. First, we address the joint dynamic pricing and lot-sizing problem when firms operate in a competitive environment. Bearing in mind that a dynamic pricing strategy is successful when customers understand it, we assume each firm selects prices from a discrete set. The problem corresponds to a Bertrand model, so the pricing strategies of the firms should constitute a Nash equilibrium. Given the combinatorial nature of the decisions, computing the equilibrium in a tractable time may not be feasible for larger instances. In order to compute the equilibrium efficiently, we propose a framework consisting of solving iteratively Mixed Integer Programming formulations. The framework reduces the complexity of the problem by using the fact that pricing and inventory planning remain stable to marginal variations in competitors’ prices. Secondly, we address the Dynamic Pricing for Multi-period Home Delivery problem, where a firm that delivers goods (or provides service) to a set customers located in an urban area. When a customer requests a delivery, the firm charges a price based on the geographical location, the available capacity and the lead-time of the delivery. Since customers and firms agree on the lead-time of the delivery, the problem for the firm consists of setting prices for deliveries in a rolling-horizon. The problem suffers from the "curse of dimensionality", thus we propose heuristic approaches for obtaining efficient solutions.