Joint dynamic pricing and lot-sizing under competition

We study 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.