Joint pricing and lot-sizing problem with variable capacity

This paper presents an extension to the classical capacitated lot-sizing problem. Demand for the products is price-dependent and modelized as an isoelastic function. The capacity is not considered as a parameter anymore, it becomes a decision variable for the company as the production, inventory and pricing decisions. This variable capacity leads to two variants of the problem: one with a time-dependent capacity and the other one a uniform capacity over the periods. We propose heuristic methods, which are based on Lagrangian multipliers, to solve variations of the problem. The methods provide high-quality results.