Production planning with price-dependent supply capacity

We consider a production planning problem in which a producer procures an input component for production by offering a price to suppliers. The available supply quantity for the production input depends on the price the producer offers, and this supply level constrains production output. The producer seeks to meet a set of demands over a finite horizon at a minimum cost, including component procurement costs. We model the problem as a discrete-time production and component supply–pricing planning problem with nonstationary costs, demands, and component supply levels. This leads to a two-level lot-sizing problem with an objective function that is neither concave nor convex. Although the most general version of the problem is NP-hard, we provide polynomial-time algorithms for two special cases of the model under particular assumptions on the cost structure. We then apply the resulting algorithms heuristically to the more general problem version and provide computational results that demonstrate the high performance quality of the resulting heuristic solution methods