A bilinear reduction based algorithm for solving capacitated multi-item dynamic pricing problems

In a capacitated multi-item dynamic pricing problem one maximizes the profit by choosing a proper production level as well as pricing policy, where the latter depends on a satisfied demand. The objective function involves inventory, production and setup costs, and revenue functions. The products are required to satisfy joined production capacities. We consider a bilinear reduction of the linear mixed integer formulation of the problem and prove that the problem is equivalent to finding a global maximum of the bilinear problem. A heuristic algorithm is proposed, based on the reduction technique. Numerical experiments confirm the efficiency of the proposed technique.