Joint optimization of lot-sizing and pricing with backlogging

Lot-sizing and pricing are two important manufacturing decisions that impact together the profit of a company. Existing works address the joint lot-sizing and pricing problem without backlogging, although it is a usual strategy that permits to satisfy customer demand with delay. In this work, we study a new multi-product joint lot-sizing and pricing problem with backlogging and limited production capacity. The objective is to maximize the total company profit over a finite planning horizon. For the problem, a mixed integer nonlinear programming (MINLP) formulation is given. Then, several optimality properties are provided and a tighter MINLP model is established based on these properties. According to the NP-hard nature and non-linearity of the model, a model based heuristic that focuses on efficiently solving small-sized instances is proposed and a genetic algorithm (GA) with new progressive repair strategy is developed to address large-sized instances. Managerial insights are drawn based an illustrative example. Numerical experiments are conducted on 64 benchmark based instances and 105 randomly generated instances with up to 10 products and 12 periods, which validates the MINLP formulation and shows the efficiency of the proposed solution methods.