Optimal Pricing and Production Planning for Multi-product Multi-period Systems with Backorders

In this paper, we develop models for production planning with coordinated dynamic pricing. The application that motivated this research is manufacturing pricing, where the products are non-perishable assets and can be stored to fulfill the future demands. We assume that the firm does not change the price list very frequently. However, the developed model and its solution strategy have the capability to handle the general case of manufacturing systems with frequent time-varying price lists. We consider a multi-product capacitated setting and introduce a demand-based model, where the demand is a function of the price. The key parts of the model are that the planning horizon is discrete-time multi-period, and backorders are allowed. As a result of this, the problem becomes a nonlinear programming problem with the nonlinearities in both the objective function and some constraints. We develop an algorithm which computes the optimal production and pricing policy on a finite time horizon. We illustrate the application of the algorithm through a detailed numerical example.