Joint Pricing and Production Planning of Multi-period Multi-product Systems with Uncertainty in Demand

In this paper, we present a multiperiod model for production planning in a make-to-stock manufacturing system with constant pricing under uncertainty. We consider a multiproduct capacitated setting and introduce a demand-based model where the demand is a function of the price. There is an assumption that the production setup costs are negligible. A key part of the model is that the uncertain price / demand function is chosen from a discrete set of scenarios. As a result of this, the problem becomes a non linear programming problem with the nonlinearities only in the objective function. We develop a robust optimization model for this problem that considers the optimality and feasibility of all scenarios. The robust solution is obtained by solving a series of nonlinear programming problems. We illustrate our methodology with detailed numerical examples