A mixed integer programming model for stochastic scheduling in new product development

This paper presents a new, real-world scheduling problem concerning the New Product Development process of an agricultural chemical or pharmaceutical company. A Research and Development (R&D) department must schedule the tasks needed to bring a new product to market, in the face of uncertainty about the costs and durations of the tasks, and in the income resulting from introducing the new product. There is a risk that a product will fail a mandatory task, such as an environmental or safety test, and never reach the market. The objective of the schedule is to maximize the expected Net Present Value of the research. A model of this problem initially has a nonlinear, nonconvex objective. The objective is convexified and linearized by appropriate transformations, giving a Mixed Integer Linear Program (MILP). The model uses a continuous time representation and discrete distributions for the stochastic parameters. Different representations of the disjunctive scheduling constraints are discussed. A small numerical example is presented, followed by some conclusions.