A MIXED-INTEGER PROGRAMMING-MODEL FOR STOCHASTIC SCHEDULING IN NEW PRODUCT DEVELOPMENT

This paper presents a new, real-world scheduling problem concerning th e New Product Development process of an agricultural chemical or pharm aceutical company. A Research and Development (R&D) department must sc hedule 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 tha t a product will fail a mandatory task, such as an environmental or sa fety test, and never reach the market. The objective of the schedule i s to maximize the expected Net Present Value of the research. A model of this problem initially has a nonlinear, nonconvex objective. The ob jective is convexified and linearized by appropriate transformations, giving a Mixed Integer Linear Program (MILP). The model uses a continu ous time representation and discrete distributions for the stochastic parameters. Different representations of the disjunctive scheduling co nstraints are discussed. A small numerical example is presented, follo wed by some conclusions.