Logic Inference and a Decomposition Algorithm for the Resource-Constrained Scheduling of Testing Tasks in Development of New Pharmaceuticals and Agrochemicals

In highly regulated industries, such as agrochemical and pharmaceutical, new products have to pass a number of regulatory tests related to safety, efficacy, and environmental impact to gain FDA approval. If a product fails one of these tests it cannot enter the market place and the investment in previous tests is wasted. Depending on the nature of the products, testing may last up to 15 years, and their scheduling should be made with the goal of minimizing the time to market and the cost of the testing. Maravelias and Grossmann (2001) proposed a mixed-integer linear program that considers a set of candidate products for which their cost, duration and probability of success of the tests is given, as well as their potential income. Furthermore, there are limited resources in terms of laboratories and number of technicians. If needed, a test may be outsourced at a higher cost. The major decisions in the model are (i) the assignment of resources to testing tasks, and (ii) the sequencing and timing of tests. The objective is to maximize the net present value. The mixed-integer linear program can become very expensive for solving real world problems (2-10 products and 50-200 tests). In order to improve the linear programming relaxation, we propose the use of logic cuts that are derived from implied precedences that arise in the graphs of the corresponding schedules. The solution of a single large-scale problem is avoided with a heuristic decomposition algorithm that relies on solving a reduced mixed-integer program that embeds the optimal schedules obtained for the individual products. It is shown that a tight upper bound can be easily determined for this decomposition algorithm. On a set of test problems the proposed algorithm is shown to be one or two orders of magnitude faster than the full space method, yielding solutions that are optimal or near optimal. Introduction The problem of selecting, testing and launching new agrochemical and pharmaceutical products (RobbinsRoth, 2001) has been studied by several authors recently. Schmidt and Grossmann (1996) proposed various MILP optimization models for the case where no resource constraints are considered. The basic idea in this model is to use a discretization scheme in order to induce linearity in the cost of testing. Jain and Grossmann (1999) extended these models to account for resource constraints. Honkomp et. al. (1997) addressed the problem of scheduling R&D projects, which is very similar to the one of scheduling testing tasks for new products. Subramanian et. al. (2001) proposed a simulation-optimization framework that takes into account uncertainty in duration, cost and resource requirements. Maravelias and Grossmann (2001) proposed an MILP model that integrates the scheduling of tests with the design and production planning decisions. Schmidt et. al. (1998) solved an industrial scale problem with one product that must undergo 65 tests, without taking into account resource constraints. If resource constraints are taken into account and more than one product are to be tested, real world problems are hard to solve. ∗ Author to whom correspondence should be addressed. E-mail: [email protected], Phone: 412-268-2230