Lagrangian heuristics for scheduling new product development projects in the pharmaceutical industry

To stay ahead of their competition, pharmaceutical firms must make effective use of their new product development capabilities by efficiently allocating its analytical, clinical testing and manufacturing resources across various drug development projects. The resulting project scheduling problems involve coordinating hundreds of testing and manufacturing activities over a period of several quarters. Most conventional integer programming approaches are computationally impractical for problems of this size, while priority rule-driven heuristics seldom provide consistent solution quality. We propose a Lagrangian decomposition (LD) heuristic that exploits the special structure of these problems. Some resources (typically manpower) are shared across all on-going projects while others (typically equipment) are specific to individual project categories. Our objective function is a weighted discounted cost expressed in terms of activity completion times. The LD heuristics were subjected to a comprehensive experimental study based on typical operational instances. While the conventional ‘Reward–Risk’ priority rule heuristic generates duality gaps between 47–58%, the best LD heuristic achieves duality gaps between 10–20%. The LD heuristics also yield makespan reductions of over 30% over the Reward–Risk priority rule.