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

Abstract

To stay ahead of their competition, pharmaceutical firms must make effective use of their new product development (NPD) 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 404 G. Blau et al.LD heuristics also yield makespan reductions of over 30% over the Reward-Risk priority rule.

A survey of variants and extensions of the resource-constrained project scheduling problem

“…Recent papers on this problem class include Alcaraz et al [6], Bouleimen and Lecocq [25], Hartmann [79], Jarboui et al [94], Józefowska et al [97],Özdamar [145] and Pesch [149] while Varma et al [187] discuss a multi-mode problems without nonrenewable resources. Multi-mode problems with generalized precedence constraints have been considered by Barrios et al [14], Brucker and Knust [30], Calhoun et al [34], de Reyck and Herroelen [47], Drexl et al [64], Heilmann [82,83], Nonobe and Ibaraki [141], and Sabzehparvar and Seyed-Hosseini [156] (see also Section 3).…”

“…In the notation of Brucker et al [31], the objective to optimize the NPV is represented by ∑ c F j β C j for γ, where c F j is the cash flow of activity j and β is the discount factor. Furthermore, NPV objectives have been investigated for the multi-mode RCPSP (see Ulusoy et al [176], Varma et al [187], and Waligóra [190]), the resource investment problem (see Najafi and Niaki [131]), and the RCPSP with minimal and maximal time lags (see Neumann and Zimmermann [135,137]). Icmeli and Rom [92] employ the NPV objective in a problem with continuous activity durations and time-dependent resource capacities.…”

An Entropy-Based Upper Bound Methodology for Robust Predictive Multi-Mode RCPSP Schedules

“…Varma et al [25] considered a multi-mode problem without nonrenewable resources. Multi-mode problems with generalized precedence constraints have been considered by De Reyck and Herroelen [26], Drexl et al [21], Heilmann [27,28], Nonobe and Ibaraki [29], Brucker and Knust [30], Calhoun et al [31], Sabzehparvar and Seyed-Hosseini [32] and Barrios et al [33].…”

“…Icmeli-Tuckel and Rom [59] employed the NPV objective in a problem with continuous activity durations and time-dependent resource capacities. More examples of NPV maximization in MRCPSP can be found in Ulusoy et al [60], Varma et al [25], and Waligóra [61]. Chen and Chyu [62] maximized NPV by using a hybrid of branch-and-bound and memetic algorithm.…”

The campaign and lot size scheduling problem: a modification of the Economic Lot Scheduling Problem for the pharmaceutical industry

“…The paper focuses on modelling the post production hold time and its effect on lot sizes across this two stage chain given lost sizes in each stage are directly correlated. Verma et al (2007) studies the scheduling problem of the testing, manufacturing and process development activities on limited physical resources in pharmaceutical manufacturing. They proposed effective Lagarangian decomposition heuristics to exploit the solutions to these problems of high complexity.…”