Solving Project Scheduling Problems by Minimum Cut Computations

• Published in: Management science Vol. 49; no. 3; pp. 330 - 350
• Main Authors: Mohring, Rolf H, Schulz, Andreas S, Stork, Frederik, Uetz, Marc
• Format: Journal Article
• Language: English
• Published: Linthicum INFORMS 01.03.2003; Institute for Operations Research and Management Sciences; Institute for Operations Research and the Management Sciences
• Series: Management Science
• Subjects: Algorithms; Approximation; Business studies; Costs; Employment; Heuristics; Industrial projects; Integer programming; Integers; Job shops; Lagrangian function; Lagrangian Relaxation; Linear programming; Linear Programming Relaxation; Management; Mathematical programming; Mathematics; Minimization of cost; Minimum Cut; Net present value; Operations research; Optimal solutions; Optimization techniques; Planning methods; Production; Production planning; Project management; Project Scheduling; Renewable resources; Resource Constraints; Scheduling; Studies; Tabu search
• ISSN: 0025-1909; 1526-5501
• DOI: 10.1287/mnsc.49.3.330.12737

In project scheduling, a set of precedence-constrained jobs has to be scheduled so as to minimize a given objective. In resource-constrained project scheduling, the jobs additionally compete for scarce resources. Due to its universality, the latter problem has a variety of applications in manufacturing, production planning, project management, and elsewhere. It is one of the most intractable problems in operations research, and has therefore become a popular playground for the latest optimization techniques, including virtually all local search paradigms. We show that a somewhat more classical mathematical programming approach leads to both competitive feasible solutions and strong lower bounds, within reasonable computation times. The basic ingredients of our approach are the Lagrangian relaxation of a time-indexed integer programming formulation and relaxation-based list scheduling, enriched with a useful idea from recent approximation algorithms for machine scheduling problems. The efficiency of the algorithm results from the insight that the relaxed problem can be solved by computing a minimum cut in an appropriately defined directed graph. Our computational study covers different types of resource-constrained project scheduling problems, based on several notoriously hard test sets, including practical problem instances from chemical production planning.