Using column generation to solve parallel machine scheduling problems with minmax objective functions

• Published in: Journal of scheduling Vol. 15; no. 6; pp. 801 - 810
• Main Authors: van den Akker, J. M., Hoogeveen, J. A., van Kempen, J. W.
• Format: Journal Article
• Language: English
• Published: Boston Springer US 01.12.2012; Springer Science + Business Media; Springer Nature B.V
• Subjects: Algorithms; Artificial Intelligence; Business and Management; Calculus of Variations and Optimal Control; Optimization; Deadlines; Decision analysis; Employment; Feasibility; Job shops; Lateness; Linear programming; Lower bounds; Mathematical analysis; Mathematical models; Operations Research/Decision Theory; Optimization; Precedence constraints; Production scheduling; Release dates; Schedules; Scheduling; Strategy; Studies; Supply Chain Management; Precedence constraints; Column generation; Release dates; Time-indexed formulation; Maximum lateness
• ISSN: 1094-6136; 1099-1425
• DOI: 10.1007/s10951-010-0191-z

In this paper we consider the parallel machine scheduling problem of minimizing an objective function of the minmax type, like maximum lateness, subject to release dates, deadlines, and/or generalized precedence constraints. We use a destructive strategy to compute a lower bound. Here we test the feasibility of a decision problem by applying column generation to compute a bound on the number of machines that we need to feasibly accommodate all jobs. After having derived the lower bound, we try to find a matching upper bound by identifying a feasible schedule with objective function value equal to this lower bound. Our computational results show that our lower bound is so strong that this is almost always possible. We are able to solve problems with up to 160 jobs and 10 machines in 10 minutes on average.