Time-Indexed Formulations for Machine Scheduling Problems: Column Generation

Time-indexed formulations for machine scheduling problems have received a great deal of attention; not only do the linear programming relaxations provide strong lower bounds, but they are good guides for approximation algorithms as well. Unfortunately, time-indexed formulations have one major disadvantage: their size. Even for relatively small instances the number of constraints and the number of variables can be large. In this paper, we discuss how Dantzig-Wolfe decomposition techniques can be applied to alleviate, at least partly, the difficulties associated with the size of time-indexed formulations. In addition we show that the application of these techniques still allows the use of cut generation techniques. Key words: scheduling, time-indexed formulation, Dantzig-Wolfe decomposition, column generation March 1996 Revised November 1997 1 The research was carried out while the author was at Eindhoven University of Technology. 2 Supported by NSF Grant DMI-9410102 1 

• Type: Journal
• Year: 2000
• Where: INFORMS
• Authors: Marjan van den Akker, Cor A. J. Hurkens, Martin W. P. Savelsbergh
• Keywords: Dantzig-wolfe Decomposition, INFORMS 2000, Strong Lower Bounds, Time-indexed Formulation