Time-Indexed Formulations for Machine Scheduling Problems: Column Generation

Authors:
J.M. Van Den Akker;C.A.J. Hurkens;M.W.P. Savelsbergh
Affiliations:
-;-;-
Venue:
INFORMS Journal on Computing
Year:
2000

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Abstract

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.