Abstract
The goal of a scheduling problem is to find out when each task must be performed and by which machine such that an optimal solution is obtained. Especially when the main problem is to divide the jobs over the machines, column generation turns out to be very successful. Next to a number of these ‘partitioning’ problems, we shall discuss a number of other problems that have successfully been tackled by a column generation approach.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Van den Akker, J.M., Hoogeveen, J.A., and Van de Velde, S.L. (1999). Parallel machine scheduling by column generation. Operations Research, 47:862–872.
Van den Akker, J.M., Hoogeveen, J.A., and Van de Velde, S.L. (2002). Combining column generation and Lagrangean relaxation to solve a single-machine common due date problem. INFORMS Journal on Computing, 14:37–51.
Van den Akker, J.M., and Hoogeveen, J.A. (2004). Minimizing the number of tardy jobs. In: Handbook of Scheduling (J.Y.-T. Leung, ed.), Algorithms, Models, and Performance Analysis, pp. 227–243, CRC Press, Inc. Boca Raton, Fl, USA.
Van den Akker, J.M., Hurkens, C.A.J., and Savelsbergh, M.W.P. (2000). Time-indexed formulations for single-machine scheduling problems: column generation. INFORMS Journal on Computing, 12:111–124.
Baar, T., Brucker, P., and Knust S. (1998). Tabu-search algorithms and Lower bounds for the resource-constrained project scheduling problem, In: Meta-heuristics: Advances and Trends in Local Search Paradigms for Optimization, (S. Voss, S. Martello, I. Osman, and C. Roucairol, eds.), pp. 1–18, Kluwer, Dordrecht.
Baptiste, P., Le Pape, C, and Nuijten, W. (2001). Constraint-Based Scheduling: Applying Constraint Programming to Scheduling Problems. Kluwer Academic Publishers, Dordrecht, The Netherlands.
Brucker, P., Knust, S., Schoo, A., and Thiele, O. (1998). A branch-and-bound algorithm for the resource-constrained project scheduling problem. European Journal of Operational Research, 107:272–288.
Brucker, P. and Knust, S. (2000). A linear programming and constraint propagation-based lower bound for the RCPSP. European Journal of Operational Research, 127:355–362.
Brucker, P. and Knust, S. (2002). Lower bounds for scheduling a single robot in a job-shop environment. Annals of Operations Research, 115:147–172.
Brucker, P. and Knust, S. (2003). Lower bounds for resource-constrained project scheduling problems. European Journal of Operational Research, 149:302–313.
BĂ¼lbĂ¼l, K., Kaminsky, P, and Yano, C. (2001). Preemption in single-machine earliness/tardiness scheduling. Submitted to: Naval Research Logistics for publication. Department of IEOR, University of California at Berkeley.
BĂ¼lbĂ¼l, K., Kaminsky, P, and Yano, C. (2004). Flow Shop Scheduling with Earliness, Tardiness and Intermediate Inventory Holding Costs. Naval Research Logistics, 51:1–39.
Carlier, J. (1987). Scheduling jobs with release dates and tails on identical machines to minimize makespan. European Journal of Operational Research, 29:298–306.
Chen, Z.L. and Lee, C.-Y. (2002). Parallel machine scheduling with a common due window. European Journal of Operational Research, 136:512–527.
Chen, Z.L. and Powell, W.B. (1999). Solving parallel machine scheduling problems by column generation. INFORMS Journal on Computing, 11:78–94.
Chen, Z.L. and Powell, W.B. (1999). A column generation based decomposition algorithm for a parallel machine just-in-time scheduling problem. European Journal of Operational Research, 116:220–232.
Chen, Z.L. and Powell, W.B. (2003). Exact algorithms for scheduling multiple families of jobs on parallel machines. Naval Research Logistics, 50:823–840.
Graham, R.L., Lawler, E.L., Lenstra, J.K., and Rinnooy Kan A.H.G. (1979). Optimization and approximation in deterministic sequencing and scheduling: A survey. Annals of Discrete Mathematics, 5:287–326.
Hall, L.A., Schulz, A.S., Shmoys, D.B., and Wein, J. (1997). Scheduling to minimize average completion time: Off-line and on-line approximation algorithms. Mathematics of Operations Research, 22:513–544.
Klein, R. and Scholl, A. (1999). Conmputing lower bounds by destructive improvement—an application to resource-constrained project scheduling. European Journal of Operational Research, 112:322–346.
Lawler, E.L., Lenstra, J.K., Rinnooy Kan, A.H.G., and Shmoys D.B. (1993). Sequencing and scheduling: Algorithms and complexity. In: Logistics of Production and Inventory (S.C. Graves, P.H. Zipkin, and A.H.G. Rinnooy Kan, eds.), Handbooks in Operations Research and Management Science, Volume 4, pp. 445–522, North-Holland, Amsterdam.
Lawler, E.L. and Moore, J.M. (1969). A functional equation and its application to resource allocation and sequencing problems. Management Science, 16:77–84.
Lee, C.-Y. and Chen, Z.L. (2000). Scheduling jobs and maintenance activities on parallel machines. Naval Research Logistics, 47:145–165.
Potts, C.N. and Van Wassenhove, L.N. (1992). Single machine scheduling to minimize total late work. Operations Research, 40:586–595.
Smith, W.E. (1956). Various optimizers for single-stage production. Naval Research Logistics Quarterly, 3:325–333.
Vandevelde, A.M.G., Hoogeveen, J.A., Hurkens, C.A.J., and Lenstra, J.K. (2004). Lower bounds for the head-body-tail problem on parallel machines: A computational study of the multiprocessor flow shop. Forthcoming in: INFORMS Journal on Computing.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2005 Springer Science+Business Media, Inc.
About this chapter
Cite this chapter
van den Akker, M., Hoogeveen, H., van de Velde, S. (2005). Applying Column Generation to Machine Scheduling. In: Desaulniers, G., Desrosiers, J., Solomon, M.M. (eds) Column Generation. Springer, Boston, MA. https://doi.org/10.1007/0-387-25486-2_11
Download citation
DOI: https://doi.org/10.1007/0-387-25486-2_11
Publisher Name: Springer, Boston, MA
Print ISBN: 978-0-387-25485-2
Online ISBN: 978-0-387-25486-9
eBook Packages: Business and EconomicsBusiness and Management (R0)