Abstract
We consider a version of the total flow time single machine scheduling problem where uncertainty about processing times is taken into account. Namely an interval of equally possible processing times is considered for each job, and optimization is carried out according to a robustness criterion. We propose the first mixed integer linear programming formulation for the resulting optimization problem and we explain how some known preprocessing rules can be translated into valid inequalities for this formulation. Computational results are finally presented.
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Altin, A., Amaldi, E., Belotti, P., Pinar, M.: Provisioning virtual private networks under traffic uncertainty. Networks (to appear)
Ambühl, C., Mastrolilli, M.: Single machine precedence constrained scheduling is a vertex cover problem. In: Proceedings of the 14th Annual European Symposium on Algorithms (ESA) (to appear)
Carpaneto, G., Martello, S., Toth, P.: Algorithms and codes for the assignment problem. Ann. Oper. Res. 7, 200–218 (1988)
Daniels, R., Kouvelis, P.: Robust scheduling to hedge against processing time uncertainty in single-stage production. Manag. Sci. 41(2), 363–376 (1995)
Dongarra, J.: Performance of various computers using standard linear algebra software in a fortran environment. Tech. Rep. CS-89-85, University of Tennessee (2006)
Graham, R., Lawler, E., Lenstra, J., Kan, A.R.: Optimization and approximation in deterministic sequencing and scheduling: A survey. Ann. Discrete Math. 5, 287–326 (1979)
Kasperski, A., Zieliński, P.: An approximation algorithm for interval data min-max regret combinatorial optimization problems. Inf. Process. Lett. 97(5), 177–180 (2006)
Kouvelis, P., Yu, G.: Robust Discrete Optimization and Its Applications. Kluwer, Massachusetts (1997)
Lawler, E.: Combinatorial Optimization: Networks and Matroids. Holt, Rinehart and Winston, New York (1976)
Pinedo, M., Schrage, L.: Stochastic shop scheduling: A survey. In: Dempster, M.A.H., et al. (eds.) Deterministic and Stochastic Scheduling. Reidel, Dordrecht (1982)
Smith, W.: Various optimizers for single-stage production. Nav. Res. Logist. Q. 3, 59–66 (1956)
Yaman, H.: Essays on some combinatorial optimization problems with interval data. Master’s thesis, Department of Industrial Engineering, Bilkent University (1999)
Yaman, H., Karaşan, O., Pinar, M.: Restricted robust uniform matroid maximization under interval uncertainty. Math. Program., Ser. A (to appear)
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Work funded by the Swiss National Science Foundation through project 200020-109854/1.
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Montemanni, R. A Mixed Integer Programming Formulation for the Total Flow Time Single Machine Robust Scheduling Problem with Interval Data. J Math Model Algor 6, 287–296 (2007). https://doi.org/10.1007/s10852-006-9044-3
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DOI: https://doi.org/10.1007/s10852-006-9044-3