Stability polyhedra of optimal permutation of jobs servicing
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Consideration was given to minimization of the sum of weighted instants of completing servicing of n customers by a single server, provided that the duration of jobs servicing may assume any real value from a given numerical interval. An algorithm of complexity O(n) was developed to construct a polyhedron (parallelepiped) of the optimality of permutation of servicing of n jobs that is contained in the domain of stability of the same permutation and comprises the polyhedron of its stability. For the randomly generated problems, experimental comparison was carried out of the dimensions and relative volumes of the optimality polyhedra and stability of the optimal permutation of servicing n jobs under randomly generated scenarios.
KeywordsRemote Control Optimal Schedule Uncertain Data Deterministic Problem Stability Radius
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- 1.Sotskov, Yu.N. and Sotskova, N.Yu., Teoriya raspisanii. Sistemy s neopredelennymi chislovymi parametrami (Schedule Theory. Systems with Uncertain Numerical Parameters), Minsk: Ob”ed. Inst. Probl. Informatiki Nats. Akad. Nauk Belarusi, 2004.Google Scholar
- 2.Sotskov, Y.N., Tanaev, V.S., and Werner, F., Stability Radius of an Optimal Schedule: A Survey and Recent Developments, in Ind. Appl. Combinat. Optim., Boston: Kluwer, 1998, pp. 72–108.Google Scholar
- 3.Sotskov, Yu.N., Egorova, N.G., Lai, T.-C., and Werner, F., The Stability Box in Interval Data for Minimizing the Sum of Weighted Completion Times, in SIMULTECH 2011: Proc. Int. Conf. Simulat. Model. Method., Technol. Appl., Noordwijkerhout, Netherlands, July 29–31, 2011, pp. 14–23.Google Scholar
- 4.Egorova, N.G., Sotskov, Yu.N., and Kosenkov, A.A., Permutation with the Greatest Stability Parallelepiped for Servicing Interval-duration Jobs, Informatika, 2012, no. 4, pp. 69–80.Google Scholar
- 20.Egorova, N.G. and Sotskov, Yu.N., Minmization of the Sum of Weighted Instants of Completion of Job Servicing with Interval Duration, Informatika, 2008, no. 3, pp. 5–16.Google Scholar