Abstract
We present an extension of the machines minimization for scheduling jobs with interval constraints, adding a limited machines workload capacity. We are motivated by the fixed-speed processors minimization problem subject to energy constraints, in which the time resolution is a critical factor for the quality of service in the system. We propose a mixed integer linear programming (MILP) model for an exact solution and explore an alternative resolution method based on a non-cooperative evolutionary theoretical-game model. Our resolution method guarantees a feasible solution to the problem and the computational experiments with a timeout of 3 minutes show that it finds a solution with a number of machines less than or equal to the number of machines for a 97,19% of instances in comparison with the MILP solution over CPLEX 12.6.1.0, in only deciseconds.
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References
Antoniadis, A., Huang, C.-C.: Non-preemptive speed scaling. Journal of Scheduling 16(4), 385–394 (2013)
Bampis, E., Letsios, D., Lucarelli, G.: Speed-scaling with no preemptions. In: Ahn, H.-K., Shin, C.-S. (eds.) ISAAC 2014. LNCS, vol. 8889, pp. 257–267. Springer, Heidelberg (2014)
Chuzhoy, J., Codenotti, P.: Resource minimization job scheduling. In: Dinur, I., Jansen, K., Naor, J., Rolim, J. (eds.) APPROX and RANDOM 2009. LNCS, vol. 5687, pp. 70–83. Springer, Heidelberg (2009)
Chuzhoy, J., Guha, S., Khanna, S., Naor, J.S.: Machine minimization for scheduling jobs with interval constraints. In: Proceedings of the 45th Annual IEEE Symposium on Foundations of Computer Science, pp. 81–90. IEEE (2004)
Cieliebak, M., Erlebach, T., Hennecke, F., Weber, B., Widmayer, P.: Scheduling with release times and deadlines on a minimum number of machines. In: Levy, J.-J., Mayr, E.W., Mitchell, J.C. (eds.) Exploring New Frontiers of Theoretical Informatics. IFIP, vol. 155, pp. 209–222. Springer, Boston (2004)
Dürr, C., Jeż, Ł., Vásquez, Ó.C.: Mechanism design for aggregating energy consumption and quality of service in speed scaling scheduling. In: Chen, Y., Immorlica, N. (eds.) WINE 2013. LNCS, vol. 8289, pp. 134–145. Springer, Heidelberg (2013)
Dürr, C., Jeż, Ł., Vásquez, O.C.: Scheduling under dynamic speed-scaling for minimizing weighted completion time and energy consumption. Discrete Applied Mathematics (2014)
Garey, M.R., Johnson, D.S.: Computers and intractability, vol. 174. Freeman, New York (1979)
Kao, M.-J., Chen, J.-J., Rutter, I., Wagner, D.: Competitive design and analysis for machine-minimizing job scheduling problem. In: Chao, K.-M., Hsu, T.-S., Lee, D.-T. (eds.) ISAAC 2012. LNCS, vol. 7676, pp. 75–84. Springer, Heidelberg (2012)
Kolen, A.W.J., Lenstra, J.K., Papadimitriou, C.H., Spieksma, F.C.R.: Interval scheduling: A survey. Naval Research Logistics (NRL) 54(5), 530–543 (2007)
Lee, S., Turner, J., Daskin, M.S., Homem-de Mello, T., Smilowitz, K.: Improving fleet utilization for carriers by interval scheduling. European Journal of Operational Research 218(1), 261–269 (2012)
Sanlaville, E., Schmidt, G.: Machine scheduling with availability constraints. Acta Informatica 35(9), 795–811 (1998)
Vásquez, Ó.C., Sepulveda, J.M., Alfaro, M.D., Osorio-Valenzuela, L.: Disaster response project scheduling problem: A resolution method based on a game-theoretical model. International Journal of Computers Communications & Control 8(2), 334–345 (2013)
Yu, G., Zhang, G.: Scheduling with a minimum number of machines. Operations Research Letters 37(2), 97–101 (2009)
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Vásquez, Ó.C., Osorio-Valenzuela, L., Quezada, F. (2015). Exploring a Resolution Method Based on an Evolutionary Game-Theoretical Model for Minimizing the Machines with Limited Workload Capacity and Interval Constraints. In: Le Thi, H., Pham Dinh, T., Nguyen, N. (eds) Modelling, Computation and Optimization in Information Systems and Management Sciences. Advances in Intelligent Systems and Computing, vol 360. Springer, Cham. https://doi.org/10.1007/978-3-319-18167-7_28
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DOI: https://doi.org/10.1007/978-3-319-18167-7_28
Publisher Name: Springer, Cham
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Online ISBN: 978-3-319-18167-7
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