In this paper we report two mixed integer linear programming models to resolve the malleable jobs scheduling problem with single resource. Jobs’ release dates and deadlines are taken into account. The total amount of available resource of the system is variable at different times. Numerical experimentation is conducted to evaluate the performance variability between two introduced models. The objective of this optimization problem is to minimize the total weighted completion time.
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Atakan, S., Lulli, G., Sen, S.: An improved mip formulation for the unit commitment problem (2015)
2.
Bixby, R.E., Fenelon, M., Gu, Z., Rothberg, E., Wunderling, R.: Mixed integer programming: a progress report. The sharpest cut: The impact of Manfred Padberg and his work, MPS-SIAM Series on Optimization, vol. 4, pp. 309–326 (2004)
Blazewicz, P.D.J., Ecker, P.D.K.H., Pesch, P.D.E., Schmidt, P.D.G., Weglarz, P.D.J.: Scheduling under resource constraints. In: Scheduling Computer and Manufacturing Processes, pp. 317–365. Springer, Heidelberg (2001)
5.
Dror, M., Stern, H.I., Lenstra, J.K.: Parallel machine scheduling: processing rates dependent on number of jobs in operation. Manage. Sci.
33(8), 1001–1009 (1987)
CrossRefMATH
6.
Dutot, P.-F., Mounié, G., Trystram, D.: Scheduling parallel tasks: approximation algorithms. Handbook of Scheduling: Algorithms, Models, and Performance Analysis, pp. 1–26 (2004)
7.
Fan, L., Zhang, F., Wang, G., Liu, Z.: An effective approximation algorithm for the malleable parallel task scheduling problem. J. Parallel Distrib. Comput.
72(5), 693–704 (2012)
CrossRefMATH
8.
Hooker, J.N.: Planning and scheduling by logic-based benders decomposition. Oper. Res.
55(3), 588–602 (2007)
MathSciNetCrossRefMATH
9.
Jansen, K., Zhang, H.: Scheduling malleable tasks with precedence constraints. J. Comput. Syst. Sci.
78(1), 245–259 (2012)
MathSciNetCrossRefMATH
10.
Jedrzejowicz, P., Skakovski, A.: Population learning with differential evolution for the discrete-continuous scheduling with continuous resource discretisation. In: 2013 IEEE International Conference on Cybernetics (CYBCONF), pp. 92–97 (2013)
11.
Lima, R.M., Grossmann, I.E.: Computational advances in solving mixed integer linear programming problems (2011)
12.
Lodi, A.: 50 Years of Integer Programming 1958–2008. Mixed integer programming computation, pp. 619–645. Springer, Heidelberg (2010)
MATH
13.
Nguyen, N.-Q., Yalaoui, F., Amodeo, L., Chehade, H., Toggenburger, P.: Total completion time minimization for machine scheduling problem under time windows constraints with jobs’ linear processing rate function. Journal of Scheduling, manuscript submitted for publication (2015)
14.
Rozycki, R., Weglarz, J.: Power-aware scheduling of preemptable jobs on identical parallel processors to meet deadlines. Eur. J. Oper. Res.
218(1), 68–75 (2012)
MathSciNetCrossRefMATH
15.
Sadykov, R.: A dominant class of schedules for malleable jobs in the problem to minimize the total weighted completion time. Comput. Oper. Res.
39(6), 1265–1270 (2012)
MathSciNetCrossRefMATH
16.
Sirikum, J., Techanitisawad, A., Kachitvichyanukul, V.: A new efficient ga-benders’ decomposition method: for power generation expansion planning with emission controls. IEEE Trans. Power Syst.
22(3), 1092–1100 (2007)
CrossRef
17.
Tahar, D.N., Yalaoui, F., Chu, C., Amodeo, L.: A linear programming approach for identical parallel machine scheduling with job splitting and sequence-dependent setup times. Int. J. Prod. Econ.
99(1), 63–73 (2006)
CrossRef
18.
Yalaoui, F., Chu, C.: New exact method to solve the
\({P_{m}}/r_{j}/\sum {C_{j}}\) schedule problem. Int. J. Prod. Econ.
100(1), 168–179 (2006)
CrossRef
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Titel
Solving a Malleable Jobs Scheduling Problem to Minimize Total Weighted Completion Times by Mixed Integer Linear Programming Models
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