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2015 | OriginalPaper | Buchkapitel

An Exact and a Hybrid Approach for a Machine Scheduling Problem with Job Splitting

verfasst von : Luís Florêncio, Carina Pimentel, Filipe Alvelos

Erschienen in: Operational Research

Verlag: Springer International Publishing

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Abstract

The unrelated parallel machine scheduling problem with job splitting and setup times is addressed in this paper.
A time-indexed integer programming formulation of the problem to minimize a weighted function of the processing occurring both before and after jobs’ due dates is proposed. Moreover, we apply to a suitable decomposition of the integer programming model a recently proposed framework for decomposable integer programming/combinatorial optimization problems (SearchCol, meta-heuristic search by column generation) based on the combination of column generation and meta-heuristics.
A problem specific heuristic to use in the column generation component of the SearchCol is developed. To evaluate the effectiveness of the models and the proposed algorithms, computational tests are performed.

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Literatur
1.
Zurück zum Zitat Allahverdi, A., Gupta, J.N., Aldowaisan, T.: A review of scheduling research involving setup considerations. Omega 27(2), 219–239 (1999)CrossRef Allahverdi, A., Gupta, J.N., Aldowaisan, T.: A review of scheduling research involving setup considerations. Omega 27(2), 219–239 (1999)CrossRef
2.
Zurück zum Zitat Allahverdi, A., Ng, C., Cheng, T., Kovalyov, M.: A survey of scheduling problems with setup times or costs. Eur. J. Oper. Res. 187(3), 985–1032 (2008)MATHMathSciNetCrossRef Allahverdi, A., Ng, C., Cheng, T., Kovalyov, M.: A survey of scheduling problems with setup times or costs. Eur. J. Oper. Res. 187(3), 985–1032 (2008)MATHMathSciNetCrossRef
3.
Zurück zum Zitat Alvelos, F., Sousa, A., Santos, D.: Combining column generation and metaheuristics. In: Talbi, E.G. (ed.) Hybrid Metaheuristics. Studies in Computational Intelligence, vol. 434, pp. 285–334. Springer, Berlin/Heidelberg (2013)CrossRef Alvelos, F., Sousa, A., Santos, D.: Combining column generation and metaheuristics. In: Talbi, E.G. (ed.) Hybrid Metaheuristics. Studies in Computational Intelligence, vol. 434, pp. 285–334. Springer, Berlin/Heidelberg (2013)CrossRef
4.
Zurück zum Zitat Blum, C., Puchinger, J., Raidl, G.R., Roli, A.: Hybrid metaheuristics in combinatorial optimization: a survey. Appl. Soft Comput. 11(6), 4135–4151 (2011)CrossRef Blum, C., Puchinger, J., Raidl, G.R., Roli, A.: Hybrid metaheuristics in combinatorial optimization: a survey. Appl. Soft Comput. 11(6), 4135–4151 (2011)CrossRef
5.
Zurück zum Zitat Chen, J.F.: Scheduling on unrelated parallel machines with sequence-and machine-dependent setup times and due-date constraints. Int. J. Adv. Manuf. Technol. 44(11), 1204–1212 (2009)CrossRef Chen, J.F.: Scheduling on unrelated parallel machines with sequence-and machine-dependent setup times and due-date constraints. Int. J. Adv. Manuf. Technol. 44(11), 1204–1212 (2009)CrossRef
6.
Zurück zum Zitat Chen, J.F., Wu, T.H.: Total tardiness minimization on unrelated parallel machine scheduling with auxiliary equipment constraints. Omega 34(1), 81–89 (2006)CrossRef Chen, J.F., Wu, T.H.: Total tardiness minimization on unrelated parallel machine scheduling with auxiliary equipment constraints. Omega 34(1), 81–89 (2006)CrossRef
7.
Zurück zum Zitat Dantzig, G., Wolfe, P.: Decomposition principle for linear programs. Oper. Res. 8, 101–111 (1960)MATHCrossRef Dantzig, G., Wolfe, P.: Decomposition principle for linear programs. Oper. Res. 8, 101–111 (1960)MATHCrossRef
8.
Zurück zum Zitat Desaulniers, G., Desrosiers, J., Solomon, M.: Column Generation, vol. 5. Springer, New York (2005)MATHCrossRef Desaulniers, G., Desrosiers, J., Solomon, M.: Column Generation, vol. 5. Springer, New York (2005)MATHCrossRef
9.
Zurück zum Zitat Desrosiers, J., Lübbecke, M.: A primer in column generation. In: Column Generation, pp. 1–32. Springer, New York (2005) Desrosiers, J., Lübbecke, M.: A primer in column generation. In: Column Generation, pp. 1–32. Springer, New York (2005)
10.
Zurück zum Zitat Fanjul-Peyro, L., Ruiz, R.: Scheduling unrelated parallel machines with optional machines and jobs selection. Comput. Oper. Res. 39, 1745–1753 (2012)MATHMathSciNetCrossRef Fanjul-Peyro, L., Ruiz, R.: Scheduling unrelated parallel machines with optional machines and jobs selection. Comput. Oper. Res. 39, 1745–1753 (2012)MATHMathSciNetCrossRef
11.
Zurück zum Zitat Florêncio, L.: A searchcol algorithm for the unrelated parallel machine scheduling problem with job splitting. Master’s thesis, Universidade do Minho (2013) Florêncio, L.: A searchcol algorithm for the unrelated parallel machine scheduling problem with job splitting. Master’s thesis, Universidade do Minho (2013)
12.
Zurück zum Zitat ILOG: IBM ILOG CPLEX Optimization Studio V12.2 (2010) ILOG: IBM ILOG CPLEX Optimization Studio V12.2 (2010)
13.
Zurück zum Zitat Kim, D.W., Kim, K.H., Jang, W., Frank Chen, F.: Unrelated parallel machine scheduling with setup times using simulated annealing. Robot. Comput.-Integr. Manuf. 18(3), 223–231 (2002)CrossRef Kim, D.W., Kim, K.H., Jang, W., Frank Chen, F.: Unrelated parallel machine scheduling with setup times using simulated annealing. Robot. Comput.-Integr. Manuf. 18(3), 223–231 (2002)CrossRef
14.
Zurück zum Zitat Kim, Y., Shim, S., Kim, S., Choi, Y., Yoon, H.: Parallel machine scheduling considering a job-splitting property. Int. J. Prod. Res. 42(21), 4531–4546 (2004)MATHCrossRef Kim, Y., Shim, S., Kim, S., Choi, Y., Yoon, H.: Parallel machine scheduling considering a job-splitting property. Int. J. Prod. Res. 42(21), 4531–4546 (2004)MATHCrossRef
15.
Zurück zum Zitat Lee, J.H., Yu, J.M., Lee, D.H.: A tabu search algorithm for unrelated parallel machine scheduling with sequence- and machine-dependent setups: minimizing total tardiness. Int. J. Adv. Manuf. Technol. 69(9–12), 2081–2089 (2013)CrossRef Lee, J.H., Yu, J.M., Lee, D.H.: A tabu search algorithm for unrelated parallel machine scheduling with sequence- and machine-dependent setups: minimizing total tardiness. Int. J. Adv. Manuf. Technol. 69(9–12), 2081–2089 (2013)CrossRef
16.
Zurück zum Zitat Liaw, C.F., Lin, Y.K., Cheng, C.Y., Chen, M.: Scheduling unrelated parallel machines to minimize total weighted tardiness. Comput. Oper. Res. 30(12), 1777–1789 (2003)MATHMathSciNetCrossRef Liaw, C.F., Lin, Y.K., Cheng, C.Y., Chen, M.: Scheduling unrelated parallel machines to minimize total weighted tardiness. Comput. Oper. Res. 30(12), 1777–1789 (2003)MATHMathSciNetCrossRef
17.
Zurück zum Zitat Lin, Y., Pfund, M., Fowler, J.: Heuristics for minimizing regular performance measures in unrelated parallel machine scheduling problems. Comput. Oper. Res. 38, 901–9016 (2011)MATHMathSciNetCrossRef Lin, Y., Pfund, M., Fowler, J.: Heuristics for minimizing regular performance measures in unrelated parallel machine scheduling problems. Comput. Oper. Res. 38, 901–9016 (2011)MATHMathSciNetCrossRef
18.
Zurück zum Zitat Logendran, R., Subur, F.: Unrelated parallel machine scheduling with job splitting. IIE Trans. 36(4), 359–372 (2004)CrossRef Logendran, R., Subur, F.: Unrelated parallel machine scheduling with job splitting. IIE Trans. 36(4), 359–372 (2004)CrossRef
19.
Zurück zum Zitat Logendran, R., McDonell, B., Smucker, B.: Scheduling unrelated parallel machines with sequence-dependent setups. Comput. Oper. Res. 34(11), 3420–3438 (2007)MATHMathSciNetCrossRef Logendran, R., McDonell, B., Smucker, B.: Scheduling unrelated parallel machines with sequence-dependent setups. Comput. Oper. Res. 34(11), 3420–3438 (2007)MATHMathSciNetCrossRef
20.
Zurück zum Zitat Lopes, M.P., Carvalho, J.d.: A branch-and-price algorithm for scheduling parallel machines with sequence dependent setup times. Eur. J. Oper. Res. 176(3), 1508–1527 (2007) Lopes, M.P., Carvalho, J.d.: A branch-and-price algorithm for scheduling parallel machines with sequence dependent setup times. Eur. J. Oper. Res. 176(3), 1508–1527 (2007)
21.
Zurück zum Zitat Nait, T.D., 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 Nait, T.D., 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
22.
Zurück zum Zitat Park, T., Lee, T., Kim, C.O.: Due-date scheduling on parallel machines with job splitting and sequence-dependent major/minor setup times. Int. J. Adv. Manuf. Technol. 59(1), 325–333 (2012)CrossRef Park, T., Lee, T., Kim, C.O.: Due-date scheduling on parallel machines with job splitting and sequence-dependent major/minor setup times. Int. J. Adv. Manuf. Technol. 59(1), 325–333 (2012)CrossRef
23.
Zurück zum Zitat Pfund, M., Fowler, J.W., Gupta, J.N.: A survey of algorithms for single and multi-objective unrelated parallel-machine deterministic scheduling problems. J. Chin. Inst. Ind. Eng. 21(3), 230–241 (2004) Pfund, M., Fowler, J.W., Gupta, J.N.: A survey of algorithms for single and multi-objective unrelated parallel-machine deterministic scheduling problems. J. Chin. Inst. Ind. Eng. 21(3), 230–241 (2004)
24.
Zurück zum Zitat Pinedo, M.L.: Scheduling: Theory, Algorithms, and Systems, 2nd edn. Springer, New York (2002) Pinedo, M.L.: Scheduling: Theory, Algorithms, and Systems, 2nd edn. Springer, New York (2002)
26.
Zurück zum Zitat Rocha, P., Ravetti, M., Mateus, G., Pardalos, P.: Exact algorithms for a scheduling problem with unrelated parallel machines and sequence and machine-dependent setup times. Comput. Oper. Res. 35(4), 1250–1264 (2008)MATHMathSciNetCrossRef Rocha, P., Ravetti, M., Mateus, G., Pardalos, P.: Exact algorithms for a scheduling problem with unrelated parallel machines and sequence and machine-dependent setup times. Comput. Oper. Res. 35(4), 1250–1264 (2008)MATHMathSciNetCrossRef
27.
Zurück zum Zitat Rodriguez, F.J., Lozano, M., Blum, C., García-Martínez, C.: Exact algorithms for a scheduling problem with unrelated parallel machines and sequence and machine-dependent setup times. Comput. Oper. Res. 40, 1829–1841 (2013)MathSciNetCrossRef Rodriguez, F.J., Lozano, M., Blum, C., García-Martínez, C.: Exact algorithms for a scheduling problem with unrelated parallel machines and sequence and machine-dependent setup times. Comput. Oper. Res. 40, 1829–1841 (2013)MathSciNetCrossRef
28.
Zurück zum Zitat Sarıçiçek, İ., Çelik, C.: Two meta-heuristics for parallel machine scheduling with job splitting to minimize total tardiness. Appl. Math. Model. 35(8), 4117–4126 (2011)MATHMathSciNetCrossRef Sarıçiçek, İ., Çelik, C.: Two meta-heuristics for parallel machine scheduling with job splitting to minimize total tardiness. Appl. Math. Model. 35(8), 4117–4126 (2011)MATHMathSciNetCrossRef
29.
Zurück zum Zitat Shim, S.O., Kim, Y.D.: Minimizing total tardiness in an unrelated parallel-machine scheduling problem. J. Oper. Res. Soc. 58(3), 346–354 (2006)MathSciNetCrossRef Shim, S.O., Kim, Y.D.: Minimizing total tardiness in an unrelated parallel-machine scheduling problem. J. Oper. Res. Soc. 58(3), 346–354 (2006)MathSciNetCrossRef
30.
Zurück zum Zitat Shim, S., Kim, Y.: A branch and bound algorithm for an identical parallel machine scheduling problem with a job splitting property. Comput. Oper. Res. 35(3), 863–875 (2008)MATHMathSciNetCrossRef Shim, S., Kim, Y.: A branch and bound algorithm for an identical parallel machine scheduling problem with a job splitting property. Comput. Oper. Res. 35(3), 863–875 (2008)MATHMathSciNetCrossRef
31.
Zurück zum Zitat Talbi, E.G.: Hybrid Metaheuristics. Studies in Computational Intelligence, vol. 434. Springer, Berlin/Heidelberg (2013) Talbi, E.G.: Hybrid Metaheuristics. Studies in Computational Intelligence, vol. 434. Springer, Berlin/Heidelberg (2013)
32.
Zurück zum Zitat Unlu, Y., Mason, S.: Evaluation of mixed integer programming formulations for non-preemptive parallel machine scheduling problems. Comput. Ind. Eng. 58(4), 785–800 (2010)CrossRef Unlu, Y., Mason, S.: Evaluation of mixed integer programming formulations for non-preemptive parallel machine scheduling problems. Comput. Ind. Eng. 58(4), 785–800 (2010)CrossRef
33.
Zurück zum Zitat Vallada, E., Ruiz, R.: A genetic algorithm for the unrelated parallel machine scheduling problem with sequence dependent setup times. Eur. J. Oper. Res. 211(3), 612–622 (2011)MathSciNetCrossRef Vallada, E., Ruiz, R.: A genetic algorithm for the unrelated parallel machine scheduling problem with sequence dependent setup times. Eur. J. Oper. Res. 211(3), 612–622 (2011)MathSciNetCrossRef
34.
Zurück zum Zitat Wang, W.L., Wang, H.Y., Zhao, Y.W., Zhang, L.P., Xu, X.L.: Parallel machine scheduling with splitting jobs by a hybrid differential evolution algorithm. Comput. Oper. Res. 40(5), 1196–1206 (2013)MathSciNetCrossRef Wang, W.L., Wang, H.Y., Zhao, Y.W., Zhang, L.P., Xu, X.L.: Parallel machine scheduling with splitting jobs by a hybrid differential evolution algorithm. Comput. Oper. Res. 40(5), 1196–1206 (2013)MathSciNetCrossRef
35.
36.
Zurück zum Zitat Yalaoui, F., Chu, C.: An efficient heuristic approach for parallel machine scheduling with job splitting and sequence-dependent setup times. IIE Trans. 35(2), 183–190 (2003)CrossRef Yalaoui, F., Chu, C.: An efficient heuristic approach for parallel machine scheduling with job splitting and sequence-dependent setup times. IIE Trans. 35(2), 183–190 (2003)CrossRef
37.
Zurück zum Zitat Yang, W.H.: Survey of scheduling research involving setup times. Int. J. Syst. Sci. 30(2), 143–155 (1999)MATHCrossRef Yang, W.H.: Survey of scheduling research involving setup times. Int. J. Syst. Sci. 30(2), 143–155 (1999)MATHCrossRef
38.
Zurück zum Zitat Zhu, Z., Heady, R.: Minimizing the sum of earliness/tardiness in multi-machine scheduling: a mixed integer programming approach. Comput. Ind. Eng. 38(2), 297–305 (2000)CrossRef Zhu, Z., Heady, R.: Minimizing the sum of earliness/tardiness in multi-machine scheduling: a mixed integer programming approach. Comput. Ind. Eng. 38(2), 297–305 (2000)CrossRef
Metadaten
Titel
An Exact and a Hybrid Approach for a Machine Scheduling Problem with Job Splitting
verfasst von
Luís Florêncio
Carina Pimentel
Filipe Alvelos
Copyright-Jahr
2015
DOI
https://doi.org/10.1007/978-3-319-20328-7_12

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