How to cite this paper
Safarzadeh, H & Niaki, S. (2023). Unrelated parallel machine scheduling with machine processing cost.International Journal of Industrial Engineering Computations , 14(1), 33-48.
Refrences
Branke, J., Branke, J., Deb, K., Miettinen, K., & Slowiński, R. (Eds.). (2008). Multiobjective optimization: Interactive and evolutionary approaches (Vol. 5252). Springer Science & Business Media.
Che, A., Wu, X., Peng, J., & Yan, P. (2017). Energy-efficient bi-objective single-machine scheduling with power-down mechanism. Computers & Operations Research, 85, 172-183.
Coello, C. A. C., Lamont, G. B., & Van Veldhuizen, D. A. (2007). Evolutionary algorithms for solving multi-objective problems (Vol. 5, pp. 79-104). New York: Springer.
CPLEX 12.6.0 Manual, ILOG Reference of "Running out of memory troubleshooting" - Retrieved from .
Demir, Y., & İşleyen, S. K. (2013). Evaluation of mathematical models for flexible job-shop scheduling problems. Applied Mathematical Modelling, 37(3), 977-988.
Ding, J. Y., Song, S., & Wu, C. (2016). Carbon-efficient scheduling of flow shops by multi-objective optimization. European Journal of Operational Research, 248(3), 758-771.
Dósa, G., & Tan, Z. (2010). New upper and lower bounds for online scheduling with machine cost. Discrete Optimization, 7(3), 125-135.
Ham, A. (2017). Flexible job shop scheduling problem for parallel batch processing machine with compatible job families. Applied Mathematical Modelling, 45, 551-562.
Hasani, A., & Hosseini, S. M. H. (2020). A bi-objective flexible flow shop scheduling problem with machine-dependent processing stages: Trade-off between production costs and energy consumption. Applied Mathematics and Computation, 386, 125533.
Heydar, M., Mardaneh, E., & Loxton, R. (2022). Approximate dynamic programming for an energy-efficient parallel machine scheduling problem. European Journal of Operational Research, 302(1), 363-380.
Ho, W. H., Chiu, Y. H., & Chen, Y. J. (2018). Multi-objective Pareto adaptive algorithm for capacitated lot-sizing problems in glass lens production. Applied Mathematical Modelling, 53, 731-738.
Ji, M., Wang, J. Y., & Lee, W. C. (2013). Minimizing resource consumption on uniform parallel machines with a bound on makespan. Computers & Operations Research, 40(12), 2970-2974.
Karhi, S., & Shabtay, D. (2018). Single machine scheduling to minimise resource consumption cost with a bound on scheduling plus due date assignment penalties. International Journal of Production Research, 56(9), 3080-3096.
Karimi, S., Kwon, S., & Ning, F. (2021). Energy-aware production scheduling for additive manufacturing. Journal of Cleaner Production, 278, 123183.
Keha, A. B., Khowala, K., & Fowler, J. W. (2009). Mixed integer programming formulations for single machine scheduling problems. Computers & Industrial Engineering, 56(1), 357-367.
Kolahan, F., & Kayvanfar, V. (2009). A heuristic algorithm approach for scheduling of multi-criteria unrelated parallel machines. International Journal of Industrial and Manufacturing Engineering, 3(11), 1406-1409.
Kong, M., Pei, J., Liu, X., Lai, P. C., & Pardalos, P. M. (2020). Green manufacturing: Order acceptance and scheduling subject to the budgets of energy consumption and machine launch. Journal of Cleaner Production, 248, 119300.
Kononov, A. V., Kovalyov, M. Y., & Lin, B. M. (2019). Minimizing machine assignment costs over Δ-approximate solutions of the scheduling problem P|| Cmax. Theoretical Computer Science, 793, 70-78.
Ku, W. Y., & Beck, J. C. (2016). Mixed integer programming models for job shop scheduling: A computational analysis. Computers & Operations Research, 73, 165-173.
Lee, K., Leung, J. Y., Jia, Z. H., Li, W., Pinedo, M. L., & Lin, B. M. (2014). Fast approximation algorithms for bi-criteria scheduling with machine assignment costs. European Journal of Operational Research, 238(1), 54-64.
Leung, J. Y. T., Lee, K., & Pinedo, M. L. (2012). Bi-criteria scheduling with machine assignment costs. International Journal of Production Economics, 139(1), 321-329.
Li, K., Zhang, H. J., Cheng, B. Y., & Pardalos, P. M. (2018). Uniform parallel machine scheduling problems with fixed machine cost. Optimization Letters, 12(1), 73-86.
Li, K., Zhang, X., Leung, J. Y. T., & Yang, S. L. (2016). Parallel machine scheduling problems in green manufacturing industry. Journal of Manufacturing Systems, 38, 98-106.
Liang, P., Yang, H. D., Liu, G. S., & Guo, J. H. (2015). An ant optimization model for unrelated parallel machine scheduling with energy consumption and total tardiness. Mathematical Problems in Engineering, e907034.
Liu, Z., Lee, W. C., & Wang, J. Y. (2016). Resource consumption minimization with a constraint of maximum tardiness on parallel machines. Computers & Industrial Engineering, 97, 191-201.
Meng, L., Zhang, C., Shao, X., & Ren, Y. (2019). MILP models for energy-aware flexible job shop scheduling problem. Journal of Cleaner Production, 210, 710-723.
Mokhtari, H., & Hasani, A. (2017). An energy-efficient multi-objective optimization for flexible job-shop scheduling problem. Computers & Chemical Engineering, 104, 339-352.
Naderi, B., Gohari, S., & Yazdani, M. (2014). Hybrid flexible flowshop problems: Models and solution methods. Applied Mathematical Modelling, 38(24), 5767-5780.
Nasiri, M. M., Abdollahi, M., Rahbari, A., Salmanzadeh, N., & Salesi, S. (2018). Minimizing the energy consumption and the total weighted tardiness for the flexible flowshop using NSGA-II and NRGA. Journal of Industrial and Systems Engineering, 11(Special issue: 14th International Industrial Engineering Conference), 150-162.
Özgüven, C., Özbakır, L., & Yavuz, Y. (2010). Mathematical models for job-shop scheduling problems with routing and process plan flexibility. Applied Mathematical Modelling, 34(6), 1539-1548.
Pan, J. C. H., & Chen, J. S. (2005). Mixed binary integer programming formulations for the reentrant job shop scheduling problem. Computers & Operations Research, 32(5), 1197-1212.
Pan, R., Wang, Q., Li, Z., Cao, J., & Zhang, Y. (2022). Steelmaking-continuous casting scheduling problem with multi-position refining furnaces under time-of-use tariffs. Annals of Operations Research, 310(1), 119-151.
Pinedo, M.L. (2016). Scheduling: Theory, Algorithms, and Systems. 5th ed. 2016 edition. ed. Springer, New York.
Safarzadeh, H., & Niaki, S. T. A. (2019). Bi-objective green scheduling in uniform parallel machine environments. Journal of Cleaner Production, 217, 559-572.
Unlu, Y., & Mason, S. J. (2010). Evaluation of mixed integer programming formulations for non-preemptive parallel machine scheduling problems. Computers & Industrial Engineering, 58(4), 785-800.
Wang, H., & Alidaee, B. (2018). Unrelated parallel machine selection and job scheduling with the objective of minimizing total workload and machine fixed costs. IEEE Transactions on Automation Science and Engineering, 15(4), 1955-1963.
Wang, S., Wang, X., Chu, F., & Yu, J. (2020). An energy-efficient two-stage hybrid flow shop scheduling problem in a glass production. International Journal of Production Research, 58(8), 2283-2314.
Wei, Z., Liao, W., & Zhang, L. (2022). Hybrid energy-efficient scheduling measures for flexible job-shop problem with variable machining speeds. Expert Systems with Applications, 197, 116785.
Wu, X., & Che, A. (2019). A memetic differential evolution algorithm for energy-efficient parallel machine scheduling. Omega, 82, 155-165.
Xie, F., Xu, Z., Zhang, Y., & Bai, Q. (2015). Scheduling games on uniform machines with activation cost. Theoretical Computer Science, 580, 28-35.
Yeh, W. C., Chuang, M. C., & Lee, W. C. (2015). Uniform parallel machine scheduling with resource consumption constraint. Applied Mathematical Modelling, 39(8), 2131-2138.
Zeng, Y., Che, A., & Wu, X. (2018). Bi-objective scheduling on uniform parallel machines considering electricity cost. Engineering Optimization, 50(1), 19-36.
Zhang, L., Deng, Q., Gong, G., & Han, W. (2020). A new unrelated parallel machine scheduling problem with tool changes to minimise the total energy consumption. International Journal of Production Research, 58(22), 6826-6845.
Ziaee, M., & Sadjadi, S. J. (2007). Mixed binary integer programming formulations for the flow shop scheduling problems. A case study: ISD projects scheduling. Applied Mathematics and Computation, 185(1), 218-228.
Che, A., Wu, X., Peng, J., & Yan, P. (2017). Energy-efficient bi-objective single-machine scheduling with power-down mechanism. Computers & Operations Research, 85, 172-183.
Coello, C. A. C., Lamont, G. B., & Van Veldhuizen, D. A. (2007). Evolutionary algorithms for solving multi-objective problems (Vol. 5, pp. 79-104). New York: Springer.
CPLEX 12.6.0 Manual, ILOG Reference of "Running out of memory troubleshooting" - Retrieved from .
Demir, Y., & İşleyen, S. K. (2013). Evaluation of mathematical models for flexible job-shop scheduling problems. Applied Mathematical Modelling, 37(3), 977-988.
Ding, J. Y., Song, S., & Wu, C. (2016). Carbon-efficient scheduling of flow shops by multi-objective optimization. European Journal of Operational Research, 248(3), 758-771.
Dósa, G., & Tan, Z. (2010). New upper and lower bounds for online scheduling with machine cost. Discrete Optimization, 7(3), 125-135.
Ham, A. (2017). Flexible job shop scheduling problem for parallel batch processing machine with compatible job families. Applied Mathematical Modelling, 45, 551-562.
Hasani, A., & Hosseini, S. M. H. (2020). A bi-objective flexible flow shop scheduling problem with machine-dependent processing stages: Trade-off between production costs and energy consumption. Applied Mathematics and Computation, 386, 125533.
Heydar, M., Mardaneh, E., & Loxton, R. (2022). Approximate dynamic programming for an energy-efficient parallel machine scheduling problem. European Journal of Operational Research, 302(1), 363-380.
Ho, W. H., Chiu, Y. H., & Chen, Y. J. (2018). Multi-objective Pareto adaptive algorithm for capacitated lot-sizing problems in glass lens production. Applied Mathematical Modelling, 53, 731-738.
Ji, M., Wang, J. Y., & Lee, W. C. (2013). Minimizing resource consumption on uniform parallel machines with a bound on makespan. Computers & Operations Research, 40(12), 2970-2974.
Karhi, S., & Shabtay, D. (2018). Single machine scheduling to minimise resource consumption cost with a bound on scheduling plus due date assignment penalties. International Journal of Production Research, 56(9), 3080-3096.
Karimi, S., Kwon, S., & Ning, F. (2021). Energy-aware production scheduling for additive manufacturing. Journal of Cleaner Production, 278, 123183.
Keha, A. B., Khowala, K., & Fowler, J. W. (2009). Mixed integer programming formulations for single machine scheduling problems. Computers & Industrial Engineering, 56(1), 357-367.
Kolahan, F., & Kayvanfar, V. (2009). A heuristic algorithm approach for scheduling of multi-criteria unrelated parallel machines. International Journal of Industrial and Manufacturing Engineering, 3(11), 1406-1409.
Kong, M., Pei, J., Liu, X., Lai, P. C., & Pardalos, P. M. (2020). Green manufacturing: Order acceptance and scheduling subject to the budgets of energy consumption and machine launch. Journal of Cleaner Production, 248, 119300.
Kononov, A. V., Kovalyov, M. Y., & Lin, B. M. (2019). Minimizing machine assignment costs over Δ-approximate solutions of the scheduling problem P|| Cmax. Theoretical Computer Science, 793, 70-78.
Ku, W. Y., & Beck, J. C. (2016). Mixed integer programming models for job shop scheduling: A computational analysis. Computers & Operations Research, 73, 165-173.
Lee, K., Leung, J. Y., Jia, Z. H., Li, W., Pinedo, M. L., & Lin, B. M. (2014). Fast approximation algorithms for bi-criteria scheduling with machine assignment costs. European Journal of Operational Research, 238(1), 54-64.
Leung, J. Y. T., Lee, K., & Pinedo, M. L. (2012). Bi-criteria scheduling with machine assignment costs. International Journal of Production Economics, 139(1), 321-329.
Li, K., Zhang, H. J., Cheng, B. Y., & Pardalos, P. M. (2018). Uniform parallel machine scheduling problems with fixed machine cost. Optimization Letters, 12(1), 73-86.
Li, K., Zhang, X., Leung, J. Y. T., & Yang, S. L. (2016). Parallel machine scheduling problems in green manufacturing industry. Journal of Manufacturing Systems, 38, 98-106.
Liang, P., Yang, H. D., Liu, G. S., & Guo, J. H. (2015). An ant optimization model for unrelated parallel machine scheduling with energy consumption and total tardiness. Mathematical Problems in Engineering, e907034.
Liu, Z., Lee, W. C., & Wang, J. Y. (2016). Resource consumption minimization with a constraint of maximum tardiness on parallel machines. Computers & Industrial Engineering, 97, 191-201.
Meng, L., Zhang, C., Shao, X., & Ren, Y. (2019). MILP models for energy-aware flexible job shop scheduling problem. Journal of Cleaner Production, 210, 710-723.
Mokhtari, H., & Hasani, A. (2017). An energy-efficient multi-objective optimization for flexible job-shop scheduling problem. Computers & Chemical Engineering, 104, 339-352.
Naderi, B., Gohari, S., & Yazdani, M. (2014). Hybrid flexible flowshop problems: Models and solution methods. Applied Mathematical Modelling, 38(24), 5767-5780.
Nasiri, M. M., Abdollahi, M., Rahbari, A., Salmanzadeh, N., & Salesi, S. (2018). Minimizing the energy consumption and the total weighted tardiness for the flexible flowshop using NSGA-II and NRGA. Journal of Industrial and Systems Engineering, 11(Special issue: 14th International Industrial Engineering Conference), 150-162.
Özgüven, C., Özbakır, L., & Yavuz, Y. (2010). Mathematical models for job-shop scheduling problems with routing and process plan flexibility. Applied Mathematical Modelling, 34(6), 1539-1548.
Pan, J. C. H., & Chen, J. S. (2005). Mixed binary integer programming formulations for the reentrant job shop scheduling problem. Computers & Operations Research, 32(5), 1197-1212.
Pan, R., Wang, Q., Li, Z., Cao, J., & Zhang, Y. (2022). Steelmaking-continuous casting scheduling problem with multi-position refining furnaces under time-of-use tariffs. Annals of Operations Research, 310(1), 119-151.
Pinedo, M.L. (2016). Scheduling: Theory, Algorithms, and Systems. 5th ed. 2016 edition. ed. Springer, New York.
Safarzadeh, H., & Niaki, S. T. A. (2019). Bi-objective green scheduling in uniform parallel machine environments. Journal of Cleaner Production, 217, 559-572.
Unlu, Y., & Mason, S. J. (2010). Evaluation of mixed integer programming formulations for non-preemptive parallel machine scheduling problems. Computers & Industrial Engineering, 58(4), 785-800.
Wang, H., & Alidaee, B. (2018). Unrelated parallel machine selection and job scheduling with the objective of minimizing total workload and machine fixed costs. IEEE Transactions on Automation Science and Engineering, 15(4), 1955-1963.
Wang, S., Wang, X., Chu, F., & Yu, J. (2020). An energy-efficient two-stage hybrid flow shop scheduling problem in a glass production. International Journal of Production Research, 58(8), 2283-2314.
Wei, Z., Liao, W., & Zhang, L. (2022). Hybrid energy-efficient scheduling measures for flexible job-shop problem with variable machining speeds. Expert Systems with Applications, 197, 116785.
Wu, X., & Che, A. (2019). A memetic differential evolution algorithm for energy-efficient parallel machine scheduling. Omega, 82, 155-165.
Xie, F., Xu, Z., Zhang, Y., & Bai, Q. (2015). Scheduling games on uniform machines with activation cost. Theoretical Computer Science, 580, 28-35.
Yeh, W. C., Chuang, M. C., & Lee, W. C. (2015). Uniform parallel machine scheduling with resource consumption constraint. Applied Mathematical Modelling, 39(8), 2131-2138.
Zeng, Y., Che, A., & Wu, X. (2018). Bi-objective scheduling on uniform parallel machines considering electricity cost. Engineering Optimization, 50(1), 19-36.
Zhang, L., Deng, Q., Gong, G., & Han, W. (2020). A new unrelated parallel machine scheduling problem with tool changes to minimise the total energy consumption. International Journal of Production Research, 58(22), 6826-6845.
Ziaee, M., & Sadjadi, S. J. (2007). Mixed binary integer programming formulations for the flow shop scheduling problems. A case study: ISD projects scheduling. Applied Mathematics and Computation, 185(1), 218-228.