Abstract
This research investigates a new notion in just-in-time philosophy on the identical parallel machines considering allowable job preemption with respect to a bi-objective approach. The work-in-process (WIP) is also allowed, since minimization of WIP is desirable in many industrial applications specifically those including perishable items. In this new notion, a new model is defined in which the earliness costs depend on the start times of the jobs. The goal of this study is to minimize two objectives simultaneously: (1) total weighted earliness and tardiness as well as holding cost of all jobs which are waiting to be processed as WIP costs and (2) number of jobs interruptions. In this context, two multi-objective meta-heuristic algorithms, i.e., the non-dominated sorting genetic algorithm II (NSGAII) and non-dominated ranking genetic algorithm (NRGA) are employed to solve such bi-objective problems. Three measurement factors are then employed to evaluate the algorithms performances. Computational results demonstrate that NRGA outperforms NSGAII in all small- and medium-to-large-sized sample-generated problems; however, intangibly.
Similar content being viewed by others
References
Al Jadaan O, Rajamani L, Rao CR (2008) Non-dominated ranked genetic algorithm for solving multi-objective optimisation problems: NRGA. J Theor Appl Inf Technol 2:60–67
Azizoglu M (2003) Preemptive scheduling on identical parallel machines subject to deadlines. Eur J Oper Res 148(1):205–210
Bülbül K, Kaminsky P, Yano C (2007) Preemption in single machine earliness/tardiness scheduling. J Sched 10:271–292
Coello CA, Lamont GB, Van Veldhuizen DA (2007) Evolutionary algorithms for solving multi-objective problems, 2nd edn. Springer, New York
Davis JS, Kanet JJ (1993) Single-machine scheduling with early and tardy completion costs. Nav Res Log 40:85–101
Deb K (2001) Multi objective optimization using evolutionary algorithms. Wiley, Chichester
Deb K, Sachin J (2004) Running performance metrics for evolutionary multi-objective optimization. Kanpur Genetic Algorithm Labratory (KanGAL), Report No. 2002004
Deb K, Agarwal S, Pratap A, Meyarivan T (2000) A fast and elitist multi objective genetic algorithm: NSGA-II. Technical Report 200001, Indian Institute of Technology, Kanpur Genetic Algorithms Laboratory (KanGAL), Kanpur
Deb K, Pratap A, Agarwal S, Meyarivan T (2002) A fast and elitist multi-objective genetic algorithm: NSGA-II. IEEE Trans Evol Comput 6(2):182–197
Djellab Kh (1999) Scheduling preemptive jobs with precedence constraints on parallel machines. Eur J Oper Res 117:355–367
Esteve B, Aubijoux C, Chartier A, T’kindt, V (2006) A recovering beam search algorithm for the single machine just-in-time scheduling problem. Eur J Oper Res 127:798–813
Hall NG, Posner ME (2001) Generating experimental date for computational testing with machine scheduling applications. Oper Res 49:854–865
Hendel Y, Sourd F (2006) Efficient neighborhood search for the one-machine earliness/tardiness scheduling problem. Eur J Oper Res 173:108–119
Hendel Y, Runge N, Sourd F (2009) The one-machine just-in-time scheduling problem with preemption. Discret Optim 6(1):10–22
Hiraishi K, Levner E, Vlach M (2002) Scheduling of parallel identical machines to maximize the weighted number of just-in-time jobs. Comput Oper Res 29:841–848
Hoogeveen JA, Van de Velde SL (1996) A branch-and-bound algorithm for single-machine earliness/tardiness scheduling with idle time. INFORMS J Comput 8:402–412
Hoogeveen JA, Van de Velde SL (2001) Scheduling with target start times. Eur J Oper Res 129:87–94
Horn J, Nafploitis N, Goldberg DE (1994) A niched Pareto genetic algorithm for multiobjective optimization. In: 1st IEEE conference on evolutionary computation. IEEE Press, pp 82–87
Józefowska J (2007) Just-in-time scheduling. Springer, Berlin
Kayvanfar V, Mahdavi I, Komaki GM (2013) A drastic hybrid heuristic algorithm to approach to JIT policy considering controllable processing times. Int J Adv Manuf Technol 69(1–4):257–267
Kayvanfar V, Komaki GM, Aalaei A, Zandieh M (2014) Minimizing total tardiness and earliness on unrelated parallel machines with controllable processing times. Comput Oper Res 41:31–43
Kayvanfar V, Zandieh M, Teymourian E (2015) An intelligent water drop algorithm to identical parallel machine scheduling with controllable processing times: a just-in-time approach. Comput Appl Math 1–26. doi:10.1007/s40314-015-0218-3
Khorshidian H, Javadian N, Zandieh M, Rezaeian J, Rahmani K (2011) A genetic algorithm for JIT single machine scheduling with preemption and machine idle time. Expert Syst Appl 38:7911–7918
Kravchenko S, Werner F (2009) Preemptive scheduling on uniform machines to minimize mean flowtime. Comput Oper Res 36:2816–2821
Lenstra JK, Rinnooy Kan AH, Brucker GP (1977) Complexity of machine scheduling problems. Ann Discret Math 1:343–362
Liao CJ, Cheng CC (2007) A variable neighborhood search for minimizing single machine weighted earliness and tardiness with common due date. Comput Ind Eng 52:404–413
Luo X, Chu CH, Wang CH (2006) Some dominance properties for single-machine tardiness problem with sequence-dependent setup times. Int J Prod Res 44:3367–3378
Lushchakova IN (2006) Two machine preemptive scheduling problem with release dates, equal processing times and precedence constraints. Eur J Oper Res 171:107–122
Nowicki E, Zdrzalka S (1995) A bicriterion approach to preemptive scheduling of parallel machines with controllable job processing times. Discret Appl Math 63:237–256
Runge N, Sourd F (2009) A new model for the preemptive earliness–tardiness scheduling problem. Comput Oper Res 36:2242–2249
Sariçiçek I, Çelik C (2011) Two meta-heuristics for parallel machine scheduling with job splitting to minimize total tardiness. Appl Math Model 35(8):4117–4126
Schott JR (1995) Fault tolerant design using single and multi-criteria genetic algorithms. Master’s thesis, Department of Aeronautics and Astronautics, Massachusetts Institute of Technology, Boston
Sourd F, Kedad-Sidhoum S (2003) The one-machine scheduling with earliness and tardiness penalties. J Sched 6:533–549
Srinivas N, Deb K (1995) Multi-objective optimization function optimization using non-dominated sorting genetic algorithms. Evol Comput 2:221–248
Su LH (2009) Minimizing earliness and tardiness subject to total completion time in an identical parallel machine system. Comput Oper Res 36(2):461–471
Sun H, Wang G (2003) Parallel machine earliness and tardiness scheduling with proportional weights. Comput Oper Res 30(5):801–808
Wan G, Yen BPC (2002) Tabu search for single machine with distinct due windows and weighted earliness/tardiness penalties. Eur J Oper Res 142:271–281
Wan G, Yen BPC (2009) Single machine scheduling to minimize total weighted earliness subject to minimal number of tardy jobs. Eur J Oper Res 195:89–97
Xing W, Zhang J (2000) Parallel machine scheduling with splitting jobs. Discret Appl Math 103:259–269
Zarandi MHF, Kayvanfar V (2015) A bi-objective identical parallel machine scheduling problem with controllable processing times: a just-in-time approach. Int J Adv Manuf Tech 77(1–4):545–563
Zitzler E (1999) Evolutionary algorithms for multiobjective optimization: methods and applications. Ph.D. dissertation ETH 13398, Swiss Federal Institute of Technology (ETH), Zurich
Zitzler E, Laumanns M, Thiele L (2001) SPEA2: improving the strength Pareto evolutionary algorithm. Technical Report 103, Computer Engineering and Networks Laboratory (TIK), Swiss Federal Institute of Technology (ETH) Zurich, Zurich
Author information
Authors and Affiliations
Corresponding author
Additional information
Communicated by José Mario Martínez.
Rights and permissions
About this article
Cite this article
Aalaei, A., Kayvanfar, V. & Davoudpour, H. A multi-objective optimization for preemptive identical parallel machines scheduling problem. Comp. Appl. Math. 36, 1367–1387 (2017). https://doi.org/10.1007/s40314-015-0298-0
Received:
Revised:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s40314-015-0298-0
Keywords
- Earliness and tardiness
- Just-in-time
- Identical parallel machines
- Preemption
- Non-dominated sorting genetic algorithm