Abstract
In this paper, an open-shop scheduling problem with stochastic process times is considered. The objective function is to minimize the weighted sum of earliness and tardiness costs. This type of objective function, in addition to the optimal schedule, puts forward the issue of finding optimal values of start times of jobs. In scheduling problems with stochastic process times, unlike the deterministic variants, it is not possible to determine the schedule before the random variables are realized. Whenever a machine becomes available (for example finishes processing some jobs) a job should be selected to be passed on it from the set of available jobs. This selection process is carried out in real-time. We have devised a simulation-optimization algorithm which calculates the distribution functions of the completion times of jobs via central limit theorem. These distribution functions are used for cost estimation in the real-time job selecting process. In other words, whenever some jobs are competing for a free machine, a pair wise cost competition is raised among them and the winner is passed on the free machine. Moreover, the distribution function of the completion time of each job is also used to adjust its start time. Finally, some test problems are generated and solved by our algorithm. The results demonstrate that our algorithm, even without adjusting the start times, outperforms the algorithm which acts randomly in the real-time job selecting process.
Similar content being viewed by others
References
Pinedo M (2012) Scheduling: theory, algorithms and systems, 4th edn. New York, Springer
Pinedo M, Ross S (1982) Minimizing expected makespan in stochastic open shops. Adv Appl Probab 14:898–911
Pinedo M (1984) A note on the flow time and the number of tardy jobs in stochastic open shops. Eur J Oper Res 18(1):81–85
Chung C, Mohanty B (1988) Minimizing expected makespan in a two-machine stochastic open shop with Poisson arrival. J Anal Appl 133(2):498–508
Frostig E (1991) On the optimality of static policy in stochastic open shop. Oper Res Lett 10(9):509–512
Koryakin RA (2003) On the stochastic open shop problem. In: Albrecht A, Steinhöfel K (eds) SAGA. LNSC 2827: 117–124
Alcaide D, Rodriguez-Gonzalez A, Sicilia J (2006) A heuristic approach to minimize expected makespan in open shops subject to stochastic processing times and failures. Int J Flex Manuf Syst 17:201–226
Ahmadizar F, Ghazanfari M, Fatemi Ghomi SMT (2010) Group shops scheduling with makespan criterion subject to random release dates and processing times. Comput Oper Res 37:152–162
Gu J, Gu X, Gu M (2009) A novel parallel quantum genetic algorithm for stochastic job shop scheduling. J Math Anal Appl 355(1):63–81
Gu J, Gu M, Cao C, Gu X (2010) A novel competitive co-evolutionary quantum genetic algorithm for stochastic job shop scheduling problem. Comput Oper Res 37(5):927–937
Lei D (2011) Simplified multi-objective genetic algorithms for stochastic job shop scheduling. Appl Soft Comput 11(8):4991–4996
Lei D (2012) Minimizing makespan for scheduling stochastic job shop with random breakdown. Appl Math Comput 218(24):11851–11858
Palacios JJ, Puente J, Vela CR, González-Rodríguez I (2009) A genetic algorithm for the open shop problem with uncertain durations. In: Mira J, Ferrández JM, Álvarez JR, de la Paz F, Toledo FJ (eds) IWINAC. Part I, LNCS 5601: 255–264
Noori-Darvish S, Mahdavi I, Mahdavi-Amiri N (2012) A bi-objective possibilistic programming model for open shop scheduling problems with sequence-dependent setup times, fuzzy processing times, and fuzzy due dates. Appl Soft Comput 12(4):1399–1416
Golenko-Ginzburg D, Gonik A (2002) Optimal job-shop scheduling with random operations and cost objectives. Int J Prod Econ 76:147–157
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Morady Gohareh, M., Karimi, B. & Khademian, M. A simulation-optimization approach for open-shop scheduling problem with random process times. Int J Adv Manuf Technol 70, 821–831 (2014). https://doi.org/10.1007/s00170-013-5318-x
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s00170-013-5318-x