# MIP models and a matheuristic algorithm for an identical parallel machine scheduling problem under multiple copies of shared resources constraints

- 6 Downloads

## Abstract

If parallel machines use shared resources during production, jobs on machines must wait until the required resources are available. If the shared resource is single, only one job can use it at a time, but if there are multiple copies of this resource, multiple jobs can be scheduled up to the number of copies at a time. For this reason, it is crucial to consider resource usage when scheduling this type of machine. In recent years, various studies have been carried out to address identical parallel machine scheduling problems. However, although shared resources in parallel machines are an important aspect of this problem, resources are rarely considered in these studies and, in fact, have not been studied for this particular aspect. In this study, an identical parallel machine scheduling problem with sequence-dependent setup times, machine eligibility restrictions and multiple copies of shared resources (IPMS-SMS) is considered. Mixed-integer programming (MIP) models and a model-based genetic algorithm (matheuristic) are proposed, and the objective function of the problem seeks to minimize the total weighted completion time. Randomly generated instances are solved using the proposed models and the matheuristic. Optimal schedules are obtained for almost all small problems using a mixed-integer programming model. However, better solutions are obtained for medium and large instances using the proposed matheuristic.

## Keywords

Matheuristic Genetic algorithm Identical parallel machine scheduling problem Sequence-dependent setup times Machine eligibility restrictions Multiple copies of shared resources## Notes

### Acknowledgements

This research did not receive any specific grant from funding agencies in the public, commercial, or not-for-profit sectors.

## References

- Afzalirad, Rezaeian, & (2016) Resource-constrained unrelated parallel machine scheduling problem with sequence dependent setup times, precedence constraints and machine eligibility restrictions. Comput Ind Eng 98:40–52CrossRefGoogle Scholar
- Alagoz O, Azizoglu M (2003) Rescheduling of identical parallel machines under machine eligibility constraints. Eur J Oper Res 149(3):523–532CrossRefGoogle Scholar
- Arnaout JP (2010) Heuristics for the maximization of operating rooms utilization using simulation. Simulation 86(8–9):573–583CrossRefGoogle Scholar
- Avalos-Rosales O, Angel-Bello F, Alvarez A (2015) Efficient metaheuristic algorithm and re-formulations for the unrelated parallel machine scheduling problem with sequence and machine-dependent setup times. Int J Adv Manuf Technol 76:1705–1718CrossRefGoogle Scholar
- Billaut JC, Croce Federico D, Grosso A (2015) A single machine scheduling problem with two-dimensional vector packing constraints. Eur J Oper Res 243:399–411CrossRefGoogle Scholar
- Chan TS, Choy KL, Bibhushan (2011) A genetic algorithm-based scheduler for multiproduct parallel machine sheet metal job shop. Expert Syst Appl 38(7):8703–8715CrossRefGoogle Scholar
- Chaudhry IA, Drake PR (2009) Minimizing total tardiness for the machine scheduling and worker assignment problems in identical parallel machines using genetic algorithms. Int J Adv Manuf Technol 42(5–6):581–594CrossRefGoogle Scholar
- Chen CL, Chen CL (2009) Hybrid meta-heuristics for unrelated parallel machine scheduling with sequence-dependent setup times. Int J Adv Manuf Technol 43(1–2):161–169CrossRefGoogle Scholar
- Chung SH, Tai YT, Pearn WL (2009) An effective scheduling approach for maximizing polyimide printing weighted throughput in cell assembly factories. IEEE Trans Electron Packag Manuf 32(3):185–197CrossRefGoogle Scholar
- Driessel R, Moench L (2009) Scheduling jobs on parallel machines with sequence-dependent setup times, precedence constraints and ready times using variable neighborhood search. In: International Conference on Computers and Industrial Engineering, Troyes, France, July 06-09Google Scholar
- Driessel R, Moench L (2011) Variable neighborhood search approaches for scheduling jobs on parallel machines with sequence-dependent setup times, precedence constraints, and ready times. Comput Ind Eng 61(2):336–345CrossRefGoogle Scholar
- Edis EB, Oguz C (2012) Parallel machine scheduling with flexible resources. Comput Ind Eng 63(2):433–447CrossRefGoogle Scholar
- Edis EB, Ozkarahan I (2011) A combined integer/constraint programming approach to a resource constrained parallel machine scheduling problem with machine eligibility restrictions. Eng Optim 43(2):135–157CrossRefGoogle Scholar
- Edis EB, Ozkarahan I (2012) Solution approaches for a real-life resource-constrained parallel machine scheduling problem. Int J Adv Manuf Technol 58(9–12):1141–1153CrossRefGoogle Scholar
- Edis EB, Oguz C, Ozkarahan I (2012) Solution approaches for simultaneous scheduling of jobs and operators on parallel machines. J Fac Eng Arch Gazi Univ 27(3):527–535Google Scholar
- Eliiyi D, Azizoglu M (2009) A fixed job scheduling problem with machine-dependent job weights. Int J Prod Res 47(9):2231–2256CrossRefGoogle Scholar
- Fanjul-Peyro L, Perea F, Ruiz R (2017) Models and matheuristics for the unrelated parallel machine scheduling problem with additional resources. Eur J Oper Res 260(2):482–493CrossRefGoogle Scholar
- Gacias B, Artigues C, Lopez P (2010) Parallel machine scheduling with precedence constraints and setup times. Comput Oper Res 37(12):2141–2151CrossRefGoogle Scholar
- Gedik R, Rainwater C, Nachtmann H, Pohl E (2016) Analysis of a parallel machine scheduling problem with sequence dependent setup times and job availability intervals. Eur J Oper Res 251(2):640–650CrossRefGoogle Scholar
- Gokhale R, Mathirajan M (2012) Scheduling identical parallel machines with machine eligibility restrictions to minimize total weighted flow time in automobile gear manufacturing. Int J Adv Manuf Technol 60(9–12):1099–1110CrossRefGoogle Scholar
- Guimaraes L, Klabjan D, Almada-Lobo B (2013) Pricing, relaxing and fixing under lot sizing and scheduling. Eur J Oper Res 230:75–81CrossRefGoogle Scholar
- Joo CM, Kim BY (2012) Parallel machine scheduling problem with ready times, due times and sequence-dependent setup times using meta-heuristic algorithms. Eng Optim 44(9):1021–1034CrossRefGoogle Scholar
- Keskinturk T, Yildirim MB, Barut M (2012) An ant colony optimization algorithm for load balancing in parallel machines with sequence-dependent setup times. Comput Oper Res 39(6):1225–1235CrossRefGoogle Scholar
- Kim BK, Kim YD (2011) Heuristic algorithms for assigning and scheduling flight missions in a military aviation unit. Comput Ind Eng 61(4):1309–1317CrossRefGoogle Scholar
- Lee K, Leung JYT, Pinedo ML (2013) Makespan minimization in online scheduling with machine eligibility. Ann Oper Res 204(1):189–222CrossRefGoogle Scholar
- Li X, Yalaoui F, Amodeo L (2010) A multi objective meta-heuristic with a fuzzy logic controller for solving a scheduling problem. In: Computational intelligence: foundations and applications: proceedings of the 9th international FLINS conference, Emei, CHINA, August 02–04Google Scholar
- Li K, Shia Y, Yanga S, Cheng B (2011) Parallel machine scheduling problem to minimize the makespan with resource dependent processing times. Appl Soft Comput 11(8):5551–5557CrossRefGoogle Scholar
- Li X, Chehade H, Yalaoui F, Amodeo L (2012) Fuzzy logic controller based multi-objective meta-heuristics to solve a parallel machines scheduling problem. J Mult Val Logic Soft Comput 18(5–6):617–636Google Scholar
- Lin SW, Lee ZJ, Ying KC, Lu CC (2011) Minimization of maximum lateness on parallel machines with sequence-dependent setup times and job release dates. Comput Oper Res 38(5):809–815CrossRefGoogle Scholar
- Liu M, Wu C (2003) Scheduling algorithm based on evolutionary computing in identical parallel machine production line. Robot Comput Integr Manuf 19(2003):401–407CrossRefGoogle Scholar
- Montoya-Torres JR, Soto-Ferrari M, Gonzalez-Solano F, Alfonso-Lizarazo EH (2009) Machine scheduling with sequence-dependent setup times using a randomized search heuristic. In: International conference on computers and industrial engineering troyes, France, July 06–09Google Scholar
- Montoya-Torres JR, Soto-Ferrari M, Gonzalez-Solano F (2010) Production scheduling with sequence-dependent setups and job release times. Dyn Colomb 77(163):260–269Google Scholar
- Nessah R, Chengbin C, Yalaoui F (2007) An exact method for P
_{m}/sds/Σ_{i=1}^{n}c_{i}problem. Comput Oper Res 34(9):2840–2848CrossRefGoogle Scholar - Park T, Lee T, Kim CO (2012) Due-date scheduling on parallel machines with job splitting and sequence-dependent major/minor setup times. Int J Adv Manuf Technol 59(1–4):325–333CrossRefGoogle Scholar
- Pinedo ML (2009) Planning and scheduling in manufacturing and services. Springer, New YorkCrossRefGoogle Scholar
- Pinedo ML (2011) Scheduling theory, algorithms, and systems. Springer, New YorkGoogle Scholar
- Ruiz R, Andrés-Romano C (2011) Scheduling unrelated parallel machines with resource-assignable sequence-dependent setup times. Int J Adv Manuf Technol 57(5–8):777–794CrossRefGoogle Scholar
- Singha A, Rossi A, Sevaux M (2012) Matheuristic approaches for Q-coverage problem versions in wireless sensor networks. Eng Optim 45(5):609–626CrossRefGoogle Scholar
- Su LH, Chang WY, Chou FD (2011) Minimizing maximum lateness on identical parallel machines with flexible resources and machine eligibility constraints. Int J Adv Manuf Technol 56(9–12):1195–1204CrossRefGoogle Scholar
- Tahar DN, Yalaoui F, Chu C, Amodeo L (2006) A linear programming approach for identical parallel machine scheduling with job splitting and sequence-dependent setup times
*International*. J Prod Econ 99:1–2CrossRefGoogle Scholar - Turker AK, Sel C (2011) A hybrid approach on single server parallel machines scheduling problem with sequence-dependent setup times. J Fac. Eng Arch Gazi Univ 26(4):731–740Google Scholar