Minimizing the operational costs in a flexible flow shop scheduling problem with unrelated parallel machines

Subject Areas : Operation and Chain Management

Ali  Hassani ¹ (Department on industrial engineering and management, Shahrood university of technology, Shahrood, Iran.)
Seyed Mohamad Hasan  Hosseini ² (Department on industrial engineering and management, Shahrood university of technology, Shahrood, Iran.)
Foroogh  Behroozi ³ (Department of Engineering, Alzahra University, Tehran, Iran.)

Received: 2020-01-14 Accepted : 2021-01-24 Published : 2021-06-01

Keywords: Scheduling, Flexible flow shop, Unrelated parallel machines, Operational costs,

Abstract :

This paper investigates a flexible flow shop scheduling problem with the aim of minimizing the operational costs as a new objective function. In this production system, there are some unrelated parallel machines with different performances and different technology levels in the first stage and each other stage consists of a single machine. Setup times are assumed as sequence-dependent and are need when a machine starts to process a new job. Some of the parallel machines in the first stage are multifunctional and can do several processes on jobs. So, the jobs that are assigned to these machines do not need to be processed in some next stages. This problem is described with an example, and its parameters and decision variables are defined. Then a mathematical model based on mixed-integer linear programming (MIP) is developed to solve the problem in small-sized scales. As this problem is discussed in an Np-hard environment, the Genetic Algorithm (GA) is applied to solve the considered problem on practical-sized scales. Due to the result, the operational costs conflict with makespan as a common objective function in scheduling problems. Therefore, the supplementary analysis has been presented considering a restriction on the makespan.

References:

Afzalirad M, Rezaeian J (2016) Resource-constrained unrelated parallel machine scheduling problem with sequence dependent setup times, precedence constraints and machine eligibility restrictions. Comput Ind Eng 98:40–52

Ahonen H, de Alvarenga AG (2017) Scheduling flexible flow shop with recirculation and machine sequence-dependent processing times: formulation and solution procedures. Int J Adv Manuf Technol 89:765–777

Arroyo JEC, Leung JY-T (2017a) Scheduling unrelated parallel batch processing machines with non-identical job sizes and unequal ready times. Comput Oper Res 78:117–128

Arroyo JEC, Leung JY-T (2017b) An effective iterated greedy algorithm for scheduling unrelated parallel batch machines with non-identical capacities and unequal ready times. Comput Ind Eng 105:84–100

Blazewicz J, Ecker K, Pesch E, Schmidt G, Weglarz J (2019) Handbook on scheduling. Springer

Chen C-L, Chen C-L (2009) A bottleneck-based heuristic for minimizing makespan in a flexible flow line with unrelated parallel machines. Comput Oper Res 36:3073–3081

Choi SH, Wang K (2012) Flexible flow shop scheduling with stochastic processing times: A decomposition-based approach. Comput Ind Eng 63:362–373

Cummings DH, Egbelu MPJ (1998) Minimizing production flow time in a process and assembly job shop. Int J Prod Res 36:2315–2332

Ebrahimi M, Ghomi SMTF, Karimi B (2014) Hybrid flow shop scheduling with sequence dependent family setup time and uncertain due dates. Appl Math Model 38:2490–2504

Enayati M, Asadi-Gangraj E, Paydar MM (2021) Scheduling on flexible flow shop with cost-related objective function considering outsourcing options. Journal of Optimization in Industrial Engineering, 14(2), 69–88.

Fattahi P, Hosseini S, Jolai F (2013a) Some heuristics for the hybrid flow shop scheduling problem with setup and assembly operations. Int J Ind Eng Comput 4:393–416

Fattahi P, Hosseini SMH, Jolai F (2012) Using the Simulated Annealing to Solve a JIT Scheduling Problem in the Two-Machine Flow Shop. Int J Ind Eng 23:265–281

Fattahi P, Hosseini SMH, Jolai F (2013b) A mathematical model and extension algorithm for assembly flexible flow shop scheduling problem. Int J Adv Manuf Technol 65:787–802

Garavito-Hernández EA, Peña-Tibaduiza E, Perez-Figueredo LE, Moratto-Chimenty E (2019) A meta-heuristic based on the Imperialist Competitive Algorithm (ICA) for solving Hybrid Flow Shop (HFS) scheduling problem with unrelated parallel machines. J Ind Prod Eng 1–9

Geng K, Ye C, Liu L (2020) Bi-Objective Re-Entrant Hybrid Flow Shop Scheduling considering Energy Consumption Cost under Time-of-Use Electricity Tariffs. Complexity 2020:

Gupta JND, Tunc EA (1991) Schedules for a two-stage hybrid flowshop with parallel machines at the second stage. Int J Prod Res 29:1489–1502

Hasani A, Hosseini SMH (2020) A bi-objective flexible flow shop scheduling problem with machine-dependent processing stages: Trade-off between production costs and energy consumption. Appl Math Comput 386:in press . https://doi.org/10.1016/j.amc.2020.125533

Hosseini SMH (2016) Modeling the hybrid flow shop scheduling problem followed by an assembly stage considering aging effects and preventive maintenance activities. Int J Supply Oper Manag 3:1215

Hosseini SMH (2019) Modelling and solving the job shop scheduling Problem followed by an assembly stage considering maintenance operations and access restrictions to machines. Journal of Optimization in Industrial Engineering, 12(1), 63–78.

Hosseini SMH (2017) A multi-objective genetic algorithm (MOGA) for hybrid flow shop scheduling problem with assembly operation. J Ind Syst Eng 10:132–154

Huang W, Li S (1998) A two-stage hybrid flowshop with uniform machines and setup times. Math Comput Model 27:27–45

Jenabi M, Ghomi SMTF, Torabi SA, Karimi B (2007) Two hybrid meta-heuristics for the finite horizon ELSP in flexible flow lines with unrelated parallel machines. Appl Math Comput 186:230–245

Jungwattanakit J, Reodecha M, Chaovalitwongse P, Werner F (2008) Algorithms for flexible flow shop problems with unrelated parallel machines, setup times, and dual criteria. Int J Adv Manuf Technol 37:354–370

Kianfar K, Ghomi SMTF, Jadid AO (2012) Study of stochastic sequence-dependent flexible flow shop via developing a dispatching rule and a hybrid GA. Eng Appl Artif Intell 25:494–506

Lee TS, Loong YT (2019) A review of scheduling problem and resolution methods in flexible flow shop. Int J Ind Eng Comput 10:67–88 . https://doi.org/10.5267/j.ijiec.2018.4.001

Li D, Meng X, Liang Q, Zhao J (2015) A heuristic-search genetic algorithm for multi-stage hybrid flow shop scheduling with single processing machines and batch processing machines. J Intell Manuf 26:873–890

Li S (1997) A hybrid two-stage flowshop with part family, batch production, major and minor set-ups. Eur J Oper Res 102:142–156

Low C (2005) Simulated annealing heuristic for flow shop scheduling problems with unrelated parallel machines. Comput Oper Res 32:2013–2025

Maleki-Darounkolaei A, Modiri M, Tavakkoli-Moghaddam R, Seyyedi I (2012) A three-stage assembly flow shop scheduling problem with blocking and sequence-dependent set up times. J Ind Eng Int 8:26 . https://doi.org/10.1186/2251-712X-8-26

Meng L, Zhang C, Shao X, Ren Y, Ren C (2019) Mathematical modelling and optimisation of energy-conscious hybrid flow shop scheduling problem with unrelated parallel machines. Int J Prod Res 57:1119–1145

Raissi S, Rooeinfar R, Ghezavati VR (2019) Three Hybrid Metaheuristic Algorithms for Stochastic Flexible Flow Shop Scheduling Problem with Preventive Maintenance and Budget Constraint. Journal of Optimization in Industrial Engineering, 12(1),131–147.

Ruiz R, Vázquez-Rodríguez JA (2010) The hybrid flow shop scheduling problem. Eur J Oper Res 205:1–18

Sawik T (2006) Hierarchical approach to production scheduling in make-to-order assembly. Int J Prod Res 44:801–830

Schulz S, Buscher U, Shen L (2020) Multi-objective hybrid flow shop scheduling with variable discrete production speed levels and time-of-use energy prices. J Bus Econ 1–29

Shahvari O, Logendran R (2017) An enhanced tabu search algorithm to minimize a bi-criteria objective in batching and scheduling problems on unrelated-parallel machines with desired lower bounds on batch sizes. Comput Oper Res 77:154–176

Ünal AT, Ağralı S, Taşkın ZC (2019) A strong integer programming formulation for hybrid flowshop scheduling. J Oper Res Soc 1–11

Wang H (2005) Flexible flow shop scheduling: optimum, heuristics and artificial intelligence solutions. Expert Syst 22:78–85

Wang I-L, Wang Y-C, Chen C-W (2013) Scheduling unrelated parallel machines in semiconductor manufacturing by problem reduction and local search heuristics. Flex Serv Manuf J 25:343–366