Mathematical Modeling and Solving Flexible Job-Shop Production Scheduling with Reverse Flows

Document Type : Research Paper


Department of Industrial and Mechanical Engineering, Qazvin Branch, Islamic Azad University, Qazvin, Iran


One of the important issues in the field of flexible job-shop production scheduling is reverse flows within a single production unit, as is the case in the assembly/disassembly plants. This paper studies the flexible job-shop scheduling by employing reverse flows approach, which consists of two flows of jobs at each stage in opposite directions. The problem can be used only if you have two flows: the first one going from first stage to last stage, and the second flow going from last stage to first stage. Then, a mathematical model of problem is provided to minimize the maximal completion time of the jobs (i.e., the makespan). Because of the complexity solving and proving that this problem ranked on NP-hard problems, we proposed meta-heuristic algorithm genetic (GA). Also, The parameters of these algorithm GA and their appropriate operators are obtained by the use of the Taguchi experimental design. The computational results validate outperforms proposed algorithm GA.


Main Subjects

1-        Beheshtinia, M.A., Ghasemi, A. and Farokhnia, M. (2016). “Production and Transportation Scheduling and Allocation of Orders in the Supply Chan”, Journal of Industrial Engineering,University of Tehran, Vol.50, No.2,PP. 191-203.
2-        YousefiBabadi, A. and Shishebori, D. (2015). “Robust Optimization of integrated reverse logistic network design at uncertain conditions”, Journal of Industrial Engineering,University of Tehran, Vol.49, No.2,PP. 299-313.
3-        Kim, H.J., Lee, D.H. and Xirouchakis, P. (2007). ‌“Disassembly scheduling: literature review and future research directions.”International Journal of Production Research, Vol.45, No.18-19, PP.4465-4484.
4-        Brennan, L., Gupta, S.M. and Taleb, K.N.  (1994). “Operations planning issues in an assembly/disassembly environment, International Journal of Operations & Production Management, Vol.14, No.9, PP.57-67.
5-        Duta, L., Filip, F.G. and Popescu, C. (2008), Evolutionary programming in disassembly decision making”, Int. J. Comput. Commun. Control, Vol.3, No.3, PP.282-286.
6-        Dondo, R.G. and Méndez, C.A. (2016). “Operational planning of forward and reverse logistic activities on multi-echelon supply-chain networks”, Computers and Chemical Engineering, Vol.88, No.??? , PP.170-184.
7-        Osmani, A. and Zhang, J. (2017), Multi-period stochastic optimization of a sustainable multi-feedstock second generation bioethanol supply chain− A logistic case study in Midwestern United States”, Land Use Policy, Vol.61, No.1, PP.420-450.
8-        Giri, B.C., Chakraborty, A. and Maiti, T. (2017). Pricing and return product collection decisions in a closed-loop supply chain with dual-channel in both forward and reverse logistics”, Journal of Manufacturing Systems,Vol.42, No.??? , PP.104-123.
9-        Gungor, A. and Gupta, S.M. (2001). A solution approach to the disassembly line balancing problem in the presence of task failures”, International Journal of Production Research, Vol.39, No.7, PP.1427-1467.
10-      Gupta, S.M., McGovern, S.M. and Kamarthi, S.V,J .(2003). “Solving disassembly sequence planning problems using combinatorial optimization”, In Proceedings of the 2003 Northeast Decision Sciences Institute Conference (PP. 178-180).
11-      Kongar, E. and Gupta, S.M. (2002), A multi-criteria decision making approach for disassembly-to-order systems”, Journal of Electronics Manufacturing, Vol.11, No.2, PP.171-183.
12-      González, B. and Adenso-D. B. (2006). “A scatter search approach to the optimum disassembly sequence problem”, Computers and Operations Research, Vol.33, No.6, PP.1776-1793.
13-      Ziaee, M. and Sadjadi, S.J.  “Mixed binary integer programming formulations for the flow shop scheduling problems. A case study: ISD projects scheduling”, Applied mathematics and computation, Vol.185, No.1, PP.218-228.
14-      Ilgin, M.A. and Gupta, S.M. (2011). “Recovery of sensor embedded washing machines using a multi-kanban controlled disassembly line”. Robotics and Computer-IntegratedManufacturing,Vol.27, No.2, PP.318-334.
15-      Gonnuru, V.K. (2013). “Disassembly planning and sequencing for end-of-life products with RFID enriched information”, Robotics and Computer-Integrated Manufacturing, Vol.29, No.3, PP.112-118.
16-      Li, X. et al. (2015). “Assembly oriented control algorithm of collaborative disassembly and assembly operation in collaborative virtual maintenance process”, Journal of Manufacturing Systems, Vol.36, No.1 , PP.95-108.
17-    Nonomiya, H. and Tanimizu, Y. (2017). “Optimal Disassembly Scheduling with a Genetic Algorithm”, Procedia CIRP,Vol.61, No.1, PP.218-222.
18-    Abdeljaouad, M.A. et al. (2015). “Job-shop production scheduling with reverse flows”, European Journal of Operational Research, Vol.244, No.1, PP.117-128.
19-    Molla-Alizadeh-Zavardehi, S., Hajiaghaei-Keshteli, M. and Tavakkoli-Moghaddam, R. (2011). “Solving a capacitated fixed-charge transportation problem by artificial immune and genetic algorithms with a Prüfer number representation”, Expert Systems with Applications, Vol.38, No.8, PP.10462-10474.
20-      Taillard, E. (1993). “Benchmarks for basic scheduling problems”. European Journal of Operational Research, Vol.64, No.2, PP.278-285.