A two-stage stochastic supply chain scheduling problem with production in cellular manufacturing environment: A case study

Document Type : Article


Department of Industrial Engineering, Iran University of Science and Technology, University Ave. Narmak, Tehran, P.O. Box 1684613114, Iran


An integrated decision in supply chain is a significant principle in order to compete in today’s market. This paper proposes a novel mathematical model in a two-stage supply chain scheduling to cooperate procurement and manufacturing activities. The supply chain scheduling along with the production approach of cellular manufacturing under demand, processing time, and transportation time uncertainties makes business environment sustainably responsive to the changing needs of customers. Uncertainties are formulated by queuing theory. In this paper, a new mixed-integer nonlinear programming formulation is used to determine types of vehicles to carry raw materials, suppliers to procure, priority of each part in order to process, and cell formation to configure work centers. The goal is to minimize total tardiness. A linearization method is used to ease tractability of the model. A genetic algorithm is developed due to the NP-hard nature of the problem. The parameters of the genetic algorithm are set and estimated by Taguchi’s experimental design. Numerous test problems are employed to validate the effectiveness of the modeling and the efficiency of solution approaches. Finally, a real case study and a sensitivity analysis are discussed to provide significant managerial insights and assess the applicability of the proposed model.


1. Chopra, S. and Meindl, P. "Supply chain management; Strategy, planning and operation", In Das Summa Summarum des Management, Springer, Gabler, pp. 265-275 (2007).
2. Sadeghi, A., Suer, G., Sinaki, R.Y., et al. "Cellular manufacturing design and replenishment strategy in a capacitated supply chain system: A simulation-based analysis", Comput Ind Eng., 141, pp. 106-282 (2020).
3. Croom, S., Romano, P., and Giannakis, M. "Supply chain management: an analytical framework for critical literature review", J. Purch. Supply Manag, 6(1), pp. 67-83 (2000).
4. Tang, L., Jin, Z., Qin, X., et al. "Supply chain scheduling in a collaborative manufacturing mode: model construction and algorithm design", Ann. Oper. Res., 275(2), pp. 685-714 (2019).
5. Aminzadegan, S., Tamannaei, M., and Rasti-Barzoki, M. "Multi-agent supply chain scheduling problem by considering resource allocation and transportation", Comput Ind Eng., 137(1), 106003 (2019).
6. Farzad, T., Mohammad Rasid, O., Aidy, A., et al. "A review of supplier selection methods in manufacturing industries", Suranaree J. Sci. Technol., 15(3), pp. 201- 208 (2008).
7. Ho, W., Xu, X., and Dey, P.K. "Multi-criteria decision making approaches for supplier evaluation and selection: A literature review", Eur. J. Oper. Res., 202(1), pp. 16-24 (2010).
8. Hammami, R., Frein, Y., and Hadj-Alouane, A.B. "An international supplier selection model with inventory and transportation management decisions", Flex. Serv. Manuf. J., 24(1), pp. 4-27 (2012).
9. Chai, J., Liu, J.N., and Ngai, E.W. "Application of decision-making techniques in supplier selection: A systematic review of literature", Expert Syst. Appl., 40(10), pp. 3872-3885 (2013).
10. Igarashi, M., de Boer, L., and Fet, A.M. "What is required for greener supplier selection? A literature review and conceptual model development", J. Purch. Supply Manag., 19(4), pp. 247-263 (2013).
11. Pal, O., Gupta, A.K., and Garg, R. "Supplier selection criteria and methods in supply chains: A review", Int. J. Econ. Manag., 7(10), pp. 2667-2673 (2013).
12. Erozan, I., Torkul, O., and Ustun, O. "Proposal of a nonlinear multi-objective genetic algorithm using conic scalarization to the design of cellular manufacturing systems", Flex. Serv. Manuf. J., 27(1), pp. 30-57 (2015).
13. Wemmerlov, U. and Hyer, N.L. "Cellular manufacturing in the US industry: a survey of users", Int. J. Prod. Res., 27(9), pp. 1511-1530 (1989).
14. Heragu, S.S. "Group technology and cellular manufacturing", IEEE Trans. Syst. Man Cybern. Syst., 24(2), pp. 203-215 (1994).
15. Shishebori, D. and Dehnavi-Arani, S. "A multi-stage stochastic programming approach in a dynamic cell formation problem with uncertain demand: A case study", Int J. Supply Oper Manage, 6(1), pp. 67-87 (2019).
16. Rachamadugu, R., Nandkeolyar, U., and Schriber, T. "Scheduling with sequencing flexibility", Decis. Sci., 24(2), pp. 315-342 (1993).
17. Irani, S.A., Handbook of Cellular Manufacturing Systems, In John Wiley and Sons (1999).
18. Wemmerlov U. and Hyer, N.L. "Research issues in cellular manufacturing", Int. J. Prod. Res., 25(3), pp. 413-431 (1987).
19. Xue, G. and O odile, O.F. "Integrated optimization of dynamic cell formation and hierarchical production planning problems", Comput Ind Eng., 139, 106155 (2020).
20. Kamrani, A.K., Parsaei, H.R., and Liles, D.H., Planning, Design, and Analysis of Cellular Manufacturing Systems, In Newnes (1995).
21. Wu, X., Chu, C.H., Wang, Y., et al. "Genetic algorithms for integrating cell formation with machine layout and scheduling", Comput Ind Eng., 53(2), pp. 277-289 (2007).
22. Lin, S.W. and Ying, K.C. "Makespan optimization in a no-wait  flowline manufacturing cell with sequencedependent family setup times", Comput Ind Eng., 128, pp. 1-7 (2019).
23. Wazed, M. Ahmed, S., and Nukman, Y. "Uncertainty factors in real manufacturing environment", Aust. J. Basic and Appl. Sci., 3(2), pp. 342-351 (2009).
24. Kumar, R. and Singh, S.P. "Modified SA algorithm for bi-objective robust stochastic cellular facility layout in cellular manufacturing systems", In Advanced Computing and Communication Technologies, Springer, Singapore, pp. 19-33 (2019).
25. Hall, N.G. and Potts, C.N. "Supply chain scheduling: Batching and delivery", Oper. Res., 51(4), pp. 566-584 (2003).
26. Selvarajah, E. and Steiner, G. "Batch scheduling in a two-level supply chain- a focus on the supplier", Eur. J. Oper. Res., 173(1), pp. 226-240 (2006).
27. Wang, X. and Cheng, T.E. "Machine scheduling with an availability constraint and job delivery coordination", Nav. Res. Logist., 54(1), pp. 11-20 (2007).
28. Zegordi, S.H. and Beheshti Nia, M.A. "Integrating production and transportation scheduling in a twostage supply chain considering order assignment", J. Adv. Manuf. Technol., 44(9), pp. 928-939 (2009).
29. Yimer, A.D. and Demirli, K. "A genetic approach to two-phase optimization of dynamic supply chain scheduling", Comput Ind Eng., 58(3), pp. 411-422 (2010).
30. Zegordi, S.H. Abadi, I.K., and Nia, M.B. "A novel genetic algorithm for solving production and transportation scheduling in a two-stage supply chain", Comput Ind Eng., 58(3), pp. 373-381 (2010).
31. Steinrucke, M. "An approach to integrate productiontransportation planning and scheduling in an aluminium supply chain network", Int. J. Prod. Res., 49(21), pp. 6559-6583 (2011).
32. Maheut, J. Garcia-Sabater, J.P., and Mula, J. "A supply chain operations lot-sizing and scheduling model with alternative operations", In Industrial Engineering: Innovative Networks, Springer, London, pp. 309- 316 (2012).
33. Wang, D., Grunder, O., and El Moudni, A. "Singleitem production-delivery scheduling problem with stage-dependent inventory costs and due-date considerations", Int. J. Prod. Res., 51(3), pp. 828-846 (2013).
34. Ma, H., Chan, F.T., and Chung, S. "Minimising earliness and tardiness by integrating production scheduling with shipping information", Int. J. Prod. Res., 51(8), pp. 2253-2267 (2013).
35. Hajiaghaei-Keshteli, M., Aminnayeri, M., and Fatemi Ghomi, S.M.T. "Integrated scheduling of production and rail transportation", Comput Ind Eng., 74, pp. 240-256 (2014).
36. Cheng, B., Li, K., and Hu, X. "Approximation algorithms for two-stage supply chain scheduling of production and distribution", Int. J. Syst. Sci., 2(2), pp. 78-89 (2015).
37. Pei, J., Pardalos, P.M., Liu, X., et al. "Coordination of production and transportation in supply chain scheduling", J. Ind. Manag. Optim., 11(2), pp. 399- 419 (2015).
38. Cheng, B.Y., Leung, J.Y.T., and Li, K. "Integrated scheduling of production and distribution to minimize total cost using an improved ant colony optimization method", Comput Ind Eng., 83, pp. 217-225 (2015).
39. Pei, J., Fan, W., Pardalos, P.M., et al. "Preemptive scheduling in a two-stage supply chain to minimize the makespan", Optim. Methods Softw., 30(3), pp. 727- 747 (2015).
40. Assarzadegan, P. and Rasti-Barzoki, M. "Minimizing sum of the due date assignment costs, maximum tardiness and distribution costs in a supply chain scheduling problem", Appl. Soft Comput., 47, pp. 343- 356 (2016).
41. Hassanzadeh, A. and Rasti-Barzoki, M. "Minimizing total resource consumption and total tardiness penalty in a resource allocation supply chain scheduling and vehicle routing problem", Appl. Soft Comput., 58, pp. 307-323 (2017).
42. Noroozi, A., Mazdeh, M.M., Noghondarian, K., et al."Evolutionary computation algorithms to coordinating  order acceptance and batch delivery for an integrated supply chain scheduling", Comput. Appl. Math., 37(2), pp. 1629-1679 (2018).
43. Wang, D., Zhu, J., Wei, X., et al. "Integrated production and multiple trips vehicle routing with time windows and uncertain travel times", Comput. Oper. Res., 103, pp. 1-12 (2019).
44. Arkat, J., Farahani, M.H., and Hosseini, L. "Integrating cell formation with cellular layout and operations scheduling", J. Adv. Manuf. Technol., 61(5-8), pp. 637-647 (2012).
45. Pasupuleti, V.C. "Scheduling in cellular manufacturing systems", Iberoam. J. Ind. Eng., 4(7), pp. 231-243 (2012).
46. Arkat, J., Farahani, M.H., and Ahmadizar, F. "Multiobjective genetic algorithm for cell formation problem considering cellular layout and operations scheduling", Int. J. Comput. Integr. Manuf., 25(7), pp. 625-635 (2012).
47. Kesen, S.E. and Gungor, Z. "Job scheduling in virtual manufacturing cells with lot-streaming strategy: a new mathematical model formulation and a genetic algorithm approach", J Oper Res Soc., 63(5), pp. 683- 695 (2012).
48. Eguia, I., Racero, J., Guerrero, F., et al. "Cell formation and scheduling of part families for reconfigurable cellular manufacturing systems using Tabu search", Simulation, 89(9), pp. 1056-1072 (2013).
49. Solimanpur, M. and Elmi, A. "A tabu search approach for cell scheduling problem with makespan criterion", Int. J. Prod. Econ., 141(2), pp. 639-645 (2013).
50. Taouji Hassanpour, S., Bashirzadeh, R., Adressi, A., et al. "Scheduling problem of Virtual Cellular Manufacturing Systems (VCMS); Using simulated annealing and genetic algorithm based heuristics", J. Mod Pro Manu Prod, 3(4), pp. 45-60 (2014).
51. Saravanan, M. and Karthikeyan, S. "Scheduling optimization cell formation problem for cellular manufacturing system using meta-heuristic methods", Appl. Mech. Mater, 786, pp. 340-344 (2015).
52. Fahmy, S.A. "Mixed integer linear programming model for integrating cell formation, group layout and group scheduling", 2015 IEEE International Conference on Industrial Technology (ICIT, pp. 2403-2408 (2015).
53. Halat, K. and Bashirzadeh, R. "Concurrent scheduling of manufacturing cells considering sequence-dependent family setup times and intercellular transportation times", J. Adv. Manuf. Technol., 77(9), pp. 1907-1915 (2015).
54. Liu, C. and Wang, J. "Cell formation and task scheduling considering multi-functional resource and part movement using hybrid simulated annealing", Int. J. Comput. Intell. Syst., 9(4), pp. 765-777 (2016).
55. Egilmez, G., Mese, E.M., Erenay, B., et al. "Group scheduling in a cellular manufacturing shop to minimise total tardiness and nT: a comparative genetic algorithm and mathematical modelling approach", Int J Serv Oper Manag, 24(1), pp. 125-146 (2016).
56. Rafiei, H., Rabbani, M., Gholizadeh, H., et al. "A novel hybrid SA/GA algorithm for solving an integrated cell formation-job scheduling problem with sequencedependent set-up times", Int. J. Manag. Sci, 11(3), pp. 134-142 (2016).
57. Liu, C., Wang, J., Leung, J.Y.T., et al. "Solving cell formation and task scheduling in cellular manufacturing system by discrete bacteria foraging algorithm", Int. J. Prod. Res., 54(3), pp. 923-944 (2016).
58. Deliktas, D., Torkul, O., and Ustun, O. "A flexible job shop cell scheduling with sequence-dependent family setup times and intercellular transportation times using conic scalarization method", Int. Trans. Oper. Res., 26(6), pp. 2410-2431 (2017).
59. Feng, Y., Li, G., and Sethi, S.P. "A three-layer chromosome genetic algorithm for multi-cell scheduling with  flexible routes and machine sharing", Int. J. Prod. Econ., 196, pp. 269-283 (2018).
60. Feng, H., Xia, T., Da, W., et al. "Concurrent design of cell formation and scheduling with consideration of duplicate machines and alternative process routings", J. Intell. Manuf., 30(1), pp. 275-289 (2019).
61. Forghani, K. and Fatemi Ghomi, S. "Joint cell formation, cell scheduling, and group layout problem in virtual and classical cellular manufacturing systems", Appl. Soft Comput., 97, 106719 (2020).
62. Ramezanian, R. and Khalesi, S. "Integration of multiproduct supply chain network design and assembly line balancing", Oper. Res., 21(1), pp. 1-31 (2019).
63. Mallor, F., Azcarate, C., and Barado, J. "Control problems and management policies in health systems: application to intensive care units", Flex. Serv. Manuf. J., 28(1-2), pp. 62-89 (2016).
64. Simchi-Levi, D., Kaminsky, P., and Simchi-Levi, E., Managing the Supply Chain: Definitive Guide, In Tata McGraw-Hill Education (2004).
65. Donald, G. and Carl, H., Fundamentals of Queueing Theory, In John Wiley and Sons, Hoboken, New Jersey (2008).
66. Ballakur, A. "An investigation of part family/machine group formation in designing a cellular manufacturing system", Ph. D. Thesis, University of Wisconsin (1985).
67. King, J.R. and Nakornchai, V. "Machine-component group formation in group technology: review and extension", Int. J. Prod. Res., 20(2), pp. 117-133 (1982).
68. Hazarika, M. and Laha, D. "A heuristic approach for machine cell formation problems with Alternative routings", Procedia Comput. Sci., 89, pp. 228-242 (2016).