Designing a Mathematical Model of a Collaborative Production System Based on Make to Order under Uncertainty

Document Type : Original Article


1 Master Student, Department of Industrial Engineering, Islamic Azad University, Karaj Branch.

2 Faculty Member of Academic Center for Education, Culture and Research (ACECR).

3 Assistant Professor, Department of Industrial Engineering, Islamic Azad University, Central Tehran Branch.

4 Assistant Professor, Department of Industrial Engineering, Islamic Azad University, Science and Research Branch.


We present a mathematical model for the problem of collaborative production system based on order with fairness to allocate production loads. The main objectives of the model are to minimize total production costs and maximize the use of resources in order to distribute production loads fairly in conditions of uncertainty. Fuzzy programming was used to control uncertain parameters. The results show that, with increasing the uncertainty rates, production system costs have increased. Since the capacity of factories is constant, with the increase in demand, the amount of production has increased and the maximum use of resources of each factory has also increased. Also, contrary to the trend of system cost changes, with the increase in the number of factories, the maximum use of available resources has decreased. To solve large sample problems, the NSGA II algorithm with a suitable chromosome is used to search the problem space. Numerical results of solving 15 sample problems show the high efficiency of NSGA II algorithm in solving the problem of cooperative production system in a very short time.


Main Subjects

  1. Alidoost, F., Bahrami, F., & Safari, H. (2020). Multi-Objective Pharmaceutical Supply Chain Modeling in Disaster (Case Study: Earthquake Crisis in Tehran). Journal of Industrial Management Perspective, 10(3), 99-123. (In Persian).
  2. Bank, M., Mazdeh, M. M., Heydari, M., & Teimoury, E. (2021). Coordinating lot sizing and integrated production and distribution scheduling with batch delivery and holding cost. Kybernetes.
  3. Beemsterboer, B., Land, M., & Teunter, R. (2017). Flexible lot sizing in hybrid make-to-order/make-to-stock production planning. European Journal of Operational Research, 260(3), 1014-1023.
  4. Bogers, R. R. (2018). Collaborative Planning in a High-Tech Industry with a Make-To-Forecast Environment.
  5. Brahimi, N., Dauzere-Peres, S., & Wolsey, L. (2010). Polyhedral and Lagrangian approaches for lot sizing with production time windows and setup times. Computers & Operations Research, 37(1), 182–188.
  6. Casas-Ramírez, M. S., Camacho-Vallejo, J. F., González-Ramírez, R. G., Marmolejo-Saucedo, J. A., & Velarde-Cantú, J. M. (2018). Optimizing a Biobjective Production-Distribution Planning Problem Using a GRASP. Complexity, 2018.
  7. Cheng, F., & Ye, F. (2011). A two objective optimisation model for order splitting among parallel suppliers. International Journal of Production Research, 49(10), 2759–2769.
  8. Damyad, M. H., & Jafari, D. (2021). Codify a Three echelon inventory control model in terms of inflation with allowed shortage for a deterioration items. International Journal of Innovation in Engineering, 1(1), 101-119.
  9. Ding, H., Benyoucef, L., & Xie, X. (2009). Stochastic multi-objective production-distribution network design using simulation-based optimization. International Journal of Production Research, 47(2), 479–505.
  10. Fang, W., Guo, Y., Liao, W., Huang, S., Yang, N., & Liu, J. (2020). A Parallel Gated Recurrent Units (P-GRUs) network for the shifting lateness bottleneck prediction in make-to-order production system. Computers & Industrial Engineering, 140,
  11. Feng, X., Chen, Y., & Hu, X. (2018). Co-optimizing Capacity Planning with Order Acceptance and Scheduling in Make-to-Order Production System. In IIE Annual Conference. Proceedings (pp. 1849-1854). Institute of Industrial and Systems Engineers (IISE).
  12. Ghahremani Nahr, J., Pasandideh, S. H. R., & Niaki, S. T. A. (2020). A robust optimization approach for multi-objective, multi-product, multi-period, closed-loop green supply chain network designs under uncertainty and discount. Journal of industrial and production engineering, 37(1), 1-22.
  13. Ghahremani-Nahr, J., Nozari, H., & Najafi, S. E. (2020). Design a green closed loop supply chain network by considering discount under uncertainty. Journal of Applied Research on Industrial Engineering, 7(3), 238-266.
  14. He, Z., Guo, Z., & Wang, J. (2019). Integrated scheduling of production and distribution operations in a global MTO supply chain. Enterprise Information Systems, 13(4), 490-514.
  15. Hwang, H., Jaruphongsa, W., Cetinkaya, S., & Lee, C. (2010). Capacitated dynamic lotsizing problem with delivery/production time windows. Operations Research Letters, 38(5), 408–413.
  16. Jans, R., & Degraeve, Z. (2007). Meta-heuristics for dynamic lot sizing: A review and comparison of solution approaches. European Journal of Operational Research, 177(3), 1855–1875.
  17. Laumanns, M., Thiele, L., & Zitzler, E. (2006). An efficient, adaptive parameter variation scheme for metaheuristics based on the epsilon-constraint method. European Journal of Operational Research, 169(3), 932-942.
  18. Lee, C., Cetinkaya, S., & Wagelmans, A. (2001). A dynamic lot-sizing model with demand time windows. Management Science, 47(10), 1384–1395.
  19. Liao, Z., & Rittscher, J. (2007). Integration of supplier selection, procurement lot sizing and carrier selection under dynamic demand conditions. International Journal of Production Economics, 107(2), 502–510.
  20. Liu, L., & Liu, S. (2020). Integrated Production and Distribution Problem of Perishable Products with a Minimum Total Order Weighted Delivery Time. Mathematics, 8(2), 146.
  21. Luo, H., Yang, X., & Wang, K. (2019). Synchronized scheduling of make to order plant and cross-docking warehouse. Computers & Industrial Engineering, 138,
  22. Ma, J., Tu, Y., & Feng, D. (2020). Order Acceptance Policy for Make-To-Order Supply Chain. In Data Management and Analysis (pp. 67-89). Springer, Cham.
  23. Marandi, F., & Fatemi Ghomi, S. M. T. (2019). Integrated multi-factory production and distribution scheduling applying vehicle routing approach. International Journal of Production Research, 57(3), 722-748.
  24. Meng, F., Tang, J., & Xu, Z. (2017). A 0-1 mixed programming model based method for group decision making with intuitionistic fuzzy preference relations. Computers & Industrial Engineering, 112, 289-304.
  25. Moslemipour, G., & Ghadirpour, S. M. (2021). Intelligent Design of a Dynamic Facility Layout in the Stochastic Environment of Flexible Manufacturing Systems Considering Routing Flexibility. Journal of Industrial Management Perspective, 11(1), 175-209. (In Persian).
  26. Og, C., Salman, F. S., & Yalçın, Z. B. (2010). Order acceptance and scheduling decisions in make-to-order systems. International Journal of Production Economics, 125(1), 200-211.
  27. Pasandideh, S. H. R., Niaki, S. T. A., & Asadi, K. (2015). Bi-objective optimization of a multi-product multi-period three-echelon supply chain problem under uncertain environments: NSGA-II and NRGA. Information Sciences, 292, 57-74.
  28. Pasandideh, S. H. R., Niaki, S. T. A., & Asadi, K. (2015). Optimizing a bi-objective multi-product multi-period three echelon supply chain network with warehouse reliability. Expert Systems with Applications, 42(5), 2615-2623.
  29. Rafiei, H., & Rabbani, M. (2011). Order partitioning and order penetration point location in hybrid make-to-stock/make-to-order production contexts. Computers & Industrial Engineering, 61(3), 550-560.
  30. Rafiei, H., Rabbani, M., Vafa-Arani, H., & Bodaghi, G. (2017). Production-inventory analysis of single-station parallel machine make-to-stock/make-to-order system with random demands and lead times. International Journal of Management Science and Engineering Management, 12(1), 33-44.
  31. Rajagopalan, S. (2002). Make to order or make to stock: model and application. Management Science, 48(2), 241-256.
  32. Ren, C., Guo, P., Tan, Q., & Zhang, L. (2017). A multi-objective fuzzy programming model for optimal use of irrigation water and land resources under uncertainty in Gansu Province, China. Journal of Cleaner Production, 164, 85-94.
  33. Sajadi, S. M., Ayough, A., & Sayed Isfahani, M. M. (2016). An Integrated Model for Analysis and Improvement of Scheduling “Flexible Manufacturing Systems (FMS)” and Dispatching “Automated Guided Vehicle (AGV)” Problems. Journal of Industrial Management Perspective, 6(1), 97-127. (In Persian).
  34. Salamati-Hormozi, H., Zhang, Z. H., Zarei, O., & Ramezanian, R. (2018). Trade-off between the costs and the fairness for a collaborative production planning problem in make-to-order manufacturing. Computers & Industrial Engineering, 126, 421-434.
  35. Taleizadeh, A. A. (2017). Stochastic multi-objectives supply chain optimization with forecasting partial backordering rate: a novel hybrid method of meta goal programming and evolutionary algorithms. Asia-Pacific Journal of Operational Research, 34(04),
  36. Thurer, M., Fernandes, N., Carmo-Silva, S., & Stevenson, M. (2018). Lot splitting under load-limiting order release in high-variety shops: An assessment by simulation. Journal of Manufacturing Systems, 48, 63–72.
  37. Wolsey, L. (2006). Lot-sizing with production and delivery time windows. Mathematical Programming, 107(3), 471–489.
  38. Woschank, M., Dallasega, P., & Kapeller, J. A. (2020). The impact of planning granularity on production planning and control strategies in MTO: A discrete event simulation study. Procedia Manufacturing, 51, 1502-1507.
  39. Xiong, S., Feng, Y., & Huang, K. (2020). Optimal MTS and MTO Hybrid Production System for a Single Product under the Cap-And-Trade Environment. Sustainability, 12(6), 2426.
  40. Yadegari, E., Alem-Tabriz, A., & Zandieh, M. (2019). A memetic algorithm with a novel neighborhood search and modified solution representation for closed-loop supply chain network design. Computers & Industrial Engineering, 128, 418-436.
  41. Yao, X., Zhang, J., Li, Y., & Zhang, C. (2018). Towards flexible RFID event-driven integrated manufacturing for make-to-order production. International Journal of Computer Integrated Manufacturing, 31(3), 228-242.
  42. Ylänen, J. (2017). Continuous improvement in order delivery process of make-to-order products.
  43. Zabihian, A., Tavakkoli-Moghaddam, R., Memari, P., & Jolai, F. (2018, June). Location-pricing problem in the closed-loop supply chain network design under uncertainty. In International Workshop on Service Orientation in Holonic and Multi-Agent Manufacturing (pp. 360-371). Springer, Cham.
  44. Zhai, Y., & Cheng, T. C. E. (2021). Lead-time Quotation and Hedging Coordination in Make-to-order Supply Chain. European Journal of Operational Research, 112 (2), 28-44.
  45. Zhang, Z., Guo, C., Wei, Q., Guo, Z., & Gao, L. (2021). A bi-objective stochastic order planning problem in make-to-order multi-site textile manufacturing. Computers & Industrial Engineering, 158,