A stochastic bi-objective multi-product programming model to supply chain network design under disruption risks

Document Type : Research Paper


School of Industrial Engineering, Iran University of Science and Technology, Tehran, Iran


Emphasize on cost-cutting, increasing customers' satisfaction, and trying to manage and reduce the risks are among the key strategies of decision-makers in the design of supply chain networks. This study provides a stochastic bi-objective multi-product optimization model for designing a resilient supply chain network under disruption risks. The objectives of the proposed model are minimizing the total cost of the supply chain, as well as, minimizing the non-resiliency of the network. In addition, a ε-constraint method is used to convert the bi-objective model into a single-objective formulation. The model decisions include locating manufacturers, warehouses, and distribution centers and determining the amount of production of different products in each manufacturer, the amount of product transport between the different nodes of the network, and the amount of lost sales for different products in each market. The validity of the proposed model is investigated through random examples and the results of the model implementation on these examples are presented.


Main Subjects

Azad, N., Saharidis, G. K., Davoudpour, H., Malekly, H. & Yektamaram, S. A. (2013). Strategies for protecting supply chain networks against facility and transportation disruptions: an improved Benders decomposition approach. Annals of Operations Research, 210, 125-163.
Baghalian, A., Rezapour, S. & Farahani, R. Z. (2013). Robust supply chain network design with service level against disruptions and demand uncertainties: A real-life case. European Journal of Operational Research, 227, 199-215.
Bérubé, J.-F., Gendreau, M. & Potvin, J.-Y. (2009). An exact ϵ-constraint method for bi-objective combinatorial optimization problems: Application to the Traveling Salesman Problem with Profits. European journal of operational research, 194, 39-50.
Bhamra, R., Dani, S. & Burnard, K. (2011). Resilience: the concept, a literature review and future directions. International Journal of Production Research, 49, 5375-5393.
Birge, J. R. & Louveaux, F. (2011). Introduction to stochastic programming, Springer Science & Business Media.
Cardoso, S. R., Barbosa-Póvoa, A. P., Relvas, S. & Novais, A. Q. (2015). Resilience metrics in the assessment of complex supply-chains performance operating under demand uncertainty. Omega, 56, 53-73.
Chopra, S. & Sodhi, M. S. (2004). Managing risk to avoid supply-chain breakdown. MIT Sloan management review, 46, 53.
Dixit, V., Seshadrinath, N. & Tiwari, M. (2016). Performance measures based optimization of supply chain network resilience: A NSGA-II+ Co-Kriging approach. Computers & Industrial Engineering, 93, 205-214
Farahani, M., Shavandi, H. & Rahmani, D. (2017). A location-inventory model considering a strategy to mitigate disruption risk in supply chain by substitutable products. Computers & Industrial Engineering, 108, 213-224.
Garcia-Herreros, P., Wassick, J. M. & Grossmann, I. E. (2014). Design of resilient supply chains with risk of facility disruptions. Industrial & Engineering Chemistry Research, 53, 17240-17251.
Ghavamifar, A. & Sabouhi, F. (2018). An integrated model for designing a distribution network of products under facility and transportation link disruptions. Journal of Industrial and Systems Engineering, 11, 113-126.
Giri, B. C. & Bardhan, S. (2015). Coordinating a supply chain under uncertain demand and random yield in presence of supply disruption. International Journal of Production Research, 53, 5070-5084.
Han, X., Chen, D., Chen, D. & Long, H. (2015). Strategy of production and ordering in closed-loop supply chain under stochastic yields and stochastic demands. International Journal of u-and e-Service, Science and Technology, 8, 77-84.
Hasani, A. & Khosrojerdi, A. (2016). Robust global supply chain network design under disruption and uncertainty considering resilience strategies: A parallel memetic algorithm for a real-life case study. Transportation Research Part E: Logistics and Transportation Review, 87, 20-52.
Hendricks, K. B., Singhal, V. R. & Zhang, R. (2009). The effect of operational slack, diversification, and vertical relatedness on the stock market reaction to supply chain disruptions. Journal of Operations Management, 27, 233-246.
Jabbarzadeh, A., Fahimnia, B. & Sabouhi, F. (2018). Resilient and sustainable supply chain design: sustainability analysis under disruption risks. International Journal of Production Research, 56, 5945-5968.
Jabbarzadeh, A., Fahimnia, B. & Seuring, S. (2014). Dynamic supply chain network design for the supply of blood in disasters: A robust model with real world application. Transportation Research Part E: Logistics and Transportation Review, 70, 225-244.
Li, Q. & Savachkin, A. (2013). A heuristic approach to the design of fortified distribution networks. Transportation Research Part E: Logistics and Transportation Review, 50, 138-148.
Mavrotas, G. (2009). Effective implementation of the ε-constraint method in multi-objective mathematical programming problems. Applied mathematics and computation, 213, 455-465.
Nishat Faisal, M., Banwet, D. K. & Shankar, R. (2006). Supply chain risk mitigation: modeling the enablers. Business Process Management Journal, 12, 535-552.
Nooraie, S. V. & Parast, M. M. (2016). Mitigating supply chain disruptions through the assessment of trade-offs among risks, costs and investments in capabilities. International Journal of Production Economics, 171, 8-21.
Papapostolou, C., Kondili, E. & Kaldellis, J. K. (2011). Development and implementation of an optimisation model for biofuels supply chain. Energy, 36, 6019-6026.
Peng, P., Snyder, L. V., Lim, A. & Liu, Z. (2011). Reliable logistics networks design with facility disruptions. Transportation Research Part B: Methodological, 45, 1190-1211.
Sabouhi, F., Bozorgi-Amiri, A., Moshref-Javadi, M. & Heydari, M. (2018a). An integrated routing and scheduling model for evacuation and commodity distribution in large-scale disaster relief operations: a case study. Annals of Operations Research, 1-35.
Sabouhi, F., Heydari, M. & Bozorgi-Amiri, A. (2016). Multi-objective routing and scheduling for relief distribution with split delivery in post-disaster response. Journal of Industrial and Systems Engineering, 9, 17-27.
Sabouhi, F., Pishvaee, M. S. & Jabalameli, M. S. (2018b). Resilient supply chain design under operational and disruption risks considering quantity discount: A case study of pharmaceutical supply chain. Computers & Industrial Engineering, 126, 657-672.
Sabouhi, F., Tavakoli, Z. S., Bozorgi-Amiri, A. & Sheu, J.-B. (2019). A robust possibilistic programming multi-objective model for locating transfer points and shelters in disaster relief. Transportmetrica A: transport science, 15, 326-353.
Santoso, T., Ahmed, S., Goetschalckx, M. & Shapiro, A. (2005). A stochastic programming approach for supply chain network design under uncertainty. European Journal of Operational Research, 167, 96-115.
Scheibe, K. P. & Blackhurst, J. (2018). Supply chain disruption propagation: a systemic risk and normal accident theory perspective. International Journal of Production Research, 56, 43-59.
Schütz, P. & Tomasgard, A. (2011). The impact of flexibility on operational supply chain planning. International Journal of Production Economics, 134, 300-311.
Tang, C. S. (2006a). Perspectives in supply chain risk management. International journal of production economics, 103, 451-488.
Tang, C. S. (2006b). Robust strategies for mitigating supply chain disruptions. International Journal of Logistics: Research and Applications, 9, 33-45.
Vaez, P. (2017). A New Mathematical Model for Simultaneous Lot-sizing and Production Scheduling Problems Considering Earliness/Tardiness Penalties and Setup Costs. International Journal of Supply and Operations Management, 4, 167-179.
Vaez, P., Bijari, M. & Moslehi, G. (2018). Simultaneous scheduling and lot-sizing with earliness/tardiness penalties. International Journal of Planning and Scheduling, 2, 273-291.
Vaez, P., Sabouhi, F. & Jabalameli, M. S. (2019). Sustainability in a lot-sizing and scheduling problem with delivery time window and sequence-dependent setup cost consideration. Sustainable Cities and Society, 101718.
Yin, S., Nishi, T. & Grossmann, I. E. (2015). Optimal quantity discount coordination for supply chain optimization with one manufacturer and multiple suppliers under demand uncertainty. The International Journal of Advanced Manufacturing Technology, 76, 1173-1184.
Zahiri, B., Zhuang, J. & Mohammadi, M. (2017). Toward an integrated sustainable-resilient supply chain: A pharmaceutical case study. Transportation Research Part E: Logistics and Transportation Review, 103, 109-142.
Zokaee, S., Jabbarzadeh, A., Fahimnia, B. & Sadjadi, S. J. (2017). Robust supply chain network design: an optimization model with real world application. Annals of Operations Research, 257, 15-44.