A Robust Fuzzy-Probabilistic Programming Model for a Reliable Supply Chain Network Design Problem

Document Type : Research Paper


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


Supply chain network design decisions are among the strategic decisions of supply chain management which play significant role on the efficient performance of the supply chain. However, there are two challenging factors which may have great impact on the supply chain performance. These factors are on the one hand disruptions and their attendant damages and on the other hand uncertain nature of business-as-usual parameters. Therefore, the supply chain being designed should be reliable against disruptions as well as should be robust under business-as-usual uncertainty. This paper proposes a new robust fuzzy-probabilistic programming model for designing a reliable multi-period supply chain network which can cope with the two challenging factors, simultaneously. At first, in order to design a reliable model, by taking into account two types of facilities, that are fail able and non-fail able against probabilistic disruptions, a hard worst case approach is employed. Then to deal with business-as-usual uncertainty a robust fuzzy programming is developed. Flexible constraints of customers and determining the optimum level of satisfying these constraints is also considered in the model. Furthermore, to incorporate the concept of reliability in the problem and to cover the important features of real life supply chains, uncertain partial disruption and constraints of expected delivery time of customers are taken into account in the model. Finally, an industrial case study related to a manufacturer engaged in the healthcare system of Iran is applied to demonstrate the effectiveness and the applicability of the developed model.


Main Subjects

1-           Stadler, H., Kilger, C., (2008), “Supply chain management and advanced planning: concepts, models, software, and case studies,” 4th ed., 4th,Springer, .
2-           Klibi, W., Martel, A., Guitouni, A., (2010). “The design of robust value-creating supply chain networks: A critical review.” European Journal of Operational Research. Vol. 203, No.2, PP.283–293.
3-           Kleindorfer, P.R., Saad, G.H., (2005). “Managing Disruption Risks in Supply Chains.” Production and Operations Management. Vol. 14, No.1, PP.53–68.
4-           Snyder, L. V., (2006). “Facility location under uncertainty: a review.” IIE Transactions. Vol. 38, No.7, PP.547–564.
5-           Pan, F., Nagi, R., (2010). “Robust supply chain design under uncertain demand in agile manufacturing.” Computers & Operations Research. Vol. 37, No.4, PP.668–683.
6-           Pishvaee, M.S., Rabbani, M., Torabi, S.A., (2011). “A robust optimization approach to closed-loop supply chain network design under uncertainty.” Applied Mathematical Modelling. Vol. 35, No.2, PP.637–649.
7-           Pishvaee, M.S., Razmi, J., Torabi, S.A., (2012). “Robust possibilistic programming for socially responsible supply chain network design: A new approach.” Fuzzy Sets and Systems. Vol. 206, PP.1–20.
8-           Lowrance, W.W., (1976), “Of Acceptable Risk: Science and the Determination of Safety.,” William Kaufman, Los Altos, CA., .
9-           Peng, P., Snyder, L. V., Lim, A., Liu, Z., (2011). “Reliable logistics networks design with facility disruptions.” Transportation Research Part B: Methodological. Vol. 45, No.8, PP.1190–1211.
10-        Snyder, L. V., Scaparra, M.P., Daskin, M.S., Church, R.L., (2006). “Planning for disruptions in supply chain networks.” Tutorials in Operations Research. PP.234–257.
11-        Vahdani, B., Tavakkoli-Moghaddam, R., Modarres, M., Baboli, A., (2012). “Reliable design of a forward/reverse logistics network under uncertainty: A robust-M/M/c queuing model.” Transportation Research Part E: Logistics and Transportation Review. Vol. 48, No.6, PP.1152–1168.
12-        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. Vol. 227, No.1, PP.199–215.
13-        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. Vol. 70, PP.225–244.
14-        Shishebori, D., Yousefi Babadi, A., (2015). “Robust and reliable medical services network design under uncertain environment and system disruptions.” Transportation Research Part E: Logistics and Transportation Review. Vol. 77, PP.268–288.
15-        Azad, N., Saharidis, G.K.D., Davoudpour, H., Maleky, H., Yektamaram, S.A., (2013). “Strategies for protecting supply chain networks against facility and transportation disruptions : an improved Benders decomposition approach.” Annals of Operations ….
16-        Drezner, Z., (1987). “Heuristic solution methods for two location problems with unreliable facilities.” Journal of the Operational Research Society. Vol. 38, No.6, PP.509–514.
17-        Snyder, L. V., Daskin, M.S., (2005). “Reliability Models for Facility Location: The Expected Failure Cost Case.” Transportation Science. Vol. 39, No.3, PP.400–416.
18-        Snyder, L. V., Daskin, M.S., (2006). “Stochastic p -robust location problems.” IIE Transactions. Vol. 38, No.11, PP.971–985.
19-        Shen, Z.-J.M., Zhan, R.L., Zhang, J., (2011). “The Reliable Facility Location Problem: Formulations, Heuristics, and Approximation Algorithms.” INFORMS Journal on Computing. Vol. 23, No.3, PP.470–482.
20-        Cui, T., Ouyang, Y., Shen, Z., (2010). “Reliable facility location design under the risk of disruptions.” Operations Research. Vol. 58, No.4-part-1, PP.998–1011.
21-        Chopra, S., Reinhardt, G., Mohan, U., (2007). “The importance of decoupling recurrent and disruption risks in a supply chain.” Naval Research Logistics. Vol. 54, No.5, PP.544–555.
22-        Lim, M., Daskin, M.S., Bassamboo, A., Chopra, S., (2009). “A facility reliability problem: Formulation, properties, and algorithm.” Naval Research Logistics (NRL). Vol. 57, No.1, PP.58–70.
23-        Lim, M.K., Bassamboo, A., Chopra, S., Daskin, M.S., (2013). “Facility Location Decisions with Random Disruptions and Imperfect Estimation.” Manufacturing & Service Operations Management. Vol. 15, No.2, PP.239–249.
24-        Hasani, A., Zegordi, S.H., Nikbakhsh, E., (2012). “Robust closed-loop supply chain network design for perishable goods in agile manufacturing under uncertainty.” International Journal of Production Research. Vol. 50, No.16, PP.4649–4669.
25-        De Rosa, V., Gebhard, M., Hartmann, E., Wollenweber, J., (2013). “Robust sustainable bi-directional logistics network design under uncertainty.” International Journal of Production Economics. Vol. 145, No.1, PP.184–198.
26-        Vahdani, B., Tavakkoli-Moghaddam, R., Jolai, F., (2013). “Reliable design of a logistics network under uncertainty: A fuzzy possibilistic-queuing model.” Applied Mathematical Modelling. Vol. 37, No.5, PP.3254–3268.
27-        Hatefi, S.M., Jolai, F., (2014). “Robust and reliable forward–reverse logistics network design under demand uncertainty and facility disruptions.” Applied Mathematical Modelling. Vol. 38, No.9-10, PP.2630–2647.
28-        Li, Q., Zeng, B., Savachkin, A., (2013). “Reliable facility location design under disruptions.” Computers & Operations Research. Vol. 40, No.4, PP.901–909.
29-        Berman, O., Krass, D., Menezes, M.B.C., (2013). “Location and reliability problems on a line: Impact of objectives and correlated failures on optimal location patterns.” Omega. Vol. 41, No.4, PP.766–779.
30-        Razmi, J., Zahedi-Anaraki, A., Zakerinia, M., (2013). “A bi-objective stochastic optimization model for reliable warehouse network redesign.” Mathematical and Computer Modelling. Vol. 58, No.11-12, PP.1804–1813.
31-        Wang, X., Ouyang, Y., (2013). “A continuum approximation approach to competitive facility location design under facility disruption risks.” Transportation Research Part B. Vol. 50, PP.90–103.
32-        An, Y., Zeng, B., Zhang, Y., Zhao, L., (2014). “Reliable p-median facility location problem: two-stage robust models and algorithms.” Transportation Research Part B: Methodological. Vol. 64, PP.54–72.
33-        Amaro, A.C.S., Barbosa-Póvoa, A.P.F.D., (2009). “The effect of uncertainty on the optimal closed-loop supply chain planning under different partnerships structure.” Computers & Chemical Engineering. Vol. 33, No.12, PP.2144–2158.
34-        Soyster, A.L., (1973). “Technical note—convex programming with set-inclusive constraints and applications to inexact linear programming.” Operations Research. Vol. 21, No.5, PP.1154–1157.
35-        Mulvey, J.M., Vanderbei, R.J., Zenios, S.A., (1995). “Robust Optimization of Large-Scale Systems.” Operations Research. Vol. 43, No.2, PP.264–281.
36-        Ben-Tal, A., Nemirovski, A., (1998). “Robust Convex Optimization.” Mathematics of Operations Research. Vol. 23, No.4, PP.769–805.
37-        Ben-Tal, A., Nemirovski, A., (1999). “Robust solutions of uncertain linear programs.” Operations Research Letters. Vol. 25, No.1, PP.1–13.
38-        Ben-Tal, A., Nemirovski, A., (2000). “Robust solutions of Linear Programming problems contaminated with uncertain data.” Mathematical Programming. Vol. 88, No.3, PP.411–424.
39-        El Ghaoui, L., Oustry, F., Lebret, H., (1998). “Robust Solutions to Uncertain Semidefinite Programs.” SIAM Journal on Optimization. Vol. 9, No.1, PP.33–52.
40-        Bertsimas, D., Sim, M., (2003). “Robust discrete optimization and network flows.” Mathematical Programming. Vol. 98, No.1-3, PP.49–71.
41-        Bertsimas, D., Sim, M., (2004). “The Price of Robustness.” Operations Research. Vol. 52, No.1, PP.35–53.
42-        Dubois, D., Prade, H., (1988), “Possibility theory: an approach to computerized processing of uncertainty,” Springer, Boston, .
43-        Verdegay, J.L., (1982). “Fuzzy mathematical programming.” Fuzzy Information and Decision Processes. Vol. 231, PP.237.
44-        Lodwick, W. a., Jamison, K.D., (2007). “Theoretical and semantic distinctions of fuzzy, possibilistic, and mixed fuzzy/possibilistic optimization.” Fuzzy Sets and Systems. Vol. 158, No.17, PP.1861–1872.
45-        Delgado, M., Verdegay, J., Vila, M., (1989). “A general model for fuzzy linear programming.” Fuzzy Sets and Systems. Vol. 29, No.1, PP.21–29.
46-        Untiedt, E., A Parametrized Model for Optimization with Mixed Fuzzy and Possibilistic Uncertainty, in: W. Lodwick, J. Kacprzyk (Eds.), Fuzzy Optimization SE - 9, Springer Berlin Heidelberg, : pp. 193–208.
47-        Liu, B., Iwamura, K., (1998). “Chance constrained programming with fuzzy parameters.” Fuzzy Sets and Systems. Vol. 94, No.2, PP.227–237.
48-        Heilpern, S., (1992). “The expected value of a fuzzy number.” Fuzzy Sets and Systems. Vol. 47, No.1, PP.81–86.