Abstract
In this paper, a strategic level of a supply chain is studied. To deal with its objective, restructuring distribution and manufacturing centers under the parameter uncertainty and system disruption are formulated as a mixed-integer nonlinear programming (MINLP) model. Because of the complexity of such a hard model, it is converted to a mixed-integer linear programming (MILP) model by conducting a simple linearization method. Capacity expansion and reduction, capacity consolidation, outsourcing, and transshipment strategies are used to reconfigure the considered supply chain. An inexact interval fixed-mix fuzzy approach is applied to deal with the parameter uncertainty, and an efficient two-stage model is conducted to analyze the system reliability. The developed model is solved by an efficient and effective Lagrangian relaxation procedure. Furthermore, a case study of dairy products is studied to present the model application and validation. Finally, several sensitivity analyses are carried out to identify the model behavior and solution algorithm validation.










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References
Arasteh A (2019) Supply chain management under uncertainty with the combination of fuzzy multi-objective planning and real options approaches Soft Comput 1–22
Ballou RH (1968) Dynamic warehouse location analysis. J Mark Res 5(3):271–276
Bai X, Liu Y (2016) Robust optimization of supply chain network design in fuzzy decision system. J Intell Manuf 27(6):1131–1149
Bhattacharya K, De SK (2021) A robust two layer green supply chain modelling under performance based fuzzy game theoretic approach. Comput Ind Eng 152:107005
Chouhan VK, Khan SH, Hajiaghaei-Keshteli M, Subramanian S, (2020) Multi-facility-based improved closed-loop supply chain network for handling uncertain demands Soft Comput 1–23
Dias J, Captivo ME, Clímaco J (2006) Capacitated dynamic location problems with opening, closure and reopening of facilities. IMA J Manag Math 17(4):317–348
De SK, Sana SS (2018) Two-layer supply chain model for Cauchy-type stochastic demand under fuzzy environment Int J Intell Comput Cybern
DE, S. K., & Mahata, G. C. (2019) An EPQ model for three-layer supply chain with partial backordering and disruption: Triangular dense fuzzy lock set approach. Sādhanā 44(8):1–15
De SK, Mahata GC (2020) A production inventory supply chain model with partial backordering and disruption under triangular linguistic dense fuzzy lock set approach. Soft Comput 24(7):5053–5069
De SK, Mahata GC (2021) Solution of an imperfect-quality EOQ model with backorder under fuzzy lock leadership game approach. Int J Intell Syst 36(1):421–446
De SK (2021) Solving an EOQ model under fuzzy reasoning. Appl Soft Comput 99:106892
Fisher ML (1981) The Lagrangian relaxation method for solving integer programming problems. Manag Sci 27(1):1–18
Fisher ML (2004) The Lagrangian relaxation method for solving integer programming problems. Manag Sci 50(12):1861–1871
Ghasimi SA, Ramli R, Saibani N, Narooei KD (2018) An uncertain mathematical model to maximize profit of the defective goods supply chain by selecting appropriate suppliers. J Intell Manuf 29(6):1219–1234
Held M, Karp RM (1970) The traveling-salesman problem and minimum spanning trees. Oper Res 18(6):1138–1162
Held M, Karp RM (1971) The traveling-salesman problem and minimum spanning trees: Part II. Math Program 1(1):6–25
Huang G, Baetz BW, Patry GG (1992) A grey linear programming approach for municipal solid waste management planning under uncertainty. Civ Eng Syst 9(4):319–335
Jahani H, Abbasi B, Alavifard F, Talluri S (2018) Supply chain network redesign with demand and price uncertainty. Int J Prod Econ 205:287–312
Jafarian E, Razmi J, Tavakkoli-Moghaddam R (2019) Forward and reverse flows pricing decisions for two competing supply chains with common collection centers in an intuitionistic fuzzy environment. Soft Comput 23(17):7865–7888
Kiya F, Davoudpour H (2012) Stochastic programming approach to re-designing a warehouse network under uncertainty. Transport Res Part e Logist Transport Rev 48(5):919–936
Li W, Bao Z, Huang GH Xie YL (2018) An inexact credibility chance-constrained integer programming for greenhouse gas mitigation management in regional electric power system under uncertainty J Environ Inform 31(2)
Lu HW, Cao MF, Li J, Huang GH, He L (2015) An inexact programming approach for urban electric power systems management under random-interval-parameter uncertainty. Appl Math Model 39(7):1757–1768
Ma H, Li X, Liu Y (2020) Multi-period multi-scenario optimal design for closed-loop supply chain network of hazardous products with consideration of facility expansion. Soft Comput 24(4):2769–2780
Melachrinoudis E, Messac A, Min H (2005) Consolidating a warehouse network: a physical programming approach. Int J Prod Econ 97(1):1–17
Melachrinoudis E, Min H (2000) The dynamic relocation and phase-out of a hybrid, two-echelon plant/warehousing facility: a multiple objective approach. Eur J Oper Res 123(1):1–15
Melachrinoudis E, Min H (2007) Redesigning a warehouse network. Eur J Oper Res 176(1):210–229
Melo MT, Nickel S, Da Gama FS (2006) Dynamic multi-commodity capacitated facility location: a mathematical modeling framework for strategic supply chain planning. Comput Oper Res 33(1):181–208
Min H, Melachrinoudis E (1999) The relocation of a hybrid manufacturing/distribution facility from supply chain perspectives: a case study. Omega 27(1):75–85
Paul SK, Sarker R, Essam D (2018) A reactive mitigation approach for managing supply disruption in a three-tier supply chain. J Intell Manuf 29(7):1581–1597
Peng P, Snyder LV, Lim A, Liu Z (2011) Reliable logistics networks design with facility disruptions. Transport Res Part b Methodol 45(8):1190–1211
Razmi J, Zahedi-Anaraki A, Zakerinia M (2013) A bi-objective stochastic optimization model for reliable warehouse network redesign. Math Comput Model 58(11–12):1804–1813
Sauvey C, Melo T, Correia I (2020) Heuristics for a multi-period facility location problem with delayed demand satisfaction. Comput Ind Eng 139:106171
Shi J, Chen W, Zhou Z, Zhang G (2019) A bi-objective multi-period facility location problem for household e-waste collection Int J Prod Res 1–20
Shishebori D, Yousefi-Babadi A, Noormohammadzadeh Z (2018) A Lagrangian relaxation approach to fuzzy robust multi-objective facility location network design problem. Scientia Iranica. Transaction E, Indust Eng 25(3):1750–1767
Shishebori D, Yousefi-Babadi A (2015) Robust and reliable medical services network design under uncertain environment and system disruptions. Transport Res Part e Logist Transport Rev 77:268–288
Wang Q, Batta R, Bhadury J, Rump CM (2003) Budget constrained location problem with opening and closing of facilities. Comput Oper Res 30(13):2047–2069
Wesolowsky GO (1973) Dynamic facility location. Manag Sci 19(11):1241–1248
Wesolowsky GO, Truscott WG (1975) The multiperiod location-allocation problem with relocation of facilities. Manag Sci 22(1):57–65
Wu CB, Huang GH, Li W, Zhen JL, Ji L (2016) An inexact fixed-mix fuzzy-stochastic programming model for heat supply management in wind power heating system under uncertainty. J Clean Prod 112:1717–1728
Yousefi-Babadi A, Tavakkoli-Moghaddam R, Bozorgi-Amiri A, Seifi S (2017) Designing a reliable multi-objective queuing model of a petrochemical supply chain network under uncertainty: a case study. Comput Chem Eng 100:177–197
Zhang C, Fan LW, Tian YX (2020) Optimal operational strategies of capital-constrained supply chain with logistics service and price dependent demand under 3PL financing service. Soft Comput 24(4):2793–2806
Zimmermann HJ (2010) Fuzzy set theory. Wiley Interdiscip Rev Comput Statistics 2(3):317–332
Zimmermann HJ (1978) Fuzzy programming and linear programming with several objective functions. Fuzzy Sets Syst 1(1):45–55
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This study was funded by the Iranian National Science Foundation (INSF) [grant number 96001557].
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Yousefi-Babadi, A., Bozorgi-Amiri, A. & Tavakkoli-Moghaddam, R. Redesigning a supply chain network with system disruption using Lagrangian relaxation: a real case study. Soft Comput 26, 10275–10299 (2022). https://doi.org/10.1007/s00500-022-07340-0
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DOI: https://doi.org/10.1007/s00500-022-07340-0