Abstract
In this study, There is a mixed-integer nonlinear program (MINLP) for a two-echelon supply chain that focuses on supplier location, supplier selection and order allocation with green constraints. This bi-objective model is designed and modeled with the aim of coordinating inventory and transportation among suppliers and warehouses and tries to simultaneously meet the targets of minimizing total costs and carbon dioxide emissions of polluting gas in transportation. Since some of the important parameters in this model are considered uncertain, the scenario-based analysis is proposed to deal with uncertainty. Thirty numerical examples with different values and various sizes are solved by applying two methods of MODM, LP metrics, and Multi-choice goal programming with utility functions (MCGP-U) and their results are compared with one of the soft computing methods, Genetic algorithm. TOPSIS, Coefficient of Variation (CV) and One-way analysis of variance (ANOVA) methods are employed for the comprehensive comparison of these numerical examples. Finally, the sensitivity analysis method and Tornado diagram are applied to analyze the effect of variations of the model’s inputs on the results of the model.
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References
Amin SH, Zhang G (2013) A multi-objective facility location model for closed-loop supply chain network under uncertain demand and return. Appl Math Model 37:4165–4176. https://doi.org/10.1016/j.apm.2012.09.039
Amit S (2005) Review of supply chain management and logistics research. Int J Phys Distrib Logist Manag 35:664–705. https://doi.org/10.1108/09600030510632032
Arabzad SM, Ghorbani M, Zolfani SH (2015) A multi-objective robust optimization model for a facility location-allocation problem in a supply chain under uncertainty. Eng Econ 26:227–238. https://doi.org/10.5755/j01.ee.26.3.4287
Brito J, Castellanos-Nieves D, Expósito A, Moreno JA (2018) Soft computing methods in transport and logistics. In: Pelta DA, Cruz Corona C (eds) Studies in fuzziness and soft computing. Springer International Publishing, Cham, pp 45–61
Brown CE (1998) Coefficient of variation. Applied multivariate statistics in geohydrology and related sciences. Springer, Berlin, pp 155–157
Cárdenas-Barrón LE, González-Velarde JL, Treviño-Garza G (2015) A new approach to solve the multi-product multi-period inventory lot sizing with supplier selection problem. Comput Oper Res 64:225–232. https://doi.org/10.1016/j.cor.2015.06.008
Chang CT (2011) Multi-choice goal programming with utility functions. Eur J Oper Res 215:439–445. https://doi.org/10.1016/j.ejor.2011.06.041
De Boeck L, Vandaele N (2008) Coordination and synchronization of material flows in supply chains: an analytical approach. Int J Prod Econ 116:199–207. https://doi.org/10.1016/j.ijpe.2008.06.010
Diabat A, Battaïa O, Nazzal D (2015) An improved Lagrangian relaxation-based heuristic for a joint location-inventory problem. Comput Oper Res 61:170–178. https://doi.org/10.1016/j.cor.2014.03.006
Emirhüseyinoğlu G, Ekici A (2019) Dynamic facility location with supplier selection under quantity discount. Comput Ind Eng 134:64–74. https://doi.org/10.1016/j.cie.2019.05.023
Everitt BS (1998) The Cambridge dictionary of statistics. Cambridge University Press, Cambridge (UK Google Sch)
Fakhrzad MB, Firoozpour MR, Hosseininasab H, Sadeghieh A (2020) Realistic ranking of exclusive supplier strategies based on the evaluation of real value of the risks in the supply chain. J Ambient Intell Humaniz Comput. https://doi.org/10.1007/s12652-020-01725-5
Fan Y, Schwartz F, Voß S, Woodruff DL (2017) Stochastic programming for flexible global supply chain planning. Flex Serv Manuf J 29:601–633. https://doi.org/10.1007/s10696-016-9261-7
Fernandes DRM, Rocha C, Aloise D et al (2014) A simple and effective genetic algorithm for the two-stage capacitated facility location problem. Comput Ind Eng 75:200–208. https://doi.org/10.1016/j.cie.2014.05.023
Firouz M, Keskin BB, Melouk SH (2017) An integrated supplier selection and inventory problem with multi-sourcing and lateral transshipments. Omega (United Kingdom) 70:77–93. https://doi.org/10.1016/j.omega.2016.09.003
Guo C, Li X (2014) A multi-echelon inventory system with supplier selection and order allocation under stochastic demand. Int J Prod Econ 151:37–47. https://doi.org/10.1016/j.ijpe.2014.01.017
Hashemi SH, Karimi A, Tavana M (2015) An integrated green supplier selection approach with analytic network process and improved Grey relational analysis. Int J Prod Econ 159:178–191. https://doi.org/10.1016/j.ijpe.2014.09.027
Heidari-Fathian H, Pasandideh SHR (2018) Green-blood supply chain network design: Robust optimization, bounded objective function & Lagrangian relaxation. Comput Ind Eng 122:95–105. https://doi.org/10.1016/j.cie.2018.05.051
Holland JH (1992) Adaptation in natural and artificial systems: an introductory analysis with applications to biology, control, and artificial intelligence. MIT press, New York
Hoseini AR, Ghannadpour SF, Ghamari R (2020) Sustainable supplier selection by a new possibilistic hierarchical model in the context of Z-information. J Ambient Intell Humaniz Comput. https://doi.org/10.1007/s12652-020-01751-3
Hwang C-L, Yoon K (1981) Methods for multiple attribute decision making. Springer, Heidelberg. https://doi.org/10.1007/978-3-642-48318-9_3
Hwang CL, Lai YJ, Liu TY (1993) A new approach for multiple objective decision making. Comput Oper Res 20:889–899. https://doi.org/10.1016/0305-0548(93)90109-V
Inuiguchi M, Ramík J (2000) Possibilistic linear programming: a brief review of fuzzy mathematical programming and a comparison with stochastic programming in portfolio selection problem. Fuzzy Sets Syst 111:3–28. https://doi.org/10.1016/S0165-0114(98)00449-7
Jadidi O, Zolfaghari S, Cavalieri S (2014) A new normalized goal programming model for multi-objective problems: a case of supplier selection and order allocation. Int J Prod Econ 148:158–165. https://doi.org/10.1016/j.ijpe.2013.10.005
Jadidi O, Cavalieri S, Zolfaghari S (2015) An improved multi-choice goal programming approach for supplier selection problems. Appl Math Model 39:4213–4222. https://doi.org/10.1016/j.apm.2014.12.022
Jones D (2011) A practical weight sensitivity algorithm for goal and multiple objective programming. Eur J Oper Res 213:238–245. https://doi.org/10.1016/j.ejor.2011.03.012
Kackar RN (1985) Off-line quality control, parameter design, and the Taguchi method. J Qual Technol 17:176–188. https://doi.org/10.1080/00224065.1985.11978964
Kang B, Zhang P, Gao Z et al (2019) Environmental assessment under uncertainty using Dempster-Shafer theory and Z-numbers. J Ambient Intell Humaniz Comput. https://doi.org/10.1007/s12652-019-01228-y
Kannan D, Khodaverdi R, Olfat L et al (2013) Integrated fuzzy multi criteria decision making method and multiobjective programming approach for supplier selection and order allocation in a green supply chain. J Clean Prod 47:355–367. https://doi.org/10.1016/j.jclepro.2013.02.010
Kellner F, Utz S (2019) Sustainability in supplier selection and order allocation: combining integer variables with Markowitz portfolio theory. J Clean Prod 214:462–474. https://doi.org/10.1016/j.jclepro.2018.12.315
Khalilzadeh M, Derikvand H (2018) A multi-objective supplier selection model for green supply chain network under uncertainty. J Model Manag 13:605–625. https://doi.org/10.1108/JM2-06-2017-0062
Litvinchev I, Ozuna EL (2012) Lagrangian bounds and a heuristic for the two-stage capacitated facility location problem. Int J Energy Optim Eng 1:59–71
Litvinchev I, Pérez MM, Espinosa ELO (2012) Two stage facility location problem: Lagrangian based heuristics. Braz Symp Oper Res 1:1–12
Mahaboob Sheriff KM, Gunasekaran A, Nachiappan S (2012) Reverse logistics network design: a review on strategic perspective. Int J Logist Syst Manag 12:171–194
Mendoza A, Ventura JA (2012) Analytical models for supplier selection and order quantity allocation. Appl Math Model 36:3826–3835. https://doi.org/10.1016/j.apm.2011.11.025
Moghaddam KS (2015) Fuzzy multi-objective model for supplier selection and order allocation in reverse logistics systems under supply and demand uncertainty. Expert Syst Appl 42:6237–6254. https://doi.org/10.1016/j.eswa.2015.02.010
Mohammed A, Setchi R, Filip M et al (2018) An integrated methodology for a sustainable two-stage supplier selection and order allocation problem. J Clean Prod 192:99–114. https://doi.org/10.1016/j.jclepro.2018.04.131
Mohammed A, Harris I, Kannan G (2019) A hybrid MCDM-FMOO approach for sustainable supplier selection and order allocation. Int J Prod Econ. https://doi.org/10.1016/j.ijpe.2019.02.003
Moheb-Alizadeh H, Handfield R (2019) Sustainable supplier selection and order allocation: a novel multi-objective programming model with a hybrid solution approach. Comput Ind Eng 129:192–209. https://doi.org/10.1016/j.cie.2019.01.011
Omurca SI (2013) An intelligent supplier evaluation, selection and development system. Appl Soft Comput J 13:690–697. https://doi.org/10.1016/j.asoc.2012.08.008
Opricovic S (2004) Compromise solution by MCDM methods: a comparative analysis of VIKOR and TOPSIS. Eur J Oper Res 156:445–455. https://doi.org/10.1016/S0377-2217(03)00020-1
Pal A, Chan FTS, Mahanty B, Tiwari MK (2011) Aggregate procurement, production, and shipment planning decision problem for a three-echelon supply chain using swarm-based heuristics. Int J Prod Res 49:2873–2905. https://doi.org/10.1080/00207541003730847
Papen P, Amin SH (2019) Network configuration of a bottled water closed-loop supply chain with green supplier selection. J Remanufacturing 9:109–127. https://doi.org/10.1007/s13243-018-0061-y
Pasandideh SHR, Keshavarz M (2015) A multi objective model for determining ordering strategy within different constraints. Int J Math Oper Res 7:52–68. https://doi.org/10.1504/IJMOR.2015.065957
Purohit AK, Choudhary D, Shankar R (2016) Inventory lot-sizing with supplier selection under non-stationary stochastic demand. Int J Prod Res 54:2459–2469. https://doi.org/10.1080/00207543.2015.1102354
Ranjbar Tezenji F, Mohammadi M, Pasandideh SHR, Nouri Koupaei M (2016) An integrated model for supplier location-selection & order allocation under capacity constraints in an uncertain environment. Sci Iran 23:3009–3025. https://doi.org/10.24200/sci.2016.4008
Rao RS, Kumar CG, Prakasham RS, Hobbs PJ (2008) The Taguchi methodology as a statistical tool for biotechnological applications: a critical appraisal. Biotechnol J 3:510–523. https://doi.org/10.1002/biot.200700201
Rezaee A, Dehghanian F, Fahimnia B, Beamon B (2017) Green supply chain network design with stochastic demand and carbon price. Ann Oper Res 250:463–485. https://doi.org/10.1007/s10479-015-1936-z
Rezaei J, Nispeling T, Sarkis J, Tavasszy L (2016) A supplier selection life cycle approach integrating traditional and environmental criteria using the best worst method. J Clean Prod 135:577–588. https://doi.org/10.1016/j.jclepro.2016.06.125
Sadjadi SJ, Makui A, Dehghani E, Pourmohammad M (2016) Applying queuing approach for a stochastic location-inventory problem with two different mean inventory considerations. Appl Math Model 40:578–596. https://doi.org/10.1016/j.apm.2015.06.010
Salehi H, Moghaddam RT, Nasiri GR (2015) A multi-objective location-allocation problem with lateral transshipment between distribution centres. Int J Logist Syst Manag 22:464. https://doi.org/10.1504/IJLSM.2015.072749
Sawik T (2011) Selection of supply portfolio under disruption risks. Omega 39:194–208. https://doi.org/10.1016/j.omega.2010.06.007
Sazvar Z, Mirzapour Al-E-Hashem SMJ, Baboli A, Akbari Jokar MR (2014) A bi-objective stochastic programming model for a centralized green supply chain with deteriorating products. Int J Prod Econ 150:140–154. https://doi.org/10.1016/j.ijpe.2013.12.023
Shafiei Kisomi M, Solimanpur M, Doniavi A (2016) An integrated supply chain configuration model and procurement management under uncertainty: a set-based robust optimization methodology. Appl Math Model 40:7928–7947. https://doi.org/10.1016/j.apm.2016.03.047
Smirnov AV, Sheremetov LB, Chilov N, Cortes JR (2004) Soft-computing technologies for configuration of cooperative supply chain. Appl Soft Comput 4:87–107. https://doi.org/10.1016/j.asoc.2003.10.001
Torabi SA, Baghersad M, Mansouri SA (2015) Resilient supplier selection and order allocation under operational and disruption risks. Transp Res Part E Logist Transp Rev 79:22–48. https://doi.org/10.1016/j.tre.2015.03.005
Urata T, Yamada T, Itsubo N, Inoue M (2015) Modeling and balancing for costs and CO2 emissions in global supply chain network among Asian countries. Proc CIRP 26:664–669. https://doi.org/10.1016/j.procir.2014.07.107
Vahidi F, Torabi SA, Ramezankhani MJ (2018) Sustainable supplier selection and order allocation under operational and disruption risks. J Clean Prod 174:1351–1365. https://doi.org/10.1016/j.jclepro.2017.11.012
Vital Soto A, Chowdhury NT, Allahyari MZ et al (2017) Mathematical modeling and hybridized evolutionary LP local search method for lot-sizing with supplier selection, inventory shortage, and quantity discounts. Comput Ind Eng 109:96–112. https://doi.org/10.1016/j.cie.2017.04.027
Wang F, Lai X, Shi N (2011a) A multi-objective optimization for green supply chain network design. Decis Support Syst 51:262–269. https://doi.org/10.1016/j.dss.2010.11.020
Wang KJ, Makond B, Liu SY (2011b) Location and allocation decisions in a two-echelon supply chain with stochastic demand—a genetic-algorithm based solution. Expert Syst Appl 38:6125–6131. https://doi.org/10.1016/j.eswa.2010.11.008
Xu Q (2013) A novel machine learning strategy based on two-dimensional numerical models in financial engineering. Math Probl Eng. https://doi.org/10.1155/2013/659809
Xu Q, Li M (2019) A new cluster computing technique for social media data analysis. Cluster Comput 22:2731–2738. https://doi.org/10.1007/s10586-017-1436-9
Xu Q, Wu J, Chen Q (2014) A novel mobile personalized recommended method based on money flow model for stock exchange. Math Probl Eng. https://doi.org/10.1155/2014/353910
Xu Q, Li M, Yu M (2019) Learning to rank with relational graph and pointwise constraint for cross-modal retrieval. Soft Comput 23:9413–9427. https://doi.org/10.1007/s00500-018-3608-9
Yazdani M, Chatterjee P, Zavadskas EK, Hashemkhani Zolfani S (2017) Integrated QFD-MCDM framework for green supplier selection. J Clean Prod 142:3728–3740. https://doi.org/10.1016/j.jclepro.2016.10.095
Yu F, Yang Y, Chang D (2018) Carbon footprint based green supplier selection under dynamic environment. J Clean Prod 170:880–889. https://doi.org/10.1016/j.jclepro.2017.09.165
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Hemmati, M., Pasandideh, S.H.R. A bi-objective supplier location, supplier selection and order allocation problem with green constraints: scenario-based approach. J Ambient Intell Human Comput 12, 8205–8228 (2021). https://doi.org/10.1007/s12652-020-02555-1
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DOI: https://doi.org/10.1007/s12652-020-02555-1