Abstract
The closed-loop supply chain model with an assumption of perfect produced items is used commonly in the literature. We consider the imperfect quality production to provide meaningful solutions to practical problems. In this novel model, we assume that the screening is not always perfect, and inspection errors are more likely to take place in practice. The model considers multiple periods, echelons, and uncertainties. Moreover, the proposed robust multi-objective mixed integer linear programming model considers the optimization of three objectives simultaneously. The first objective function is optimized to minimize the total cost of the supply chain. The second objective function seeks to minimize the environmental influence, and the third objective function is optimized to maximize the social benefits. The augmented weighted Tchebycheff method is used to aggregate the objective functions into one objective and produce the set of efficient solutions. Robust optimization, based on the extended Mulvey et al. (1995) approach, is used to obtain a set of solutions that are robust against the future fluctuation of parameters. Finally, numerical examples have been presented to test and analyze the tradeoff between solution robustness and model robustness.
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References
Ahmadi, M., Khoshalhan, F., & Glock, C. H. (2016). Optimal production and distribution policies for a two-stage supply chain with imperfect items and price- and advertisement-sensitive demand: A note. Applied Mathematical Modelling, 1–8. https://doi.org/10.1016/j.apm.2016.11.003
Al-e-hashem, S. M. J. M., Malekly, H., & Aryanezhad, M. B. (2011). A multi-objective robust optimization model for multi-product multi-site aggregate production planning in a supply chain under uncertainty. International Journal of Production Economics, 134(1), 28–42. https://doi.org/10.1016/j.ijpe.2011.01.027
Almaraj, I. I., & Trafalis, T. B. (2019). An integrated multi-echelon robust closed-loop supply chain under imperfect quality production. International Journal of Production Economics, 218(May), 212–227. https://doi.org/10.1016/j.ijpe.2019.04.035
Baghalian, A., Rezapour, S., & Zanjirani, R. (2013). Robust supply chain network design with service level against disruptions and demand uncertainties: A real-life case. European Journal of Operational Research, 227(1), 199–215. https://doi.org/10.1016/j.ejor.2012.12.017
Dächert, K., Gorski, J., & Klamroth, K. (2012). An augmented weighted Tchebycheff method with adaptively chosen parameters for discrete bicriteria optimization problems. Computers & Operations Research, 39, 2929–2943. https://doi.org/10.1016/j.cor.2012.02.021
Datta, S. (2012). Multi-criteria multi-facility location in Niwai block, Rajasthan. IIMB Management Review, 24(1), 16–27. https://doi.org/10.1016/j.iimb.2011.12.003
Fathollahi-fard, A. M., & Hajiaghaei-keshteli, M. (2018). A stochastic multi-objective model for a closed-loop supply chain with environmental considerations. Applied Soft Computing Journal, 69, 232–249. https://doi.org/10.1016/j.asoc.2018.04.055
Fathollahi-fard, A. M., Hajiaghaei-keshteli, M., & Mirjalili, S. (2018). Multi-objective stochastic closed-loop supply chain network design with social considerations. Applied Soft Computing Journal, 71, 505–525. https://doi.org/10.1016/j.asoc.2018.07.025
Garg, K., Kannan, D., Diabat, A., & Jha, P. C. (2015). A multi-criteria optimization approach to manage environmental issues in closed loop supply chain network design. Journal of Cleaner Production, 100, 297–314. https://doi.org/10.1016/j.jclepro.2015.02.075
Ghaderi, H., Moini, A., & Pishvaee, M. S. (2018). A multi-objective robust possibilistic programming approach to sustainable switchgrass-based bioethanol supply chain network design. Journal of Cleaner Production, 179, 368–406. https://doi.org/10.1016/j.jclepro.2017.12.218
Gholizadeh, H., Tajdin, A., & Javadian, N. (2020). A closed-loop supply chain robust optimization for disposable appliances. Neural Computing and Applications, 32(8), 3967–3985. https://doi.org/10.1007/s00521-018-3847-9
Govindan, K., Dhingra, J., Agarwal, V., & Jha, P. C. (2017a). Fuzzy multi-objective approach for optimal selection of suppliers and transportation decisions in an eco-efficient closed loop supply chain network. Journal of Cleaner Production, 165, 1598–1619. https://doi.org/10.1016/j.jclepro.2017.06.180
Govindan, K., Fattahi, M., & Keyvanshokooh, E. (2017b). Supply chain network design under uncertainty: A comprehensive review and future research directions. European Journal of Operational Research, 263, 108–141. https://doi.org/10.1016/j.ejor.2017.04.009
Govindan, K., Jafarian, A., & Nourbakhsh, V. (2018). Designing a sustainable supply chain network integrated with vehicle routing: A comparison of hybrid swarm intelligence metaheuristics. Computers and Operations Research, 110, 220–235. https://doi.org/10.1016/j.cor.2018.11.013
Govindan, K., Jha, P. C., & Garg, K. (2016). Product recovery optimization in closed-loop supply chain to improve sustainability in manufacturing. International Journal of Production Research, 54(5), 1463–1486. https://doi.org/10.1080/00207543.2015.1083625
Hu, J., Zheng, H., Xu, R., Ji, Y., & Guo, C. (2010). Supply chain coordination for fuzzy random newsboy problem with imperfect quality. International Journal of Approximate Reasoning, 51(7), 771–784. https://doi.org/10.1016/j.ijar.2010.04.002
Hwan, C., Rhee, B., & Cheng, T. C. E. (2013). Quality uncertainty and quality-compensation contract for supply chain coordination. European Journal of Operational Research, 228(3), 582–591. https://doi.org/10.1016/j.ejor.2013.02.027
Imran, M., Kang, C., & Babar, M. (2018). Medicine supply chain model for an integrated healthcare system with uncertain product complaints. Journal of Manufacturing Systems, 46, 13–28. https://doi.org/10.1016/j.jmsy.2017.10.006
Ma, R., Yao, L., Jin, M., Ren, P., & Lv, Z. (2016). Robust environmental closed-loop supply chain design under uncertainty. Chaos, Solitons and Fractals, 89, 195–202. https://doi.org/10.1016/j.chaos.2015.10.028
Masoudipour, E., Amirian, H., & Sahraeian, R. (2017). A novel closed-loop supply chain based on the quality of returned products. Journal of Cleaner Production, 151, 344–355. https://doi.org/10.1016/j.jclepro.2017.03.067
McKinnon, A., & ECTA. (2011). Guidelines for measuring and managing CO2 emission from freight transport operations.
Miettinen, K., Mäkelä, M. M., & Kaario, K. (2006). Experiments with classification-based scalarizing functions in interactive multiobjective optimization. European Journal of Operational Research, 175, 931–947. https://doi.org/10.1016/j.ejor.2005.06.019
Mohammed, F., Selim, S. Z., Hassan, A., & Naqeebuddin, M. (2017). Multi-period planning of closed-loop supply chain with carbon policies under uncertainty. Transportation Research Part D, 51, 146–172. https://doi.org/10.1016/j.trd.2016.10.033
Mulvey, J. M., Vanderbei, R., & Zenios, S. A. (1995). Robust optimization of large-scale systems. Operations Research, 43(2), 264–281.
Pal, S., & Mahapatra, G. S. (2017). A manufacturing-oriented supply chain model for imperfect quality with inspection errors, stochastic demand under rework and shortages. Computers & Industrial Engineering, 106, 299–314. https://doi.org/10.1016/j.cie.2017.02.003
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, 35(2), 637–649. https://doi.org/10.1016/j.apm.2010.07.013
Pishvaee, M. S., & Razmi, J. (2012). Environmental supply chain network design using multi-objective fuzzy mathematical programming. Applied Mathematical Modelling, 36(8), 3433–3446. https://doi.org/10.1016/j.apm.2011.10.007
Pourmehdi, M., Paydar, M. M., & Asadi-gangraj, E. (2020). Scenario-based design of a steel sustainable closed-loop supply chain network considering production technology. Journal of Cleaner Production, 277, 123298. https://doi.org/10.1016/j.jclepro.2020.123298
Puji, K., Carvalho, M. S., & Costa, L. (2017). Green supply chain design: A mathematical modeling approach based on a multi-objective optimization model. International Journal of Production Economics, 183, 421–432. https://doi.org/10.1016/j.ijpe.2016.08.028
Rahmani, D., Ramezanian, R., Fattahi, P., & Heydari, M. (2013). A robust optimization model for multi-product two-stage capacitated production planning under uncertainty. Applied Mathematical Modelling, 37(20–21), 8957–8971. https://doi.org/10.1016/j.apm.2013.04.016
Safaei, A. S., Roozbeh, A., & Paydar, M. M. (2017). A robust optimization model for the design of a cardboard closed-loop supply chain. Journal of Cleaner Production. https://doi.org/10.1016/j.jclepro.2017.08.085
Sana, S. S. (2011). A production-inventory model of imperfect quality products in a three-layer supply chain. Decision Support Systems, 50(2), 539–547. https://doi.org/10.1016/j.dss.2010.11.012
Soleimani, H., Govindan, K., Saghafi, H., & Jafari, H. (2017). Fuzzy multi-objective sustainable and green closed-loop supply chain network design. Computers & Industrial Engineering, 109, 191–203. https://doi.org/10.1016/j.cie.2017.04.038
Steuer, R. E., & Choo, E.-U. (1983). An interactive weighted Tchebycheff procedure for multiple objective programming. Mathematical Programming, 26(3), 326–344. https://doi.org/10.1007/BF02591870
Sun, H., Wang, Y., & Xue, Y. (2021). A bi-objective robust optimization model for disaster response planning under uncertainties. Computers & Industrial Engineering, 155(99), 107213. https://doi.org/10.1016/j.cie.2021.107213
Taguchi, G. (1986). Introduction to quality engineering: Designing quality into products and processes. Asian Productivity Organization, Tokyo.
Tsao, Y., Thanh, V., Lu, J., & Yu, V. (2017). Designing sustainable supply chain networks under uncertain. Journal of Cleaner Production. https://doi.org/10.1016/j.jclepro.2017.10.272
U.S. Environmental Protection Agency. (2016). Inventory of U.S. greenhouse gas emissions and sinks: 1990–2014. Retrieved from https://www.epa.gov/sites/production/files/2018-01/documents/2018_complete_report.pdf
Yu, C., & Li, H. (2000). A robust optimization model for stochastic logistic problems. International Journal Production Economics, 64, 385–397.
Acknowledgements
Dr. Theodore Trafalis was supported by RSF Grant 14-41-00039, and he conducted research at National Research University Higher School of Economics.
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Almaraj, I.I., Trafalis, T.B. A robust optimization approach in a multi-objective closed-loop supply chain model under imperfect quality production. Ann Oper Res 319, 1479–1505 (2022). https://doi.org/10.1007/s10479-021-04286-8
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DOI: https://doi.org/10.1007/s10479-021-04286-8