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A tabu search algorithm to solve a green logistics bi-objective bi-level problem

  • S.I.: CLAIO 2018
  • Published:
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Abstract

This paper addresses a supply chain situation, in which a company distributes commodities over a selected subset of customers while a manufacturer produces the commodities demanded by the customers. The distributor company has two objectives: the maximization of the profit gained by the distribution process and the minimization of \({\textit{CO}}_2\) emissions. The latter is important due to the regulations imposed by the government. A compromise between both objectives exists, since profit maximization only will attempt to include as many customers as possible. But, longer routes will be needed, causing more \({\textit{CO}}_2\) emissions. The manufacturer aims to minimize its manufacturing and shipping costs. Since a predefined hierarchy between both companies exists in the supply chain, a bi-level programming approach is employed. This problem is modelled as a bi-level programming problem with two objectives in the upper level and a single objective in the lower level. The upper level is associated with the distributor, while the lower level is associated with the manufacturer. Due to the inherent complexity to optimally solve this problem, a heuristic scheme is proposed. A nested bi-objective tabu search algorithm is designed to obtain non-dominated bi-level feasible solutions regarding the upper level. Considering simultaneously both objectives of the distributor allow us to focus on the minimization of \({\textit{CO}}_2\) emissions caused by the supply chain, but bearing in mind the distributor’s profit. Numerical experimentation shows that the Pareto frontiers obtained by the proposed algorithm provide good alternatives for the decision-making process and also, some managerial insights are given.

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References

  • Aldakhil, A. M., Nassani, A. A., Awan, U., Abro, M. M. Q., & Zaman, K. (2018). Determinants of green logistics in BRICS countries: An integrated supply chain model for green business. Journal of Cleaner Production, 195, 861.

    Article  Google Scholar 

  • Anderluh, A., Nolz, P. C., Hemmelmayr, V. C., & Crainic, T. G. (2019). “Multi objective optimization of a two echelon vehicle routing problem with vehicle synchronization and ‘grey zone’ customers arising in urban logistics” European Journal of Operational Research.

  • Barbalho, H., Rosseti, I., Martins, S. L., & Plastino, A. (2013). A hybrid data mining GRASP with path-relinking. Computers & Operations Research, 40(12), 3159.

    Article  Google Scholar 

  • Beamon, B. M. (1999). Designing the green supply chain. Logistics Information Management, 12(4), 332.

    Article  Google Scholar 

  • Bektaş, T. & Laporte, G. (2011). “The Pollution-Routing Problem” Transportation Research Part B: Methodological45(8), 1232 , Supply chain disruption and risk management.

  • Calvete, H. I., Galé, C., and Oliveros, M.-J. (2011). “Bilevel model for production–distribution planning solved by using ant colony optimization” Computers and Operations Research38(1), 320 , Project Management and Scheduling

  • Camacho-Vallejo, J.-F., Muñoz-Sánchez, R., & González-Velarde, J. L. (2015). “A heuristic algorithm for a supply chains production-distribution planning’’. Computers and Operations Research, 61, 110.

    Article  Google Scholar 

  • Cordeau, J.-F., Gendreau, M., Laporte, G., Potvin, J.-Y., & Semet, F. (2002). A guide to vehicle routing heuristics. Journal of the Operational Research Society, 53(5), 512.

    Article  Google Scholar 

  • Dekker, R., Bloemhof, J., & Mallidis, I. (2012). Operations Research for green logistics–An overview of aspects, issues, contributions and challenges. European Journal of Operational Research, 219(3), 671.

    Article  Google Scholar 

  • Demir, E., Bektaş, T., & Laporte, G. (2012). “An adaptive large neighborhood search heuristic for the Pollution-Routing Problem’’. European Journal of Operational Research, 223(2), 346.

    Article  Google Scholar 

  • Demir, E., Bektaş, T., & Laporte, G. (2014). “The bi-objective Pollution-Routing Problem’’. European Journal of Operational Research, 232(3), 464.

    Article  Google Scholar 

  • Diabat, A., & Simchi-Levi, D. (2009). A carbon-capped supply chain network problem. In 2009 IEEE International Conference on Industrial Engineering and Engineering Management, pp. 523–527, IEEE

  • Diario Oficial de la Federación (1971). Ley federal para prevenir y controlar el medio ambiente

  • Diario Oficial de la Federación (1988a). Ley general del equilibrio ecológico y la protección del medio ambiente, DOF 13-05-2016

  • Diario Oficial de la Federación (1988b) , Reglamento de la ley general del equilibrio ecológico y la protección al ambiente en materia de prevención y control de la contaminación de la atmósfera, DOF 31-10-2014

  • Diario Oficial de la Federación (1993) , Norma oficial mexicana nom-043-semarnat-1993

  • Diario Oficial de la Federación (1999a) , Norma oficial mexicana nom-041-ecol-1999

  • Diario Oficial de la Federación (1999b) , Norma oficial mexicana nom-042-ecol-1999

  • Erdoğan, S., & Miller-Hooks, E. (2012). A green vehicle routing problem. Transportation Research Part E: Logistics and Transportation Review, 48(1), 100.

    Article  Google Scholar 

  • Eskandarpour, M., Ouelhadj, D., Hatami, S., Juan, A. A., & Khosravi, B. (2019). “Enhanced multi directional local search for the biobjective heterogeneous vehicle routing problem with multiple driving ranges’’. European Journal of Operational Research, 277(2), 479.

    Article  Google Scholar 

  • Faulin, J., Grasman, S., Juan, A., & Hirsch, P. (2019). Sustainable Transportation and Smart Logistics: DecisionMaking Models and Solutions

  • Figliozzi, M., Saenz, J., & Faulin, J. (2020). “Minimization of urban freight distribution lifecycle CO2e emissions: Results from an optimization model and a real-world case study’’. Transport Policy, 86, 60.

    Article  Google Scholar 

  • Forster, P., Ramaswamy, V., Artaxo, P., Berntsen, T., Betts, R., Fahey, D. W., Haywood, J., Lean, J., Lowe, D. C., & Myhre, G., et al. (2007). Changes in atmospheric constituents and in radiative forcing. Chapter 2. In Climate Change 2007. The Physical Science Basis

  • Franceschetti, A., Demir, E., Honhon, D., Van Woensel, T., Laporte, G., & Stobbe, M. (2017). “A metaheuristic for the time-dependent pollution-routing problem’’. European Journal of Operational Research, 259(3), 972.

    Article  Google Scholar 

  • Franceschetti, A., Honhon, D., Woensel, T. V., Bektaş, T., & Laporte, G. (2013). “The time-dependent pollution-routing problem’’. Transportation Research Part B: Methodological, 56, 265.

    Article  Google Scholar 

  • Glover, F. (1986). Future paths for integer programming and links to artificial intelligence. Computers & Operations Research, 13(5), 533.

    Article  Google Scholar 

  • Harris, I., Mumford, C., & Naim, M. (2009). The multi-objective uncapacitated facility location problem for green logistics. In 2009 IEEE Congress on Evolutionary Computation, pp. 2732–2739, IEEE

  • Harris, I., Mumford, C. L., & Naim, M. M. (2014). A hybrid multi-objective approach to capacitated facility location with flexible store allocation for green logistics modeling. Transportation Research Part E: Logistics and Transportation Review, 66, 1.

    Article  Google Scholar 

  • Hill, N., Venfield, H., Dun, C., & James, K. (2013). Government GHG conversion factors for company reporting: methodology paper for emission factors. DEFRA and DECC

  • Hızır, A. E. (2006). Using emission functions in mathematical programming models for sustainable urban transportation: An application in bilevel optimization. Ph.D. thesis.

  • Kalashnikov, V. V., Dempe, S., Pérez-Valdés, G. A., Kalashnykova, N. I., & Camacho-Vallejo, J.-F. (2015). Bilevel programming and applications. Mathematical Problems in Engineering 2015.

  • Kannan, D., Khodaverdi, R., Olfat, L., Jafarian, A., & Diabat, A. (2013). Integrated fuzzy multi criteria decision making method and multi-objective programming approach for supplier selection and order allocation in a green supply chain. Journal of Cleaner Production, 47, 355.

    Article  Google Scholar 

  • Koç, Ça. ğrı, Bektaş, T., Jabali, O., & Laporte, G. (2014). The fleet size and mix pollution-routing problem. Transportation Research Part B: Methodological, 70, 239.

    Article  Google Scholar 

  • Koç, Ça. ğrı, & Karaoglan, I. (2016). The green vehicle routing problem: A heuristic based exact solution approach. Applied Soft Computing, 39, 154.

    Article  Google Scholar 

  • Kulturel-Konak, S., Smith, A. E., & Norman, B. A. (2006). Multi-objective tabu search using a multinomial probability mass function. European Journal of Operational Research, 169(3), 918.

    Article  Google Scholar 

  • Lai, K.-H., & Wong, C. W. (2012). Green logistics management and performance: Some empirical evidence from Chinese manufacturing exporters. Omega, 40(3), 267.

    Article  Google Scholar 

  • Leggieri, V., & Haouari, M. (2017). “A practical solution approach for the green vehicle routing problem’’. Transportation Research Part E: Logistics and Transportation Review, 104, 97.

    Article  Google Scholar 

  • Li, F., Liu, T., Zhang, H., Cao, R., Ding, W., & Fasano, J. P. (2008). Distribution center location for green supply chain. In 2008 IEEE International Conference on Service Operations and Logistics, and Informatics, Vol. 2, pp. 2951–2956, IEEE

  • Li, X., Leung, S. C., & Tian, P. (2012). “A multistart adaptive memory-based tabu search algorithm for the heterogeneous fixed fleet open vehicle routing problem’’. Expert Systems with Applications, 39(1), 365.

    Article  Google Scholar 

  • Lin, C., Choy, K., Ho, G., Chung, S., & Lam, H. (2014). Expert Systems with Applications41(4, Part 1), 1118.

  • Linton, J. D., Klassen, R., & Jayaraman, V. (2007). Sustainable supply chains: An introduction. Journal of Operations Management, 25(6), 1075.

    Article  Google Scholar 

  • Li, Y., Soleimani, H., & Zohal, M. (2019). “An improved ant colony optimization algorithm for the multi-depot green vehicle routing problem with multiple objectives’’. Journal of Cleaner Production, 227, 1161.

    Article  Google Scholar 

  • Liu, J., Yuan, C., Hafeez, M., & Yuan, Q. (2018). The relationship between environment and logistics performance: evidence from Asian countries. Journal of Cleaner Production, 204, 282.

    Article  Google Scholar 

  • Marinakis, Y., & Marinaki, M. (2008). A Bilevel Genetic Algorithm for a real life location routing problem. International Journal of Logistics Research and Applications, 11(1), 49.

    Article  Google Scholar 

  • Marinakis, Y., Migdalas, A., & Pardalos, P. (2007). A new bilevel formulation for the Vehicle Routing Problem and a solution method using a genetic algorithm. Journal of Global Optimization, 38, 555.

    Article  Google Scholar 

  • Mathew, T. V. & Sharma, S. (2006). Continuous network design with emission pricing as a bi-level optimization problem. In Applications of Advanced Technology in Transportation, pp. 804–809

  • Mauttone, A., Labbé, M., & Figueiredo, R. (2008). A Tabu Search approach to solve a network design problem with user-optimal flows. In ALIO/EURO Workshop on Applied Combinatorial Optimization

  • Montoya, A., Guéret, C., Mendoza, J. E., & Villegas, J. G. (2016). “A multi-space sampling heuristic for the green vehicle routing problem’’. Transportation Research Part C: Emerging Technologies, 70, 113.

    Article  Google Scholar 

  • Nourifar, R., Mahdavi, I., Mahdavi-Amiri, N., & Paydar, M. M. (2020). Mathematical modelling of a decentralized multi-echelon supply chain network considering service level under uncertainty. Scientia Iranica, 27(3), 1634.

    Google Scholar 

  • Pérez-Bernabeu, E., Juan, A. A., Faulin, J., & Barrios, B. B. (2015). Horizontal cooperation in road transportation: a case illustrating savings in distances and greenhouse gas emissions. International Transactions in Operational Research, 22(3), 585.

    Article  Google Scholar 

  • Potvin, J.-Y., & Naud, M.-A. (2011). Tabu search with ejection chains for the vehicle routing problem with private fleet and common carrier. Journal of the Operational Research Society, 62(2), 326.

    Article  Google Scholar 

  • Qian, J., & Eglese, R. (2016). Fuel emissions optimization in vehicle routing problems with time-varying speeds. European Journal of Operational Research, 248(3), 840.

    Article  Google Scholar 

  • Renaud, J., Laporte, G., & Boctor, F. F. (1996). “A tabu search heuristic for the multi-depot vehicle routing problem’’. Computers & Operations Research, 23(3), 229.

    Article  Google Scholar 

  • Sawik, B., Faulin, J., & Pérez-Bernabeu, E. (2017a). Multi-criteria optimization for fleet size with environmental aspects. Transportation Research Procedia, 27, 61.

    Article  Google Scholar 

  • Sawik, B., Faulin, J., & Pérez-Bernabeu, E. (2017b). A multicriteria analysis for the green VRP: A case discussion for the distribution problem of a Spanish retailer. Transportation Research Procedia, 22, 305.

    Article  Google Scholar 

  • Sbihi, A., & Eglese, R. W. (2010). Combinatorial optimization and green logistics. Annals of Operations Research, 175(1), 159.

    Article  Google Scholar 

  • Serrano-Hernández, A., Juan, A. A., Faulin, J., & Perez-Bernabeu, E. (2017). Horizontal collaboration in freight transport: concepts, benefits and environmental challenges. Sort, 1, 393.

    Google Scholar 

  • Shen, Z., Ordòñez, F., & Dessouky, M. M. (2009). “The Stochastic Vehicle Routing Problem for Minimum Unmet Demand”. The Stochastic Vehicle Routing Problem for Minimum Unmet Demand, pp. 349–371. Springer: Boston, MA

  • Sinha, A., Malo, P., & Deb, K. (2016). Solving optimistic bilevel programs by iteratively approximating lower level optimal value function. In 2016 IEEE Congress on Evolutionary Computation (CEC), pp. 1877–1884, IEEE.

  • Talbi, E.-G. (2013) , Metaheuristics for Bi-level Optimization, Vol. 482

  • Ubeda, S., Arcelus, F. J., & Faulin, J. (2011). Green logistics at Eroski: A case study. International Journal of Production Economics, 131(1), 44.

    Article  Google Scholar 

  • Wang, J., Chi, L., Hu, X., & Zhou, H. (2014). Urban traffic congestion pricing model with the consideration of carbon emissions cost. Sustainability, 6(2), 676.

    Article  Google Scholar 

  • Wang, G.-M., Ma, L.-M., & Li, L.-L. (2011). An application of bilevel programming problem in optimal pollution emission price. Journal of Service Science and Management, 4(03), 334.

    Article  Google Scholar 

  • Wen, L., & Eglese, R. (2016). Minimizing CO2e emissions by setting a road toll. Transportation Research Part D: Transport and Environment, 44, 1.

    Article  Google Scholar 

  • Xiao, Y., & Konak, A. (2015). “A simulating annealing algorithm to solve the green vehicle routing and scheduling problem with hierarchical objectives and weighted tardiness’’. Applied Soft Computing, 34, 372.

    Article  Google Scholar 

  • Yeh, W.-C., & Chuang, M.-C. (2011). Using multi-objective genetic algorithm for partner selection in green supply chain problems. Expert Systems with Applications, 38(4), 4244.

    Article  Google Scholar 

  • Zaman, K., & Shamsuddin, S. (2017). Green logistics and national scale economic indicators: Evidence from a panel of selected European countries. Journal of Cleaner Production, 143, 51.

    Article  Google Scholar 

  • Zhang, S., Gajpal, Y., & Appadoo, S. (2018). A meta-heuristic for capacitated green vehicle routing problem. Annals of Operations Research, 269(1–2), 753.

    Article  Google Scholar 

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Authors and Affiliations

  1. Facultad de Ciencias Físico-Matemáticas, Universidad Autónoma de Nuevo León, Ave. Universidad s/n, San Nicolás de los Garza, NL, 66450, México

    José-Fernando Camacho-Vallejo & Lilian López-Vera

  2. Department of Industrial and Systems Engineering, Auburn University, Auburn, AL, USA

    Alice E. Smith

  3. Escuela de Ingeniería y Ciencias, Tecnologico de Monterrey, Monterrey, NL, México

    José-Luis González-Velarde

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  1. José-Fernando Camacho-Vallejo
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  2. Lilian López-Vera
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Correspondence to José-Fernando Camacho-Vallejo.

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Camacho-Vallejo, JF., López-Vera, L., Smith, A.E. et al. A tabu search algorithm to solve a green logistics bi-objective bi-level problem. Ann Oper Res 316, 927–953 (2022). https://doi.org/10.1007/s10479-021-04195-w

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