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A green vehicle routing problem with multi-depot, multi-tour, heterogeneous fleet and split deliveries: a mathematical model and heuristic approach

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Abstract

Vehicle Routing Problem (VRP) is one of the most studied combinatorial optimization problems with many variants and extensions. This study introduces a novel VRP variant: Green Vehicle Routing Problem with Multi-Depot, Multi-Tour, Heterogeneous Fleet and Split Deliveries. In this problem, different vehicle types (heterogeneous fleet) with limited fleet sizes are allowed and the vehicles can be assigned to different depots (multi-depot). A vehicle can be used multiple times (multi-tour) and multiple vehicles can be assigned to a route (split delivery). The problem is formulated as a Mixed Integer Linear Programming (MILP) model to minimize the total carbon emissions. A Genetic Algorithm (GA), employing a MILP model and using niching and constraint handling techniques, is also developed to solve the problem effectively. The proposed algorithm has been tested on four hypothetical but realistic distribution networks. The results demonstrate the robustness and effectiveness of the proposed GA method on practical distribution scenarios.

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Enquiries about data availability should be directed to the authors.

Notes

  1. All test instances and their optimal solutions are downloaded from the Capacitated Vehicle Routing Problem Library (http://vrp.atd-lab.inf.puc-rio.br/).

References

  • Abdulkader M, Gajpal Y, ElMekkawy TY (2018) Vehicle routing problem in omni-channel retailing distribution systems. Int J Prod Econ 196:43–55

    Google Scholar 

  • Augerat P, Naddef D, Belenguer J, Benavent E, Corberan A, Rinaldi G (1995) Computational results with a branch and cut code for the capacitated vehicle routing problem

  • Avci M, Topaloglu S (2016) A hybrid metaheuristic algorithm for heterogeneous vehicle routing problem with simultaneous pickup and delivery. Expert Syst Appl 53:160–171

    Google Scholar 

  • Bae H, Moon I (2016) Multi-depot vehicle routing problem with time windows considering delivery and installation vehicles. Appl Math Model 40(13):6536–6549

    MATH  MathSciNet  Google Scholar 

  • Baldacci R, Battarra M, Vigo D (2008) The vehicle routing problem: Latest advances and new challenges, Springer US, Boston, MA, chap Routing a heterogeneous fleet of vehicles, pp 3–27

  • Bektas T, Laporte G (2011) The pollution-routing problem. Transp Res B Methodol 45(8):1232–1250

    Google Scholar 

  • Belfiore P, Yoshizaki HTY (2009) Scatter search for a real-life heterogeneous fleet vehicle routing problem with time windows and split deliveries in brazil. Eur J Oper Res 199(3):750–758

    MATH  Google Scholar 

  • Belmecheri F, Prins C, Yalaoui F, Amodeo L (2013) Particle swarm optimization algorithm for a vehicle routing problem with heterogeneous fleet, mixed backhauls, and time windows. J Intell Manuf 24(4):775–789

    Google Scholar 

  • Bertoli F, Kilby P, Urli T (2017) Vehicle routing problems with deliveries split over days. J Vehicle Rout Algorith, pp 1–17

  • Bettinelli A, Ceselli A, Righini G (2011) A branch-and-cut-and-price algorithm for the multi-depot heterogeneous vehicle routing problem with time windows. Transp Res C Emerg Technol 19(5):723–740

    MATH  Google Scholar 

  • Bianchessi N, Drexl M, Irnich S (2017) The split delivery vehicle routing problem with time windows and customer inconvenience constraints. Tech. Rep. 1706, Gutenberg School of Management and Economics, Johannes Gutenberg-Universität Mainz

  • Bianchessi N, Drexl M, Irnich S (2019) The split delivery vehicle routing problem with time windows and customer inconvenience constraints. Transp Sci 53(4):1067–1084

    Google Scholar 

  • Cattaruzza D, Absi N, Feillet D (2016) The multi-trip vehicle routing problem with time windows and release dates. Transp Sci 50(2):676–693

    Google Scholar 

  • Cattaruzza D, Absi N, Feillet D (2016b) Vehicle routing problems with multiple trips. 4OR 14(3):223–259

  • Ceschia S, Di Gaspero L, Schaerf A (2011) Tabu search techniques for the heterogeneous vehicle routing problem with time windows and carrier-dependent costs. J Sched 14(6):601–615

    MathSciNet  Google Scholar 

  • Cheng C, Yang P, Qi M, Rousseau LM (2017) Modeling a green inventory routing problem with a heterogeneous fleet. Transp Res E Logist Transp Rev 97:97–112

    Google Scholar 

  • Choi E, Tcha DW (2007) A column generation approach to the heterogeneous fleet vehicle routing problem. Comput Oper Res 34(7):2080–2095

    MATH  Google Scholar 

  • Coelho V, Grasas A, Ramalhinho H, Coelho I, Souza M, Cruz R (2016) An ILS-based algorithm to solve a large-scale real heterogeneous fleet vrp with multi-trips and docking constraints. Eur J Oper Res 250(2):367–376

    MATH  MathSciNet  Google Scholar 

  • Deb K (2000) An efficient constraint handling method for genetic algorithms. Comput Methods Appl Mech Eng 186(2):311–338

    MATH  Google Scholar 

  • Dekker R, Bloemhof J, Mallidis I (2012) Operations research for green logistics-an overview of aspects, issues, contributions and challenges. Eur J Oper Res 219(3):671–679

    Google Scholar 

  • Demir E, Bektas T, Laporte G (2012) An adaptive large neighborhood search heuristic for the pollution-routing problem. Eur J Oper Res 223(2):346–359

    MATH  MathSciNet  Google Scholar 

  • Derbel H, Jarboui B, Bhiri R (2017) A skewed general variable neighborhood search algorithm with fixed threshold for the heterogeneous fleet vehicle routing problem. Ann Oper Res, pp 1–30

  • De la Cruz JJ, Paternina-Arboleda CD, Cantillo V, Montoya-Torres JR (2013) A two-pheromone trail ant colony system-tabu search approach for the heterogeneous vehicle routing problem with time windows and multiple products. J Heurist 19(2):233–252

    Google Scholar 

  • Dominguez O, Juan AA, Barrios B, Faulin J, Agustin A (2016) Using biased randomization for solving the two-dimensional loading vehicle routing problem with heterogeneous fleet. Ann Oper Res 236(2):383–404

    MATH  MathSciNet  Google Scholar 

  • Dondo R, Cerdá J (2007) A cluster-based optimization approach for the multi-depot heterogeneous fleet vehicle routing problem with time windows. Eur J Oper Res 176(3):1478–1507

    MATH  Google Scholar 

  • Dondo R, Cerdá J (2015) The heterogeneous vehicle routing and truck scheduling problem in a multi-door cross-dock system. Comput Chem Eng 76:42–62

    Google Scholar 

  • Erdogan S, Miller-Hooks E (2012) A green vehicle routing problem. Transp Res E Logist Transp Rev 48(1):100–114

    Google Scholar 

  • Euchi J, Chabchoub H (2010) A hybrid tabu search to solve the heterogeneous fixed fleet vehicle routing problem. Logist Res 2(1):3–11

    Google Scholar 

  • Figliozzi M (2010) Vehicle routing problem for emissions minimization. Transp Res Rec 2197(1):1–7

    Google Scholar 

  • Franceschetti A, Honhon D, Woensel TV, Bektas T, Laporte G (2013) The time-dependent pollution-routing problem. Transp Res B Methodol 56:265–293

    Google Scholar 

  • François V, Arda Y, Crama Y, Laporte G (2016) Large neighborhood search for multi-trip vehicle routing. Eur J Oper Res 255(2):422–441

  • Gayialis SP, Konstantakopoulos GD, Tatsiopoulos IP (2019) Vehicle routing problem for urban freight transportation: a review of the recent literature. In: Petridis K (ed) Sifaleras A. Operational Research in the Digital Era - ICT Challenges, Springer, pp 89–104

    Google Scholar 

  • Hernandez F, Feillet D, Giroudeau R, Naud O (2016) Branch-and-price algorithms for the solution of the multi-trip vehicle routing problem with time windows. Eur J Oper Res 249(2):551–559

    MATH  MathSciNet  Google Scholar 

  • Hiermann G, Puchinger J, Ropke S, Hartl RF (2016) The electric fleet size and mix vehicle routing problem with time windows and recharging stations. Eur J Oper Res 252(3):995–1018

    MATH  MathSciNet  Google Scholar 

  • Huang Y, Shi C, Zhao L, Woensel TV (2012) A study on carbon reduction in the vehicle routing problem with simultaneous pickups and deliveries. In: Proceedings of 2012 IEEE international conference on service operations and logistics, and informatics, pp 302–307

  • Jabali O, Van Woensel T, De Kok AG (2012) Analysis of travel times and CO\(_2\) emissions in time-dependent vehicle routing. Prod Oper Manag 21(6):1060–1074

    Google Scholar 

  • Jiang J, Ng KM, Poh KL, Teo KM (2014) Vehicle routing problem with a heterogeneous fleet and time windows. Expert Syst Appl 41(8):3748–3760

    Google Scholar 

  • Koc C, Bektas T, Jabali O, Laporte G (2014) The fleet size and mix pollution-routing problem. Transp Res B Methodol 70:239–254

    MATH  Google Scholar 

  • Konstantakopoulos GD, Gayialis SP, Kechagias EP (2020) Vehicle routing problem and related algorithms for logistics distribution: a literature review and classification. Oper Res. https://doi.org/10.1007/s12351-020-00600-7

    Article  Google Scholar 

  • Kopfer H, Vornhusen B, Dethloff J (2017) Vehicle routing with a heterogeneous fleet of combustion and battery-powered electric vehicles under energy minimization. International conference on computational logistics. Springer, Cham, pp 94–109

  • Kopfer HW, Kopfer H (2013) Emissions minimization vehicle routing problem in dependence of different vehicle classes. In: Kreowski HJ, Scholz-Reiter B, Thoben KD (eds) Dynamics in logistics. Springer, Berlin, pp 49–58

    Google Scholar 

  • Kritikos MN, Ioannou G (2013) The heterogeneous fleet vehicle routing problem with overloads and time windows. Int J Prod Econ 144(1):68–75

    Google Scholar 

  • Kwon YJ, Choi YJ, Lee DH (2013) Heterogeneous fixed fleet vehicle routing considering carbon emission. Transp Res Part D Transp Environ 23:81–89

    Google Scholar 

  • Lai DS, Demirag OC, Leung JM (2016) A tabu search heuristic for the heterogeneous vehicle routing problem on a multigraph. Transp Res E Logist Transp Rev 86:32–52

    Google Scholar 

  • Leung SC, Zhang Z, Zhang D, Hua X, Lim MK (2013) A meta-heuristic algorithm for heterogeneous fleet vehicle routing problems with two-dimensional loading constraints. Eur J Oper Res 225(2):199–210

    Google Scholar 

  • Liu G, Hu J, Yang Y, Xia S, Lim MK (2020) Vehicle routing problem in cold chain logistics: a joint distribution model with carbon trading mechanisms. Resour Conserv Recycl 156:104715

    Google Scholar 

  • Liu WY, Lin CC, Chiu CR, Tsao YS, Wang Q (2014) Minimizing the carbon footprint for the time-dependent heterogeneous-fleet vehicle routing problem with alternative paths. Sustainability 6(7):4658–4684

    Google Scholar 

  • Mingozzi A, Roberti R, Toth P (2013) An exact algorithm for the multitrip vehicle routing problem. INFORMS J Comput 25(2):193–207

    MathSciNet  Google Scholar 

  • Mladenović N, Hansen P (1997) Variable neighborhood search. Comput Oper Res 24(11):1097–1100

    MATH  MathSciNet  Google Scholar 

  • Niu Y, Yang Z, Chen P, Xiao J (2018) Optimizing the green open vehicle routing problem with time windows by minimizing comprehensive routing cost. J Clean Prod 171:962–971

    Google Scholar 

  • Penna PHV, Afsar HM, Prins C, Prodhon C (2016) A hybrid iterative local search algorithm for the electric fleet size and mix vehicle routing problem with time windows and recharging stations. IFAC-PapersOnLine 49(12):955–960

    Google Scholar 

  • Petrowski A (1996) A clearing procedure as a niching method for genetic algorithms. In: Proceedings of IEEE international conference on evolutionary computation, pp 798–803

  • Salhi S, Wassan N, Hajarat M (2013) The fleet size and mix vehicle routing problem with backhauls: formulation and set partitioning-based heuristics. Transp Res E Logist Transp Rev 56:22–35

    Google Scholar 

  • Salhi S, Imran A, Wassan NA (2014) The multi-depot vehicle routing problem with heterogeneous vehicle fleet: formulation and a variable neighborhood search implementation. Comput Oper Res 52:315–325

    MATH  MathSciNet  Google Scholar 

  • Soysal M, Bloemhof-Ruwaard JM, Bektas T (2015) The time-dependent two-echelon capacitated vehicle routing problem with environmental considerations. Int J Prod Econ 164:366–378

    Google Scholar 

  • Takahama T, Sakai S (2006) Constrained optimization by the \(\epsilon \) constrained differential evolution with gradient-based mutation and feasible elites. In: IEEE congress on evolutionary computation, pp 1–9

  • Wang J, Jagannathan AKR, Zuo X, Murray CC (2017) Two-layer simulated annealing and tabu search heuristics for a vehicle routing problem with cross docks and split deliveries. Comput Ind Eng 112:84–98

    Google Scholar 

  • Wang X, Golden B, Wasil E, Zhang R (2016) The min-max split delivery multi-depot vehicle routing problem with minimum service time requirement. Comput Oper Res 71:110–126

    MATH  MathSciNet  Google Scholar 

  • Wassan N, Wassan N, Nagy G, Salhi S (2017) The multiple trip vehicle routing problem with backhauls: formulation and a two-level variable neighbourhood search. Comput Oper Res 78:454–467

    MATH  MathSciNet  Google Scholar 

  • Wei L, Zhang Z, Lim A (2014) An adaptive variable neighborhood search for a heterogeneous fleet vehicle routing problem with three-dimensional loading constraints. IEEE Comput Intell Mag 9(4):18–30

    Google Scholar 

  • Xiao Y, Konak A (2016) The heterogeneous green vehicle routing and scheduling problem with time-varying traffic congestion. Transp Res E Logist Transp Rev 88:146–166

    Google Scholar 

  • Xiao Y, Konak A (2017) A genetic algorithm with exact dynamic programming for the green vehicle routing & scheduling problem. J Clean Prod 167:1450–1463

    Google Scholar 

  • Xu D, Li K, Zou X, Liu L (2017) An unpaired pickup and delivery vehicle routing problem with multi-visit. Transp Res E Logist Transp Rev 103:218–247

    Google Scholar 

  • Yao B, Yu B, Hu P, Gao J, Zhang M (2016) An improved particle swarm optimization for carton heterogeneous vehicle routing problem with a collection depot. Ann Oper Res 242(2):303–320

    MATH  MathSciNet  Google Scholar 

  • Zhang J, Zhao Y, Xue W, Li J (2015) Vehicle routing problem with fuel consumption and carbon emission. Int J Prod Econ 170:234–242

    Google Scholar 

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Funding

This research was supported by Yasar University BAP Program under grant BAP-042.

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Authors and Affiliations

  1. Department of Industrial Engineering, Clemson University, 108 Freeman Hall, Clemson, SC, 29634, USA

    Ozgur Kabadurmus

  2. Department of Engineering, King’s College London, Strand, London, WC2R 2ND, UK

    Mehmet S. Erdogan

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  1. Ozgur Kabadurmus
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Correspondence to Ozgur Kabadurmus.

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Kabadurmus, O., Erdogan, M.S. A green vehicle routing problem with multi-depot, multi-tour, heterogeneous fleet and split deliveries: a mathematical model and heuristic approach. J Comb Optim 45, 89 (2023). https://doi.org/10.1007/s10878-023-01016-7

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