Networks and Spatial Economics

, Volume 19, Issue 3, pp 969–1005 | Cite as

Multi-depot Two-Echelon Fuel Minimizing Routing Problem with Heterogeneous Fleets: Model and Heuristic

  • Surendra Reddy Kancharla
  • Gitakrishnan RamaduraiEmail author


We formulate the two-echelon routing problem considering multiple depots and heterogeneous fleets. Our study (a) presents a Mixed Integer Linear Programming (MILP) formulation with load-dependent fuel minimization objective, (b) uses driving cycles to represent speed variations along a path, (c) allows the vehicles to return to any depot/satellite, and (d) conserves the total number of vehicles at each depot/satellite. We call the problem a Multi-Depot Two-Echelon Fuel Minimizing Routing Problem (MD2E-FMRP). Prior studies assumed there is a fixed number of vehicles available at each satellite/depot, whereas we allow different number of vehicles of each vehicle type at each satellite and depot. Our formulation relaxes several unrealistic assumptions in existing two-echelon formulations and hence has greater practical application. Despite the relaxation of constraints, the running time of our model is comparable to existing formulations. Gurobi optimizer is used to find a better upper bound for up to 56 node instances within a given time limit of 10,000s. We also propose an Adaptive Large Neighborhood Search (ALNS) based heuristic solution technique that outperformed Gurobi in all the tested instances of MD2E-FMRP. We observe an average saving of 13.11% in fuel consumption by minimizing fuel consumed instead of minimizing distance. In general, adapting heterogeneous fleets results in fuel savings and consequently lower emissions compared to using a homogeneous fleet.


Multi-depot Heterogeneous fleet Adaptive large neighborhood search Fuel consumption Vehicle routing problem Mixed integer linear programming 



The initial ideas for this paper took shape when the first author was visiting Prof. Russell Thompson at the University of Melbourne. The authors thank the Volvo Research and Education Foundations (VREF) and Center of Excellence for Sustainable Urban Freight Systems (CoE-SUFS) for supporting the visit.


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Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Department of Civil EngineeringIndian Institute of Technology MadrasChennaiIndia

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