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Multi-depot vehicle routing problem with time windows under shared depot resources

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Abstract

A new variant of multi-depot vehicle routing problem with time windows is studied. In the new variant, the depot where the vehicle ends is flexible, namely, it is not entirely the same as the depot that it starts from. An integer programming model is formulated with the minimum total traveling cost under the constrains of time window, capacity and route duration of the vehicle, the fleet size and the number of parking spaces of each depot. As the problem is an NP-Hard problem, a hybrid genetic algorithm with adaptive local search is proposed to solve it. Finally, the computational results show that the proposed method is competitive in terms of solution quality. Compared with the classic MDVRPTW, allowing flexible choice of the stop depot can further reduce total traveling cost.

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Abbreviations

\(D\) :

The depot set

\(C\) :

The customer set

\(V\) :

The vertex set

\(A\) :

The arc set

\(K\) :

The vehicle set

\(K_{d }\) :

The set of vehicles at depot \(d\)

\(q_{i}\) :

The demand of customer \(i\)

\(s_{i}\) :

The service time of customer \(i\)

\(e_{i}\) :

The earliest start time at customer \(i\)

\(l_{i}\) :

The latest start time at customer \(i\)

\(c_{ij}\) :

The distance between customer \(i\) and \(j\)

\(Q_{k}\) :

The capacity of the vehicle \(k\)

\(T_{k}\) :

The maximum duration of vehicle \(k\)

\(L\) :

The number of vehicles

\({\vert }P_{d}{\vert }\) :

The number of parking spaces at the depot \(d\)

\({\vert }K_{d}{\vert }\) :

The number of vehicles in \(K_{d }\) set

\(x_{kij}\) :

Is the 0-1 decision variable, if vehicle \(k\) travels directly from node \(i\) to node \(j\), then \(x_{kij}=1\), otherwise, \(x_{kij}=0\)

\(a_{ki}\) :

The arrival time of vehicle \(k\) at node \(i\)

\(b_{ki}\) :

The start service time of vehicle \(k\) at node \(i\)

\(\pi _k \) :

The working duration of vehicle \(k\)

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Acknowledgments

The authors gratefully acknowledge valuable comments of three anonymous referees. This work was supported by Research Grant from National Natural Science Foundation of China (No. 71001053) and partially supported by LATNA Laboratory, NRU HSE, RF government Grant (ag. 11.G34.31.0057).

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Authors and Affiliations

  1. College of Engineering, Nanjing Agricultural University, P.O. Box 64, 40 Dianjiangtai Road, Pukou district, Nanjing , 210031, China

    Jian Li & Yang Li

  2. Department of Industrial and Systems Engineering, Center for Applied Optimization, University of Florida, 303 Weil Hall, Gainesville, FL , 32611, USA

    Panos M. Pardalos

  3. Laboratory of Algorithms and Technologies for Network Analysis, National Research University Higher School of Economics, Moscow, Russia

    Panos M. Pardalos

Authors
  1. Jian Li
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  2. Yang Li
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  3. Panos M. Pardalos
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Correspondence to Jian Li or Panos M. Pardalos.

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Li, J., Li, Y. & Pardalos, P.M. Multi-depot vehicle routing problem with time windows under shared depot resources. J Comb Optim 31, 515–532 (2016). https://doi.org/10.1007/s10878-014-9767-4

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