Survey in Operations Research and Management Science
A review of vehicle routing with simultaneous pickup and delivery

https://doi.org/10.1016/j.cor.2020.104987Get rights and content

Highlights

  • We survey the Vehicle Routing with Simultaneous Pickup and Delivery (VRPSPD).

  • We provide a performance comparison of heuristics developed for the VRPSPD.

  • We describe several problem variants, case studies and industrial applications.

  • We give an overview of the main trends observed in the literature.

  • We identify several interesting promising future research perspectives.

Abstract

In the vehicle routing problem with simultaneous pickup and delivery (VRPSPD), goods have to be transported from different origins to different destinations, and each customer has both a delivery and a pickup demand to be satisfied simultaneously. The VRPSPD has been around for about 30 years, and significant progress has since been made on this problem and its variants. This paper aims to comprehensively review the existing work on the VRPSPD. It surveys mathematical formulations, algorithms, variants, case studies, and industrial applications. It also provides an overview of trends in the literature and identifies several interesting promising future research perspectives.

Introduction

The classical vehicle routing problem (VRP) introduced around sixty years ago by Dantzig and Ramser (1959), as well as its variants, have been intensively studied. The VRP aims to determine a routing plan to serve a set of customers for a fleet of identical vehicles, such that each customer is visited once by one vehicle, each route starts and ends at the depot, and several side constraints are satisfied. Many heuristic and exact algorithms have been developed for the VRP and its variants. The interested reader is referred to the book by Toth and Vigo (2014), and to the reviews by Laporte, 2009, Koç et al., 2016, Koç and Laporte, 2018, Vidal et al., 2019.

One important variant of the VRP arises in pickup and delivery problems (PDPs). Several types of PDPs have been studied. Battarra et al. (2014) presented an overview of studies for PDPs arising in the transportation of goods, without providing detailed computational comparisons of solution methods. Table 1 presents a classification of PDPs based on Berbeglia et al., 2007, Battarra et al., 2014. It consists of three main categories. The first category includes many-to-many problems where each commodity may have more than one start node and more than one end node, and any node may be the origin and destination node of a number of commodities. In the second category, one-to-many-to-one, some commodities are carried from a depot to many customers, while other commodities are collected at customers and delivered to the depot. The third category contains one-to-one problems in which each commodity has a single start node and a single end node. The most studied and general variant of the second category or one-to-many-to-one, is the vehicle routing problem with simultaneous pickup and delivery (VRPSPD). This problem is also known as the multiple-vehicle Hamiltonian one-to-many-to-one PDP with combined demands. In the VRPSPD some customers have a delivery demand, some have a pickup demand, and at least one customer has both a pickup and a delivery demand. VRPSPDs are rooted in the seminal paper of Min (1989) and have since evolved into a rich and active research field. Typical applications of VRPSPDs arise in the distribution of beverages and the collection of empty cans and bottles.

One important variant of the VRP arises in picay have more than one start node and more than one end node, and any node may be the origin and destination node of a number of commodities. In the second category, one-to-many-to-one, some commodities are carried from a depot to many customers, while other commodities are collected at customers and delivered to the depot. The third category contains one-to-one problems in which each commodity has a single start node and a single end node. The most studied and general variant of the second category or one-to-many-to-one, is the vehicle routing problem with simultaneous pickup and delivery (VRPSPD). This problem is also known as the multiple-vehicle Hamiltonian one-to-many-to-one PDP with combined demands. In the VRPSPD some customers have a delivery demand, some have a pickup demand, and at least one customer has both a pickup and a delivery demand. VRPSPDs are rooted in the seminal paper of Min (1989) and have since evolved into a rich and active research field. Typical applications of VRPSPDs arise in the distribution of beverages and the collection of empty cans and bottles.

The problem has been extensively studied in recent years because of its practical importance for distribution companies. Parragh et al., 2008a, Parragh et al., 2008b surveyed the PDP literature until 2007. Berbeglia et al., 2007, Berbeglia et al., 2010 reviewed the static and dynamic PDP, respectively. Survey papers of Caceres-Cruz et al., 2014, Braekers et al., 2016, and Gansterer and Hartl (2018) have briefly reviewed VRPSPDs. The main focus of all of these surveys are not VRPSPDs. They briefly discussed VRPSPD, and did not provide detailed analyses on the main problem and its variants. We therefore believe that there exists merit to specifically review VRPSPDs.

Our review methodology can be summarised as follows. We mainly focus on articles and book chapters about the VRPSPD. We carried out the literature search within well-known databases such as ISI Web of Knowledge and SCOPUS with keywords “vehicle routing problem with simultaneous pickup and delivery”, and followed by reference and citation analyses to find related contributions. We summarized the resultant studies by several descriptive statistics to provide an overall view of the research area.

The contribution of this review paper is fourfold. First, we present a detailed review of the existing studies on the standard VRPSPD, including mathematical formulations. Second, we provide a performance comparison of heuristics developed for the standard VRPSPD. Third, we describe several VRPSPD variants, case studies and industrial applications, and we provide synthetic tables. Fourth, we give an overview of the main trends observed in the literature and identify several interesting promising future research perspectives.

The remainder of this paper is structured as follows. Mathematical models and exact algorithms for the VRPSPD are presented in Section 2. We survey the heuristics developed for the standard VRPSPD in Section 3, miscellaneous variants in Section 4, and case studies in Section 5. We provide a summary and comparison of recent metaheuristics in Section 6. We finally present our conclusions and future research perspectives in Section 7.

Section snippets

Mathematical models and exact algorithms

The VRPSPD is defined on a complete directed graph G=(V,A) where V is the node set and A is the arc set. Node 0 represents the depot, which is the starting node of the delivery commodities and the end node of the pickup commodities. The other nodes of V are the customers. Let V=V{0}. A homogeneous fleet of vehicles is available and each vehicle has a capacity Q. The cost of traveling on arc (i,j) is denoted by cij. For delivery and pickup commodities, each customer i has a non-negative demand

Heuristics for the standard VRPSPD

We now survey the available heuristics for the standard VRPSPD. Classical construction and improvement heuristics in Section 3.1, local search metaheuristics in Section 3.2, followed by population search heuristics in Section 3.3, and ant colony heuristics in Section 3.4.

Variants and extensions

Many variants of the VRPSPD have been studied. We now review them in this section. We first review the VRPSPD with time windows in Section 4.1, the heterogeneous VRPSPD in Section 4.2, the multi-depot VRPSPD in Section 4.3, the green VRPSPD in Section 4.4, the stochastic VRPSPD in Section 4.5, and finally miscellaneous VRPSPDs in Section 4.6.

Case studies

Several authors have solved real-life VRPSPDs.

In the context of long-haul transportation, a heterogeneous fleet variant of the VRPSPD with time windows was considered by Drexl et al. (2013). The problem allows truck and driver changes at relay stations which are geographically dispersed, and considers driver shuttles between stations. The EU legislation for driving and working times were enforced. The authors developed a two-stage large neighborhood search heuristic. The problem was motivated

Summary and metaheuristic computational comparison

This section first provides a summary of studies on VRPSPDs, and then presents a comparison of recent metaheuristics developed to solve the standard VRPSPD.

Conclusions and research perspectives

Over the last three decades, extensive research has been conducted on the vehicle routing problem with simultaneous pickup and delivery (VRPSPD) which was introduced by Min (1989). We have first surveyed and then provided a performance comparison of models and algorithms developed for the standard problem. We have classified the available heuristics as classical construction and improvement heuristics, local search metaheuristics, population search heuristics, and ant colony heuristics. We have

CRediT authorship contribution statement

Çağrı Koç: Conceptualization, Methodology, Writing - original draft, Writing - review & editing. Gilbert Laporte: Supervision, Conceptualization, Writing - review & editing. İlknur Tükenmez: Writing - original draft.

Acknowledgements

The authors thank the two anonymous referees for their insightful comments and suggestions that helped improve the content and the presentation of the paper. The authors gratefully acknowledge funding provided by the Canadian Natural Sciences and Engineering Research Council under grant 2015-06189.

References (124)

  • R.C. Cruz et al.

    GENVNS-TS-CL-PR: a heuristic approach for solving the vehicle routing problem with simultaneous pickup and delivery

    Electron. Notes Discrete Math.

    (2012)
  • B. Çatay

    A new saving-based ant algorithm for the vehicle routing problem with simultaneous pickup and delivery

    Expert Syst. Appl.

    (2010)
  • E. Demir et al.

    An adaptive large neighborhood search heuristic for the pollution-routing problem

    Eur. J. Oper. Res.

    (2012)
  • D.J. Fagnant et al.

    Preparing a nation for autonomous vehicles: opportunities, barriers and policy recommendations

    Transp. Res. Part A

    (2015)
  • J. Fan

    The vehicle routing problem with simultaneous pickup and delivery based on customer satisfaction

    Proc. Eng.

    (2011)
  • Y. Gajpal et al.

    An ant colony system (ACS) for vehicle routing problem with simultaneous delivery and pickup

    Comput. Oper. Res.

    (2009)
  • M. Gansterer et al.

    Collaborative vehicle routing: a survey

    Eur. J. Oper. Res.

    (2018)
  • M. Gendreau et al.

    Time-dependent routing problems: a review

    Comput. Oper. Res.

    (2015)
  • F.P. Goksal et al.

    A hybrid discrete particle swarm optimization for vehicle routing problem with simultaneous pickup and delivery

    Comput. Ind. Eng.

    (2013)
  • Y. Jun et al.

    New best solutions to VRPSPD benchmark problems by a perturbation based algorithm

    Expert Syst. Appl.

    (2012)
  • C.B. Kalayci et al.

    An ant colony system empowered variable neighborhood search algorithm for the vehicle routing problem with simultaneous pickup and delivery

    Expert Syst. Appl.

    (2016)
  • Ç. Koç et al.

    Thirty years of heterogeneous vehicle routing

    Eur. J. Oper. Res.

    (2016)
  • Ç. Koç et al.

    Vehicle routing with backhauls: review and research perspectives

    Comput. Oper. Res.

    (2018)
  • A. Langevin et al.

    Continuous approximation models in freight distribution: an overview

    Transp. Res. Part B

    (1996)
  • D.H. Lee et al.

    A heuristic algorithm for yard truck scheduling and storage allocation problems

    Transp. Res. Part E

    (2009)
  • J. Li et al.

    Iterated local search embedded adaptive neighborhood selection approach for the multi-depot vehicle routing problem with simultaneous deliveries and pickups

    Expert Syst. Appl.

    (2015)
  • C. Lin et al.

    A genetic algorithm-based optimization model for supporting green transportation operations

    Expert Syst. Appl.

    (2014)
  • R. Liu et al.

    Heuristic approaches for a special simultaneous pickup and delivery problem with time windows in home health care industry

    IFAC Proc. Vol.

    (2012)
  • R. Liu et al.

    Heuristic algorithms for a vehicle routing problem with simultaneous delivery and pickup and time windows in home health care

    Eur. J. Oper. Res.

    (2013)
  • R. Martí et al.

    Principles of scatter search

    Eur. J. Oper. Res.

    (2006)
  • H. Min

    The multiple vehicle routing problem with simultaneous delivery and pick-up points

    Transp. Res. Part A

    (1989)
  • L. Mingyong et al.

    An improved evolution algorithm for vehicle routing problemwith simultaneous pickups and deliveries and time windows

    Eng. Appl. Artif. Intell.

    (2010)
  • N. Mladenović et al.

    Variable neighborhood search

    Comput. Oper. Res.

    (1997)
  • G. Mosheiov

    Vehicle routing with pick-up and delivery: tour partitioning heuristics

    Comput. Ind. Eng.

    (1998)
  • G. Nagy et al.

    Heuristic algorithms for single and multiple depot vehicle routing problems with pickups and deliveries

    Eur. J. Oper. Res.

    (2005)
  • S.N. Parragh

    Introducing heterogeneous users and vehicles into models and algorithms for the dial-a-ride problem

    Transp. Res. Part C

    (2011)
  • H. Paessens

    The savings algorithm for the vehicle routing problem

    Eur. J. Oper. Res.

    (1988)
  • O. Polat et al.

    A perturbation based variable neighborhood search heuristic for solving the vehicle routing problem with simultaneous pickup and delivery with time limit

    Eur. J. Oper. Res.

    (2015)
  • Y. Qu et al.

    The heterogeneous pickup and delivery problem with configurable vehicle capacity

    Transp. Res. Part C

    (2013)
  • S. Ropke et al.

    A unified heuristic for a large class of vehicle routing problems with backhauls

    Eur. J. Oper. Res.

    (2006)
  • D. Sacramento et al.

    An adaptive large neighborhood search metaheuristic for the vehicle routing problem with drones

    Transp. Res. Part C

    (2019)
  • A. Subramanian et al.

    A parallel heuristic for the vehicle routing problem with simultaneous pickup and delivery

    Comput. Oper. Res.

    (2010)
  • A. Subramanian et al.

    Branch-and-cut with lazy separation for the vehicle routing problem with simultaneous pickup and delivery

    Oper. Res. Lett.

    (2011)
  • K. Altinkemer et al.

    Parallel savings based heuristics for the delivery problem

    Oper. Res.

    (1991)
  • Angelelli, E., Mansini, R., 2001. The vehicle routing problem with time windows and simultaneous pick-up and delivery....
  • Augerat, P., 1995. VRP problem instances. <...
  • Battarra, M., Cordeau, J.-F., Iori, M., 2014. Pickup-and-delivery problems for goods transportation. In: Toth, P.,...
  • T. Bektaş et al.

    Dynamic vehicle routing problems

  • G. Berbeglia et al.

    Static pickup and delivery problems: a classification scheme and survey

    TOP: Off. J. Spanish Soc. Stat. Oper. Res.

    (2007)
  • J. Caceres-Cruz et al.

    Rich vehicle routing problem: survey

    ACM Comput. Surv.

    (2014)
  • Cited by (111)

    • Rethinking cyclic structures in liner shipping networks

      2024, European Journal of Operational Research
    View all citing articles on Scopus
    View full text