Survey in Operations Research and Management ScienceA review of vehicle routing with simultaneous pickup and delivery
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 where is the node set and 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 are the customers. Let . A homogeneous fleet of vehicles is available and each vehicle has a capacity Q. The cost of traveling on arc is denoted by . 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)
- et al.
A particle swarm optimization for the vehicle routing problem with simultaneous pickup and delivery
Comput. Oper. Res.
(2009) - et al.
Efficiently solving very large scale routing problems
Comput. Oper. Res.
(2019) - et al.
An adaptive local search algorithm for vehicle routing problem with simultaneous and mixed pickups and deliveries
Comput. Ind. Eng.
(2015) - et al.
A hybrid metaheuristic algorithm for heterogeneous vehicle routing problem with simultaneous pickup and delivery
Expert Syst. Appl.
(2016) - et al.
Two-echelon vehicle routing problem with simultaneous pickup and delivery: mathematical model and heuristic approach
Comput. Ind. Eng.
(2018) - et al.
The pollution-routing problem
Transp. Res. Part B
(2011) - et al.
Dynamic pickup and delivery problems
Eur. J. Oper. Res.
(2010) - et al.
Heuristic algorithms for the vehicle routing problem with simultaneous pick-up and delivery
Comput. Oper. Res.
(2007) - et al.
The vehicle routing problem: state of the art classification and review
Comput. Ind. Eng.
(2016) - et al.
The self-learning particle swarm optimization approach for routing pickup and delivery of multiple products with material handling in multiple cross-docks
Transp. Res. Part E
(2016)
GENVNS-TS-CL-PR: a heuristic approach for solving the vehicle routing problem with simultaneous pickup and delivery
Electron. Notes Discrete Math.
A new saving-based ant algorithm for the vehicle routing problem with simultaneous pickup and delivery
Expert Syst. Appl.
An adaptive large neighborhood search heuristic for the pollution-routing problem
Eur. J. Oper. Res.
Preparing a nation for autonomous vehicles: opportunities, barriers and policy recommendations
Transp. Res. Part A
The vehicle routing problem with simultaneous pickup and delivery based on customer satisfaction
Proc. Eng.
An ant colony system (ACS) for vehicle routing problem with simultaneous delivery and pickup
Comput. Oper. Res.
Collaborative vehicle routing: a survey
Eur. J. Oper. Res.
Time-dependent routing problems: a review
Comput. Oper. Res.
A hybrid discrete particle swarm optimization for vehicle routing problem with simultaneous pickup and delivery
Comput. Ind. Eng.
New best solutions to VRPSPD benchmark problems by a perturbation based algorithm
Expert Syst. Appl.
An ant colony system empowered variable neighborhood search algorithm for the vehicle routing problem with simultaneous pickup and delivery
Expert Syst. Appl.
Thirty years of heterogeneous vehicle routing
Eur. J. Oper. Res.
Vehicle routing with backhauls: review and research perspectives
Comput. Oper. Res.
Continuous approximation models in freight distribution: an overview
Transp. Res. Part B
A heuristic algorithm for yard truck scheduling and storage allocation problems
Transp. Res. Part E
Iterated local search embedded adaptive neighborhood selection approach for the multi-depot vehicle routing problem with simultaneous deliveries and pickups
Expert Syst. Appl.
A genetic algorithm-based optimization model for supporting green transportation operations
Expert Syst. Appl.
Heuristic approaches for a special simultaneous pickup and delivery problem with time windows in home health care industry
IFAC Proc. Vol.
Heuristic algorithms for a vehicle routing problem with simultaneous delivery and pickup and time windows in home health care
Eur. J. Oper. Res.
Principles of scatter search
Eur. J. Oper. Res.
The multiple vehicle routing problem with simultaneous delivery and pick-up points
Transp. Res. Part A
An improved evolution algorithm for vehicle routing problemwith simultaneous pickups and deliveries and time windows
Eng. Appl. Artif. Intell.
Variable neighborhood search
Comput. Oper. Res.
Vehicle routing with pick-up and delivery: tour partitioning heuristics
Comput. Ind. Eng.
Heuristic algorithms for single and multiple depot vehicle routing problems with pickups and deliveries
Eur. J. Oper. Res.
Introducing heterogeneous users and vehicles into models and algorithms for the dial-a-ride problem
Transp. Res. Part C
The savings algorithm for the vehicle routing problem
Eur. J. Oper. Res.
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.
The heterogeneous pickup and delivery problem with configurable vehicle capacity
Transp. Res. Part C
A unified heuristic for a large class of vehicle routing problems with backhauls
Eur. J. Oper. Res.
An adaptive large neighborhood search metaheuristic for the vehicle routing problem with drones
Transp. Res. Part C
A parallel heuristic for the vehicle routing problem with simultaneous pickup and delivery
Comput. Oper. Res.
Branch-and-cut with lazy separation for the vehicle routing problem with simultaneous pickup and delivery
Oper. Res. Lett.
Parallel savings based heuristics for the delivery problem
Oper. Res.
Dynamic vehicle routing problems
Static pickup and delivery problems: a classification scheme and survey
TOP: Off. J. Spanish Soc. Stat. Oper. Res.
Rich vehicle routing problem: survey
ACM Comput. Surv.
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