Journal of Advanced Transportation

Volume 2017 (2017), Article ID 1624328, 10 pages

https://doi.org/10.1155/2017/1624328

## Analysis of an Automated Vehicle Routing Problem in Logistics considering Path Interruption

School of Transportation, Southeast University, Nanjing, China

Correspondence should be addressed to Lei Shi

Received 27 April 2017; Accepted 2 July 2017; Published 7 August 2017

Academic Editor: Vinayak Dixit

Copyright © 2017 Yong Zhang et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

#### Abstract

The application of automated vehicles in logistics can efficiently reduce the cost of logistics and reduce the potential risks in the last mile. Considering the path restriction in the initial stage of the application of automated vehicles in logistics, the conventional model for a vehicle routing problem (VRP) is modified. Thus, the automated vehicle routing problem with time windows (AVRPTW) model considering path interruption is established. Additionally, an improved particle swarm optimisation (PSO) algorithm is designed to solve this problem. Finally, a case study is undertaken to test the validity of the model and the algorithm. Four automated vehicles are designated to execute all delivery tasks required by 25 stores. Capacities of all of the automated vehicles are almost fully utilised. It is of considerable significance for the promotion of automated vehicles in last-mile situations to develop such research into real problems arising in the initial period.

#### 1. Introduction

Due to fierce competition in the global market, an intelligent, efficient logistics system has become one of the most critical assets needed for an enterprise to stand out from others. The rapid development of the urbanisation and car ownership has produced big impacts on the transport systems, leading to challenges to many transport topics/areas, including demand management [1–3], traffic signalization [4, 5], traffic safety [6, 7], and public transport [8–11]. Modern logistics industry asserts a strict claim to high efficiency.

Compared to conventional modes of transport, automated vehicles are proved to offer a huge improvement in service efficiency and quality. In dense urban cities, labour costs are high. Manpower is one of the significant elements in any logistics system, which undoubtedly leads to the high level of inputs into the logistics system. Additionally, fatigue driving and bad driving behaviours cause potential risks for the transportation safety, but automated vehicles are free from these worries. To be concluded, the application of automated vehicles in logistics can efficiently cut down the operation costs, improve the efficiency of freightage, and eliminate the potential risks caused by human beings. In this regard, the methodology of automated vehicle routing planning in logistics is proposed. Implementing automated equipment in the last mile can largely cut down the cost of the logistics and render the logistics system “smart” or “intelligent,” which thus meets consumer expectations; however, unmanned equipment is still on the test bed. Defects and instabilities in the technology limit the scale of the application of automated vehicles in the initial period. According to a report of public views on automated vehicles from the American Automobile Association (AAA), 75% of interviewees hold pessimistic views on unmanned technology: 54% of drivers maintain that automated vehicles on real roads must increase the potential risk of a traffic accident and intensify public anxiety. Thus, selectively opening or prohibiting sections of road is an essential stage in the promotion of the use of automated vehicles.

The conventional VRP model is modified by considering a traffic interruption. The partial blocking of roads is considered as a constraint in the proposed model. This work focuses on the automated vehicle routing problem with time windows (AVRPTW) model of single distribution centre-mass client mode. The purpose of the distribution centre is to plan the driving circuit and satisfy the demands of all of the consumers: the objective function is to minimise the operational cost. Thus, we examine the similarity between the conventional VRP and the AVRPTW. The greatest difference is that AVRP model is faced with stricter constraint conditions, such as path interruption. Additionally, cost structure in VRP and AVRP is different: cost in the VRP model consists of dispatching and human costs. However, these costs are simplified in the AVRPTW model. Based on the fundamental particle swarm optimisation (PSO) algorithm, an improved PSO algorithm is designed by modifying the inertia weights and learning factors to improve the performance thereof. The AVRPTW model and the improved PSO algorithm are tested in a case study: their validity and practicability are certified. Additionally, the application of automated vehicles in logistics is proved to offer a huge improvement in efficiency and other benefits.

The paper is organised as follows: Section 2 summarises the literature review, in Section 3, the AVRPTW model considering a traffic interruption is formulated, Section 4 introduces the improved PSO algorithm, the AVRPTW model and improved PSO algorithm are applied in a case study in Section 5, and Section 6 draws the conclusions.

#### 2. Literature Review

The application of unmanned vehicle technology and vehicle networking technology can effectively reduce the severity of traffic congestion, traffic accidents, and environmental pollution. Some scholars applied this technology to some fields of transportation. For example, unmanned vehicle technology was applied in intersection control to ensure the safety and efficiency thereof [12, 13]; however, as for last-mile logistics distribution, transportation, and other areas, the application of unmanned vehicles has not yet started.

Jozefowiez et al. [14] analysed a multiobjective path optimisation problem by comparing the definition of each problem, objectives, and algorithms [14]. Baldacci et al. [15] reviewed recent research into the exact algorithms for the VRP with capacity and time window constraints [15]. Nagy and Salhi [16] proposed an improved heuristic algorithm to solve the pick-up and delivery VRP with multiple depots [16].

In Europe, as a source of air pollution, transportation activities in the logistics sector activities account for 24% of all European emissions. In recent decades, more environmental problems related to economic activities have been transferred to the logistics field. Based on this background, a multiobjective vehicle routing problem was proposed [17]. Michallet et al. [18] studied a periodic VRP with time constraints in high value goods transportation. Archetti et al. [19] considered enterprises that not only used company drivers and delivery vehicles, but also allowed others willing to participate in one-way distribution runs, close to their delivery destination, so as to reduce the cost of distribution [19].

Considering a multivehicle scheduling problem, an example of a distribution enterprise was studied by Coelho et al. [20]. The problem consisted of a number of service constraints for specific customer requirements, considering fixed vehicle, and transportation costs. An adaptive search procedure with a local search and an improved process using a variable neighbourhood were designed. Coelho et al. [20] used this algorithm to derive an optimal transportation plan and reduced the cost thereof [20]. The path planning of an unmanned aerial vehicle (UCAV) was a complex global optimisation problem, which could be used to search for the optimal path on the field of combat. Zhang et al. [21] proposed a new heuristic algorithm to solve the wolf UCAV 2D path planning problem. Then, UCAV could avoid the threat by connecting the two-dimensional coordinates of the node, achieving the lowest cost while finding a safe path. The simulation results showed that the proposed method considered the quality, speed, and ultimate stability in path planning [21]. An energy-efficient path planning problem was developed: the experimental results showed that the method could save energy effectively [22]. In the last-mile logistics considering the use of electric cars as a means of conveyance, Klumpp [23] studied the logistics cost and undertook a sustainability evaluation [23]. A mixed integer linear programming optimisation algorithm was proposed to solve the VRP, to validate the algorithm. A periodic vehicle routing problem (PVRP) was used as a case study by Cacchiani et al. [24]. The results verified the effectiveness of the proposed algorithm and were the best known solutions [24]. The hybrid particle swarm optimisation algorithm was used to solve the conventional VRP [25].

VRP is an NP-hard problem, and a heuristic algorithm is usually needed to solve this kind of problem. Chen et al. [26] used system dynamics to modify the particle and established the adaptive particle swarm algorithm to solve the set of multiproduct material transport path optimisation problems. To minimise the total cost, corresponding constraints were set and this model algorithm was used to solve various problem instances, which further verified the effectiveness of the algorithm [26]. In order to generate an effective solution way to fix the VRPSPD, which was known as an NP-hard problem, Goksal et al. [27] proposed an approach which was a solution based on particle swarm optimisation algorithm. At the same time, an annealing strategy was used to maintain the diversity of population. The effectiveness of the algorithm was verified by experiments, and the optimal solution was obtained by using the improved ant colony algorithm [27]. Combined with a real-life application, Goel and Gruhn [28] studied the rich VRP. GVRP was a solution in the highly restricted search space, which was suggested to improve the iterative search process by changing the neighbourhood structure [28]. Although 2L-VRPB was often applied, few researchers studied this method. Based on this fact, Liu [29] proposed a hybrid metaheuristic algorithm to solve the problem and verified the effectiveness of the algorithm experimentally [29]. Cinar et al. [30] designed a finite time, two-phase, cumulative algorithm to solve the VRP and proposed a fast, easy way to implement their CumVRP-LD algorithm. The algorithm could change in response to changes in the actual situation; the high response speed was necessary to develop the system [30].

Yu et al. [31] proposed an improved ant colony algorithm to solve the VRP. The effectiveness of the algorithm was verified by the data of fourteen datum points [31]. Pisinger and Ropke [32] proposed a general heuristic algorithm to solve the following five kinds of VRP: VRP with time windows, capacity-limited VRP, multidepot VRP, site-dependent VRP, and open VRP [32]. Christian [33] established a relatively simple, but effective, hybrid genetic algorithm. In terms of the average cost, the performance of the hybrid genetic algorithm was better than that of most heuristic algorithms. It was proved that this algorithm was the best solution in 20 large cases studies [33]. Schyns [34] used the ant colony algorithm to solve the VRP including mixed batch arrival and dynamic capacity with time windows [34]. The ant colony algorithm is a metaheuristic algorithm, which was used to solve the VRP. Bell and McMullen [35] compared the ant colony algorithm with the TS search algorithm and genetic algorithm and found that the ant colony algorithm required less computation time [35]. Gribkovskaia et al. [36] proposed a mixed integer programming model (SVRPPD), which was compared with the classical algorithm and the improved heuristic algorithm. The results showed that the best solution was often generated by the heuristic algorithm [36]. Kumar et al. [37] used a self-learning particle swarm optimisation (PSO) algorithm to solve the multiobjective model of production and pollution, and the total operating cost was minimised [37].

Previous studies are limited with regard to their application in practice. To sum up, contributions of this paper are two twofold: (i) AVRPTW model considering a traffic interruption is built for the consideration of the policy restriction when applying automated vehicles in last-mile situations in the initial stage; (ii) an improved PSO algorithm is developed for the AVRPTW model with path interruption.

#### 3. Mathematical Model for AVRPTW

##### 3.1. Problem Statement

The automated vehicle routing problem (AVRP) model can be described as follows, and the model is shown in Figure 1: the total number of the consumers in one certain area is ; the distribution centre has to distribute a certain amount of goods to certain consumers; presently, this distribution centre is preparing to put in several automated vehicles to carry out the assignment. In the initial stage of the application of the automated vehicle, considering the restrictions imposed by the transportation policy, some sections among certain distribution paths can be seen as a break-off point, which is shown as the red line in Figure 1. Meanwhile, when vehicles arrive, consumers have to sign for the goods. Thus, the AVRP model can be identified as an automated vehicle routing problem with time windows (AVRPTW). Time windows are defined as . When the vehicle arrives before , then a vehicle has to wait, which is the cause of the penalty cost. When the vehicle arrives after , this distribution service is regarded as a failure. The distribution centre has to plan a certain path for each automated vehicle and all the consumer demands must be satisfied: the objective is to minimise the total cost of the operation.