A hybrid ACS-VTM algorithm for the vehicle routing problem with simultaneous delivery & pickup and real-time traffic condition

https://doi.org/10.1016/j.cie.2021.107747Get rights and content

Highlights

  • A mixed integer programming model for the VRPSDPTI.

  • A hybrid algorithm of ant colony system and virtual transformation method (ACS-VTM).

  • A practical case to verify the model and algorithm and to provide managerial insights.

  • The hybrid ACS-VTM algorithm effectively reduce total travel cycle for the VRPSDPTI.

Abstract

The vehicle routing problem with simultaneous delivery & pickup and real-time traffic information (VRPSDPTI) is a dynamic problem of combinatorial network optimisation in logistics and supply chain management. It is also a typical NP-hard problem that has plagued enterprises with reverse logistics operations for many years. The main objective of this research is to determine an optimal vehicle routing plan for the VRPSDPTI problem. To achieve this goal, a mixed integer programming (MIP) model is constructed, with the objective of minimising the total travel cycle for the VRPSDPTI problem. A hybrid algorithm of the ant colony system and virtual transformation method (ACS-VTM) is then designed to explore the vehicle routing plan for the VRPSDPTI problem; it adopts a flexible split of the time period for re-optimisation and an improved partial service policy for customer demand. Based on it, a practical case of the VRPSDPTI problem is used to verify the proposed model and algorithm. One major finding is proposed through the study of the practical case that adopting the hybrid ACS-VTM algorithm can effectively reduce the total travel cycle for the VRPSDPTI problem. The main contributions of this study are that it can provide an efficient decision tool to solve the VRPSDPTI, and can not only reduce the total travel cycle, but also improve the efficiency of vehicle utilisation.

Introduction

Due to economic motivation, environmental constraints, and legal requirements, reverse logistics has drawn increasing attention from enterprises and governments in the past three decades (Tasan & Gen, 2012). Reverse logistics mainly deals with the collection of used and end-of-life products for remanufacturing or reuse. The process inevitably increases companies’ energy consumption, transportation costs, and greenhouse gas emission. To lower the cost of energy and transportation and satisfy environmental and legal requirements, enterprises expend great efforts to integrate reverse logistics into their forward logistics systems (Dethloff, 2001, Wang and Hsu, 2010). Consequently, the vehicle routing problem with simultaneous delivery and pickup (VRPSDP) was introduced, first by Min (1989). A major objective of the VRPSDP is to find an optimal vehicle routing plan to minimise total travel distance or total travel cycle.

In practice, there are many VRPSDP applications. The most common cases occur in the distribution systems of soft drinks, groceries, books, and clothing. For example, empty bottles, plastic pallets, and containers are collected for reuse; unsold books and clothes are picked up for resale in the secondary market (Kalayci and Kaya, 2016, Min, 1989). In the past 20 years, many enterprises that produce electromechanical products have established a hybrid production system for manufacturing and remanufacturing, such as Ford, GM, Volkswagen, Toyota, Caterpillar, Komatsu, Cummins, Mitsubishi, HP, Xerox, and Ricoh. These enterprises usually deliver new products to brand dealers (4 s dealers) and simultaneously pick up used and end-of-life products for remanufacturing. For instance, the HP Company has implemented a “Planet Partners Program” since 1991. The company delivers new and collects used computers. Apple Inc. has had a policy of “Apple Trade In” since 2013. The company trades new iPhones and iPads for old ones, while it delivers new and picks up used iPhones and iPads simultaneously. Other companies (e.g. Ford, Caterpillar, and Ricoh) run similar operations with auto engines, copying machines, and excavators. Therefore, the VRPSDP problem that arises in the hybrid production system has been a topical concern for many scholars

When solving a VRPSDP problem, enterprises’ distribution centres usually determine an optimal vehicle routing plan in advance. However, in the actual process of delivery and pickup, various types of traffic conditions often occur, such as traffic jams, road damage, roadside breakdowns, etc. These road conditions will undoubtedly impact the original vehicle routing plan adversely, as shown in Fig. 1. For instance, a distribution centre may need to dispatch another vehicle to complete the task assigned to the broken-down vehicle, or an original vehicle route may need to be adjusted to bypass a damaged road. This generates a variant of the VRPSDP, called vehicle routing problem with simultaneous delivery & pickup and real-time traffic information (VRPSDPTI). The VRPSDP problem is usually considered as a typical nondeterministic polynomial hard (NP-hard) problem (Dethloff, 2001, Salhi and Nagy, 1999, Wang and Chen, 2012). Compared with the VRPSDP problem, the VRPSDPTI encounters a variety of traffic conditions, which makes this problem more difficult to solve within acceptable limits of computational times and solution accuracy. Therefore, the VRPSDPTI problem is also NP-hard. A real-time optimal vehicle routing plan should deal with the above difficult issues, which are mainly caused by dynamic traffic conditions; otherwise, customers’ pickup and delivery times may be delayed, which can result in a longer total travel cycle and lower customer satisfaction.

The VRPSDPTI problem is a combinatorial network optimisation problem in logistics management. Designing an efficient algorithm to determine an optimal vehicle routing plan is a central difficulty in solving this problem; it is therefore a major concern in academic and industrial circles. Some studies have focused on an optimal solution for the VRP with traffic conditions, mostly developing heuristic or metaheuristic algorithms to solve it (Kim et al., 2016, Ng et al., 2017, Novaes et al., 2015, Zhu and Hu, 2019). However, to the best of our knowledge, no study has offered an effective algorithm to determine an optimal vehicle routing plan for the VRPSDPTI problem. Consequently, this issue has become a major concern for affected enterprises. The main purpose of this study is to design a hybrid algorithm of the ant colony system and virtual transformation method (ACS-VTM) to generate an optimal vehicle routing plan with a minimum total travel cycle for the VRPSDPTI problem. This research provides a useful decision tool for reducing the total travel cycle of the VRPSDPTI and increasing the efficiency of vehicle utilisation.

The remainder of this paper is structured as follows. Section 2 presents a literature review to identify research gaps in existing studies. Section 3 briefly describes the VRPSDPTI problem and builds a mixed integer programming (MIP) model with the objective of minimising the total travel cycle in this problem. In Section 4, three difficulties in algorithm design are first explored, and then a hybrid ACS-VTM algorithm is designed to solve the above MIP model. Section 5 adopts a practical case of an auto starter and alternator service to verify the rationality and validity of the proposed model and algorithm. Two useful business suggestions for future operation are discussed in section 6. Section 7 summarises the paper and its research results and points out several directions of future research.

Section snippets

Literature review

To the best of our knowledge, there has been no research on the VRPSDPTI problem. Consequently, this section mainly reviews the literature on VRPSDP and VRP with traffic information (VRPTI), which are most relevant to the VRPSDPTI problem. Research gaps are then pointed out to position our study.

VRPSDPTI

In this section, the VRPSDPTI problem is first described in detail, followed by the construction of an MIP model for the problem.

Major obstacles and proposed solutions

To efficiently solve the above MIP model built for the VRPSDPTI problem, the algorithm design should address the following three obstacles and propose their solutions.

Experiments and results

The proposed hybrid ACS-VTM algorithm was coded in MATLAB R2019a, and run on a CPU 1.8 GHz computer with 8 GB of RAM, under Windows 10. To the best of our knowledge, there has been no study that has focused on the VRPSDPTI problem; we cannot obtain a VRPSDPTI benchmark instance. Therefore, we select the static VRPSDP benchmark instance to verify the validation of the proposed the hybrid ACS-VTM algorithm. And then we apply the hybrid metaheuristic algorithm to a practical case of the VRPSDPTI

Discussions

Re-optimisation and vehicle capability for executing a re-optimised routing plan have a major influence on total travel cycle; therefore, the effects of the two critical factors are analysed below.

  • (1)

    Adopting the hybrid ACS-VTM algorithm with re-optimisation can effectively reduce the total travel cycle

For when real-time traffic information occurs in time periods [ T3,T4 ], [ T6,T7 ], and [ T8,T9 ], we compare the total travel cycle for the VRPSDPTI problem with and without re-optimisation, as

Conclusion and future research

In logistics and supply chain management, the VRPSDPTI is a dynamic combinatorial network optimisation problem, which is also a NP-hard problem. To the best of our knowledge, no study has proposed an optimisation scheme for this dynamic real-time VRPSDPTI problem. The main contributions of this study are to provide an effective and practical decision platform to determine the optimal vehicle routing plan for the VRPSDPTI problem, to lower the total travel cycle, and to enhance the efficiency of

CRediT authorship contribution statement

Wenjie Liu: Conceptualization, Methodology, Writing – review & editing, Supervision, Software, Funding acquisition. Yutong Zhou: Writing – original draft. Wei Liu: Data curation, Formal analysis. Jing Qiu: Investigation, Visualization. Naiming Xie: Project administration, Funding acquisition. Xiangyun Chang: Resources, Funding acquisition. Jian Chen: Validation, Funding acquisition.

Declaration of Competing Interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

Acknowledgment

This research is partially supported by grants from the National Natural Science Foundation of China (71871117, 71671090, 72074078, 52075259), Humanities and Social Science Foundation of the Ministry of Education of China (18YJA630066), Aeronautical Science Foundation of China (2017ZG52080), and the Royal Society of UK (IEC\NSFC\201348).

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