Optimisation of takeaway delivery routes considering the mutual satisfactions of merchants and customers

doi:10.1016/j.cie.2021.107728

Computers & Industrial Engineering

Volume 162, December 2021, 107728

https://doi.org/10.1016/j.cie.2021.107728 Get rights and content

Highlights

•
A vehicle routing optimization model considering dual satisfaction is established.
•
An improved GA with forward continuous crossover and differential mutation is given.
•
A case study is conducted to compare the improved GA with the two algorithms.

Abstract

To solve a series of problems (including high cost and delivery delay) during takeaway delivery, a model for the vehicle routing problem (VRP) during goods pickup and delivery is developed by considering constraints such as the capacity of delivery vehicles, delivery mileage and time window. The model is constructed by transforming the satisfactions of merchants and customers into a penalty function and aiming to minimise the total delivery cost. As for the drawbacks in a conventional genetic algorithm (CGA), such as a low convergence rate and locally optimum solutions, an improved GA (IGA) is designed by separately using the insertion heuristic algorithm to construct initial solutions and introducing the forward continuous crossover and differential mutation strategies. On the one hand, the numerical analysis and test of weights indicate that the model can reduce the delivery cost of enterprises offering takeaway service and improve satisfactions of merchants and customers. It verifies that reasonably considering satisfactions of merchants and customers during vehicle routing is conducive to cost-reduction and increased efficiency of enterprises. On the other hand, a simulation is conducted to compare and analyse various algorithms based on two different scales of test examples, which validates the proposed algorithm as effective. The study provides a theoretical basis and decision reference for enterprises offering takeaway service to improve delivery efficiency and competitiveness.

Introduction

In recent years, pickup and delivery delays of takeaway orders occur from time to time as the scales of various takeaway platforms are constantly expanded. It not only reduces customer and merchant satisfaction, but restricts the further development of enterprises offering a takeaway service. Therefore, how to improve this situation while considering the delivery cost to enterprises so as to provide beneficial strategies for the long-term development of enterprises is a matter of concern. The differences between takeaway delivery and traditional logistics mainly lie in four aspects: (1) the goods picked up are not delivered to several fixed distribution centres; (2) each order is constrained by pickup at first and then delivery; (3) an electric-bike rider (the rider, hereinafter) needs to deliver all goods being picked up in a delivery task to the corresponding destinations; (4) as for takeaway delivery, it is generally required to deliver the food within a certain time after the food is done in order not to influence the quality and taste of food. Moreover, merchants also need some time to prepare the food after taking an order. Therefore, both merchants and customers have a certain requirement on the arrival time of a rider. Collectively, the optimisation process of the takeaway delivery routes is more complex than the traditional vehicle routing problem (VRP).

The currently related research mainly concentrates on various aspects including the spatial distribution characteristics of takeaway food industry (Wang, Lin, & Feng, 2019), food safety (Zhang, 2020), and business pattern of a takeaway service (Xing & He, 2020). Research on VRP of takeaway delivery is sparse, while the VRP of goods pickup and delivery under time window constraints (VRPPDTW) has been studied in much greater depth. Parragh, Doerner, and Hartl (2008) discussed the mathematical model for VRPPDTW from problem type. Mahmoudi and Zhou (2016) proposed a VRPPDTW time discretization multi-commodity network flow model with vehicle load status integration, and used dynamic programming algorithm to calculate it. Chen and Li (2016) found a satisfactory solution based on an improved genetic algorithm by aiming to maximise the total client satisfaction with time against the background of online to offline (O2O) takeaway service. Furtado, Munari, and Morabito (2017) proposed a novel compact bi-exponential equation to solve the VRPPDTW. Zhou, Tong, and Mahmoudi (2018) conducts research based on the unique perspective of the time-related and state-related route search framework, aiming to provide a high-quality solution engine for transportation applications. Andres, Laurence, and Nacima (2018) have studied VRPPDTW and used a multi-group memetic algorithm to solve it taking the uncertain journey distance into consideration and achieved good results. Ghilas and Cordeau (2018) proposed the use of an exact branch and bound algorithm to solve the type of problems. Wang, Li, and Zhang (2018) established a VRPPDTW model aimed at minimising the transportation cost, and further designed a two-stage heuristic algorithm to solve the model. Under the background of O2O takeaway delivery service, Wu, Chen, and Jianm et al. (2018) proposed an online travelling salesman problem with goods pickup and delivery and further designed a TAIB algorithm to solve the problem. Aiming to minimise the scheduling cost of enterprises, Li, Yu, and Li (2019) took the time-based penalty cost as the variable cost to modify the objective function and then attained a heuristic routing scheme by using a genetic algorithm (GA). To solve the VRPPDTW, Wang, Gao, and Liu, et al. (2019) designed a backtracking search optimisation algorithm (BSA). Aiming to minimise the total service cost, Li, Zhou, and Xu (2020) constructed a VRPPDTW model for a closed area and solved the model by using an improved genetic algorithm. Ibrahim, Nurhakiki, and Utama (2021) do researches aiming to find the best solution for VRPPDTW, and design an improved genetic algorithm. Sitek, Wikarek, and Rutczyńska-Wdowiak (2021) separately explored the vehicle routing models with goods pickup and delivery and time window constraints and they proposed a hybrid method combining constraint programming, GA, and mathematical programming. Nevertheless, these studies still show some limitations: the current research on the routing problem of takeaway delivery vehicles mainly focuses on how to decrease the enterprise cost or improve client satisfaction; by contrast, research considering both benefits to the enterprise, and merchants’ and customers’ satisfactions with time during takeaway delivery is sparse. To solve the problem, a model for minimising the total delivery cost is established by considering the mutual satisfaction of merchants and customers; in addition, an IGA is designed to solve the model aiming at the VRPPDTW under the background of a takeaway service. The mutual satisfaction of merchants and customers is incorporated into the model construction and analysed. On the one hand, this provides a theoretical basis for increasing the delivery service level of takeaway platforms and enhancing the competitiveness of enterprises offering takeaway service; on the other hand, there is little research available on VRP for takeaway pickup and delivery considering benefits of merchants and customers and the present study will further enrich this field.

VRPPDTW is a type of the VRP, which is defined as a non-deterministic polynomial-time hard (NP-hard) problem by scholars. With the growing problem scale, the application of an exact algorithm fails to produce timeous solutions (Yang, Zhang, & Bai, 2019). Thus, many scholars try heuristic algorithms to solve the VRP and its associated problems, for example, the simulated annealing algorithm (Wang, Shen, & Wang, 2015), co-evolutionary algorithm (Wang, Mu, & Fu, 2015), particle swarm optimisation (Kumar et al., 2016, Yang et al., 2017), tabu search (Fu, Liu, & Qiu, 2018), chemical reaction optimisation (Li & Wang, 2018), differential evolution algorithm (Liao, Hu, & Wu, 2017), and GA (Fan et al., 2020, Hsiao et al., 2018, Ma et al., 2017) have been used to good effect. GA, as an adaptive random search algorithm, shows strong robustness and inherent mechanism for parallel computing, so it is applicable to the solution of complex optimisation problems (Wang, Deng, & Wang, 2016). Therefore, by applying the GA solution model and considering problems in the conventional GA (CGA) (ease to finding only local optima and their low convergence rate), an IGA is designed to solve the constructed model based on the practical scenario of takeaway delivery.

Section snippets

Problem description and assumptions

The VRP under non-full loads with soft time windows and pickup followed by delivery within an area is assessed, which can be described by using the network G = (N, A). $N = {0} \cup N^{+} \cup N^{-}$ refers to a set of all client nodes, which includes the distribution centre {0}, a set $N^{+}$ of all Merchants in n orders and a set $N^{-}$ of all customers; among them, the merchant represents the starting node of meal picking, the customer represents the destination node of meal delivery, and merchants and customers are

Model parameters

The parameters of the model for optimising takeaway delivery routes are displayed in Table 3-1.

Decision variables

For convenience, the serial number 0 represents the distribution centre and the client nodes are expressed as i, j ( $i, j = 1, 2, 3, \dots, N$ ).

The decision variable $x_{ijk}$ is expressed as follows: $x_{ijk} = \{\begin{matrix} 1, kth rider goes from client point i to client point j \\ 0, o t h e r w i s e \end{matrix}$

When the kth rider directly comes to client node j directly from client node i, that is, rider k travels along route (i, j), $x_{ijk}$ equals 1; otherwise; $x_{}$

Model establishment

A VRPPDTW model is established to consider simultaneously the delivery cost of enterprises and client satisfaction. The model aims to minimise the total delivery cost, which involves the start-up cost of electric bikes, riding cost of riders and penalty cost dependent on satisfactions of clients (briefly called penalty cost, hereinafter). Based on the complexity of takeaway pickup and delivery, the total delivery cost is expressed by using the method of calculating the weight sum of costs of

Design of the algorithm

The GA is an iterative heuristic search algorithm (Cheng, Wang, & Wu, 2018). By virtue of various advantages such as the favourable global search ability, high robustness and inherent mechanism for parallel computing, the GA is applicable when solving the complex optimisation problems. However, as a heuristic global optimisation algorithm, the GA had drawbacks as stated (Li, Liu, & Zhou, 2019). On the one hand, the insertion heuristic algorithm is utilized during population initialisation

Examples construction

The order-related data pertaining to a takeaway platform acquired at a distribution centre (Tianxin District, Changsha, Hunan Province, China) within the range of 6 km within a time period are taken as the test set. To verify the effectiveness of the algorithm under different sizes of data, two different scales of test examples are generated, including examples B₁ (30 orders at a distribution centre) and B₂ (60 orders at a distribution centre). The scale of example B₂ is larger than that of

Conclusions

A mathematical model for optimising the delivery routes is established by aiming to minimise the total delivery cost based on consideration of the interests to enterprises and the satisfaction of merchants, and customers. An IGA is designed by using the insertion heuristic algorithm to construct initial solutions and introducing the forward continuous crossover and differential mutation strategies. The sensitivity on different cost weights is analysed, and the effectiveness of proposed

CRediT authorship contribution statement

Ren Teng: Conceptualization, Methodology, Formal analysis, Writing – review & editing. Xu Hong-bo: Writing – original draft, Software, Validation. Jin Kang-ning: Writing – original draft, Software, Validation. Luo Tian-yu: Writing – original draft, Software, Validation. Wang Ling: Writing – review & editing, Supervision, Project administration, Funding acquisition. Xing Li-ning: Writing – review & editing, Supervision, Project administration, 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.

Acknowledgements

We appreciate the support of National Natural Science Foundation of China (No. 61773120, No. 71690233, No. 61802063), Hunan Provincial Key Laboratory of Smart Logistics Technology (2019TP1015), and the Innovation Team of Guangdong Provincial Department of Education (2018KCXTD031).

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View full text

Optimisation of takeaway delivery routes considering the mutual satisfactions of merchants and customers

Highlights

Abstract

Introduction

Section snippets

Problem description and assumptions

Model parameters

Decision variables

Model establishment

Design of the algorithm

Examples construction

Conclusions

CRediT authorship contribution statement

Declaration of Competing Interest

Acknowledgements

Operations Research Letters

Computers & Industrial Engineering

Transportation Research Part B: Methodological

Neurocomputing

Computers & Industrial Engineering

Control and Decision

Urban Development Studies

Journal of Shanghai Maritime University

A multi-population algorithm to solve the VRP with stochastic service and travel times

Computers & Industrial Engineering

Optimization model and algorithm based on time satisfaction for O2O food delivery

Chinese Journal of Management Science

Swarm intelligence optimization algorithm

Journal of Zhengzhou University (Engineering Science)

Improved genetic algorithm variable neighborhood search for solving hybrid flow shop scheduling problem

Computer Integrated Manufacturing System

Hybrid and genetic algorithm for solving fuzzy demand time windows vehicle routing problem

Journal of System & Management

Research on cold chain logistics distribution path optimization based on hybrid ant colony algorithm

China Journal of Management Science

A tabu search algorithm for the vehicle routing problem with soft time windows and split deliveries by order

China Journal of Management Science

Branch-and-price for the pickup and delivery problem with time windows and sch-eduled lines

Transportation Science

Last-mile distribution planning for fruit-and-vegetable cold chains

The International Journal of Logistics Management

Parallel machine scheduling with setup time in the MapReduce system

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Optimised genetic algorithm crossover and mutation stage for vehicle routing problem pick-up and delivery with time windows

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