Route optimization in township logistics distribution considering customer satisfaction based on adaptive genetic algorithm

Highlights

• A new mathematical model of customer satisfaction is proposed.

• Accurate mathematical expression of the new customer satisfaction model is given.

• Some improvements are made to the adaptive genetic algorithm.

Abstract

With the development of the logistics economy, problems such as the timeliness of logistics distribution and the high cost of distribution have emerged. A new adaptive genetic algorithm is proposed to solve these problems. The $p_c$ and $p_m$ values of the algorithm are related to the number of iterations and the individual fitness values. To improve the local optimization ability of the algorithm, a large neighborhood search algorithm is proposed. In addition, this study establishes a soft time window town logistics distribution model with constraints. The model considers the optimal cost as the objective function and customer satisfaction as the influencing factor. In the experiment, the proposed adaptive genetic algorithm is compared with the traditional genetic algorithm, validating the effectiveness of the proposed algorithm.

Introduction

The logistics industry is an integrated that ensures social production and social life supply, including transportation, storage, communication, and other industries. Therefore, the development of the modern economy and the improvement of the quality of people’s livelihood are inseparable from the development of the logistics industry.

In recent years, the optimization of logistics vehicle distribution routes has been a hot topic in the field of logistics. The vehicle routing problem (VRP) [5], [6] was first proposed by Dantzig and Ramser in 1959. It means that a certain number of customers have different quantities of goods demand. The distribution center provides goods for customers, and vehicles are used to distribute goods to customers via a planned distribution route. The goal is to satisfy the customers’ needs and achieve the shortest distance under certain constraints, such as minimum cost and shortest time. This problem typically assumes that the distribution center and the customer’s geographic location, as well as the customer’s demand for goods, are known.

Further investigation of the problem reveals that the delivery point has certain requirements for the arrival time of vehicles. Thus, the time window constraint is considered in the VRP; then, VRPs with a time window (VRPTW) [10] are formed. These problems can be divided into two forms. One is a hard time window, which requires a vehicle to arrive within the time window, and if the vehicle arrives early, it must wait. If the vehicle arrives late, it will be rejected. The other is a soft time window, in which the vehicle can arrive outside the time window but must be punished.

In reality, most of the logistics vehicle distribution problems are soft time window problems. The untimely delivery of goods causes customers to be dissatisfied with the distribution service, resulting in losses to the distribution company. Scholars have conducted the following research on the soft time window logistics and distribution problem to better and more quickly choose the optimal distribution route under the soft time window.

Research regarding logistics VRP models with a soft time window. W. Liu [14] studied a path optimization model of the last kilometer of logistics transportation chain under a soft time window distribution and used an improved ant colony algorithm to solve the problem of enterprise profit maximization. A. H. Golsefidi, M. R. A. Jokar [8] proposed a mixed-integer linear programming model for the VRP considering both pickup and delivery, as well as multiple uncertain conditions, and described the performance of the annealing and genetic algorithms in the uncertainty solving model. Y. Niu et al. [16] studied the goods distribution business of third-party logistics and established a variant of an open VRP, i.e., service vehicles do not return to the distribution site after delivering goods. In the context of social environmental protection, including energy savings and emission reduction, an open VRP of green logistics is investigated by considering the time window. Z.-J. Ma et al. [15] studied the delivery problem of perishable products in cities and developed a European model of vehicle delivery route combining order selection and time correlation for the damage of goods caused by late delivery time, especially when the accepted delivery orders exceed the delivery capacity of distributors.

Research on optimization algorithms for logistics VRPs with a soft time window. K. Sethanan, T. Jamrus [20] published an article on a multi-travel VRP. In this article, to solve the problem, they studied integer linear programming formulas and new hybrid differential evolution algorithms. It includes a genetic operator and fuzzy logic controller. A. P. Afra, J. Behnamian [2] studied a multiproduct production route problem with startup costs and environmental factors. To investigate this problem, the authors adopted and optimized the Lagrangian relaxation algorithm. Experimental numerical analysis proves that the optimized Lagrangian algorithm is effective in solving such problems of medium scale. Y. Li et al. [12] develop a multi-depot green VRP by maximizing revenue and minimizing costs, time, and emission. Then, after applying an improved ant colony algorithm to solve the problem model, the results were compared with the traditional ant colony algorithm. They concluded that the improved ant colony algorithm outperforms the traditional ant colony algorithm. M. Gmira et al. [7] proposed a solution to a time-dependent vehicle problem with time windows that uses a tabu search heuristic algorithm to determine the shortest path between any two customers at different times of the day. The main contribution of this solution is to evaluate the feasibility and approximate cost of a solution within a constant time frame. H. Zhang [26] proposed a multi-objective optimization strategy based on the ant colony algorithm and three mutation operators. The performance of the proposed method is evaluated by solving the Solomon problem, and the results show the effectiveness of the method.

A logistics distribution system is an NP-hard problem with numerous interference factors, indicating why obtaining the exact solution to such a problem is difficult. The above references also show that customer satisfaction [22] for logistics distribution problems is idealized, and the given algorithm tends to fall into local optimum during the iteration process, increasing the solution time. If the delivery vehicles arrive at the customer point outside the delivery time window, customer satisfaction does not follow a simple linear decline; therefore, designing a more realistic expression of customer satisfaction is critical for solving the path optimization problem more effectively.

In summary, to improve the solutions concerning the above problems, the innovations of this article are as follows:

(1) Establish a new mathematical model of customer satisfaction, which is more realistic than other customer satisfaction models.

(2) Establish an accurate mathematical expression of the new customer satisfaction model.

(3) The values of $p_c$ and $p_m$ in adaptive genetic algorithms are not only related to individual fitness but also the number of algorithm iterations.