1. Introduction
With the accelerated development of global integration, the competition between assembly and manufacturing companies has become increasingly fierce, and higher operating costs have put the development of companies to the test. In discrete-oriented manufacturing companies, the auxiliary time in production logistics (storage and handling of materials, etc.) accounts for 90 to 95% of the total operation time [
1], and so increasing the optimization of the logistics distribution path has become an effective way to reduce operating costs and improve economic efficiency [
2]. Therefore, optimizing the level of operation of production plant logistics plays a vital role in the survival and development of enterprises. Assembly and manufacturing enterprises are often faced with handling many types and models of materials, making it difficult to carry out sorting storage and distribution, and material distribution is the intermediate link between storage and production, playing an important connecting role in the whole system of production logistics, which will directly affect the production efficiency and delivery speed of products. At the same time, in the operational aspects of production logistics in contemporary assembly and manufacturing plants, problems such as high transport costs, low distribution efficiency, untimely distribution and poor service satisfaction at workstations are common [
3]. As the “third source of profit”, logistics plays a vital role in reducing production costs, improving production efficiency and enhancing market competitiveness. With the continuous development of lean, intelligent, collaborative and green production, improving the transport efficiency of existing production logistics in assembly and manufacturing workshops, improving the satisfaction of workplace services and achieving green and low-carbon logistics have become some of the major challenges that assembly and manufacturing enterprises need to solve.
The development of intelligent green logistics in assembly manufacturing enterprises will be conducive to promoting the optimization of the production mode of enterprises, driving the manufacturing industry to achieve industrial structure upgrades, and is now becoming one of the important driving forces for the transformation of the manufacturing industry. In 2015, China released the “Made in China 2025” strategic plan, highlighting that its main goal of taking intelligent and green manufacturing is an important measure for China’s manufacturing industry in order for it to shift from low-end manufacturing to high-end manufacturing, and complete the strategic goal of manufacturing power [
4]. There has been a long history of research on production logistics systems, but there is not much literature with a focus on intelligent manufacturing; no practical application models for intelligent production logistics systems have so far been proposed, and research on the vehicle routing problem (VRP) has focused on the design of optimization algorithms and their application in sales logistics. Therefore, this paper combines the production characteristics of K Company, a discrete assembly manufacturing company, and introduces the VRP to solve the problem of real-time material distribution in the production logistics process, to achieve intelligent and low-carbon logistics distribution and to lay the foundation for intelligent manufacturing in the workshop.
The workshop material distribution path optimization problem is essentially a vehicle-routing problem, and VRP was first proposed by Danting and Ramser in 1959 [
5]. The vehicle routing problem refers to a distribution routing solution with the goal of minimizing distribution costs under certain constraints. These constraints include, but are not limited to, the following: customer demand, customer demand time, vehicle capacity, etc. The sequence of distribution vehicles visiting customers needs to be reasonably planned so as to develop a vehicle distribution path scheme that maximizes the above objectives [
6,
7,
8]. However, the optimization of logistics distribution routes is a complex mathematical problem involving modern optimization algorithms, which are highly difficult to solve and computationally intensive. At the beginning of the research period, attempts to solve this type of problem are mainly focused on the shortest driving path, the lowest cost of consumption or the least time spent on single-objective optimization. With the development of technology, though, research hotspots gradually shift to multi-objective optimization, considering more diverse factors that are more in line with the actual process of shop material distribution.
At this stage of research on the shop floor material distribution problem in manufacturing enterprises, scholars have focused on two aspects of the vehicle path problem: model building and solution algorithms. In model building, the main focus is the transition from single-objective to multi-objective, from optimization objectives and constraints, etc., so as to improve the model, and the use of a variety of algorithms to solve the algorithmic synthesis. Based on the idea of two-layer planning, Lou Zhenkai established a multi-objective optimization model with fuzzy time windows, considering the number of vehicles used and the total transport mileage, and applied the simulated annealing algorithm to solve the multi-objective optimization problem for distribution [
9]. Muller decomposed the multi-objective optimization problem and solved it using a heuristic algorithm, taking into account the soft time window [
10]. Murao et al. investigated VRP using soft time window constraints, with fuzzy variables and penalty functions [
11]. Xia Y developed a bi-objective open vehicle routing problem (OVRP) model considering soft time windows and satisfaction rates, in which the OVRP was analyzed and an improved taboo search algorithm (ITSA) fusion algorithm with an adaptive penalty mechanism and multi-neighborhood structure was applied to solve the problem [
12]. Yan Zhengfeng et al. proposed a distribution path optimization method based on fuzzy soft time windows for complex mechanical assembly workshops in order to solve the problem of uncertain material demand time at work stations in the actual production process, established a material distribution path optimization model with fuzzy soft time windows with the objective of minimizing distribution costs, and used a hybrid algorithm combining a dynamic programming algorithm and a simulated annealing algorithm to solve the model [
13]. Li Siguo and Guo Yu et al. established a material distribution model in a real-time environment for a discrete manufacturing workshop with a complex environment and many external disturbing factors, combined with considerations of the material distribution time window requirement and the minimum material distribution cost as the optimization objective, and used an improved genetic algorithm to solve the model [
14]. Ferani et al. proposed a green vehicle path problem that optimizes the transportation costs, spoilage costs, and carbon emissions of perishable products with high transportation costs and serious air pollution issues, and solved it using a multi-objective gradient evolutionary algorithm [
15]. Asma et al. proposed a new hybrid vehicle path planning algorithm for the capacitated vehicle path problem to improve the solution quality and speed up convergence [
16]. After studying the two-stage vehicle route problem (2S-VRP) in logistics distribution, Zhong X et al. applied a hybrid algorithm combining an artificial bee colony and genetic algorithm (ABCGA) to solve it [
17]. In addition, some scholars have applied Flexsim, Arena, Witness and other types of system simulation software to model and simulate various aspects of production logistics in order to find the bottlenecks and optimize the system by adjusting parameters; in this way, they sought to achieve goals such as the highest efficiency, lowest cost and best service [
18,
19,
20]. To this day, the vehicle routing problem is a popular research topic not only in China but also abroad in the field of logistics research. The problem model is mainly studied in terms of three main pairs of considerations: vehicle capacity, time constraint and vehicle class. For the vehicle path problem with capacity constraints, Lee et al. (2010) combined the properties of the simulated annealing algorithm and designed an improved ant colony algorithm, which was experimentally shown to outperform both the original ant colony algorithm and the simulated annealing algorithm [
21]. Nishi and Izuno (2014) proposed a column generation-based heuristic algorithm to solve and compared the performance with branch delimitation algorithm and manual operator, and then verified the feasibility and effectiveness of the algorithm [
22]. Ahmed (2018) proposed an efficient particle swarm optimization algorithm based on two-layer local search and verified that the proposed algorithm outperforms other particle swarm optimization algorithms [
23]. Reihaneh and Ghoniem (2018) developed a branch-and-cut algorithm for solving [
24]. Ana Moura et al. (2023) proposed a commodity-flow model and a formulation of the Three-Dimensional Packing Problem to solve a distribution problem of a Portuguese company in the automotive industry as time windows and loading due to the limited capacity of the fleet in terms of weight and volume. [
25]. Smiti et al. (2020) addressed the cumulative capacity constrained vehicle path problem, a mathematical model with the shortest arrival time to the customer as the optimization objective was developed and two optimization models were proposed to solve it [
26].
For the vehicle path problem with time windows, Vidal et al. (2013) proposed a hybrid genetic search algorithm that effectively solves a variety of large-scale vehicle path problems such as route duration constraints and those involving customer assignment to specific vehicle types [
27]. Nalepa and Blocho (2016) proposed an improved modal algorithm to solve an optimization model with the objective of using the minimum number of vehicles and the shortest vehicle travel distance, and verified its effectiveness through extensive experimental studies [
28]. Molina et al. (2020) proposed a hybrid ant colony algorithm with local search and verified experimentally that the method has good performance [
29]. Bogue et al. (2020) proposed a column generation algorithm and a post-optimization heuristic algorithm for solving [
30]. Jalilvand et al. (2021) developed a two-stage stochastic model and proposed a recursive hedging algorithm for a vehicle path problem with a two-level time window allocation and stochastic service times [
31]. Tilk et al. (2021) and designed a branch pricing-cut algorithm to solve the model [
32]. Hoogeboom et al. (2021) solved the model using a branch-and-cut approach with the objective of minimizing the travel time and the risk of violating the time window [
33].
For the problem of multiple paths for pairs of vehicles, Pietrabissa (2016) developed an algorithm for the multi-model vehicle path problem without communication and showed through simulation experiments that the algorithm has better performance [
34]. Avci and Topaloglu (2016) studied the heterogeneous vehicle path problem with simultaneous pickup and delivery and proposed a hybrid local search algorithm for solving it [
35]. Gholami et al. (2019) used a genetic algorithm to solve a mixed integer nonlinear model with cost minimization as an objective when studying a multi-vehicle path problem considering product transfer between vehicles in a dynamic situation [
36]. Wang et al. (2019) developed a mathematical model with the optimization objective of minimizing total carbon emissions when considering an integrated single-vehicle scheduling and multi-vehicle path problem, and then proposed a forbidden search hybrid algorithm to solve it [
37]. Behnke et al. (2021) proposed a column generation method for solving the vehicle path problem with heterogeneous vehicles and heterogeneous roads [
38]. It is known from the research of foreign scholars that most of the current research in this field is based on vehicle path problems that consider both vehicle capacity and time window or vehicle path problems that consider both vehicle capacity and vehicle type, while relatively few studies consider vehicle capacity, service attitude, carbon emission, time window and vehicle type simultaneously.
How to reduce carbon emissions in the process of vehicle transportation has received the attention of domestic scholars, and a series of studies on low-carbon logistics has been launched. Montoya A et al. proposed a two-stage heuristic algorithm suitable for solving the green vehicle path problem (G-VRP), incorporating the case of a vehicle visiting a gas station on its way to distribution, and finally verified the effectiveness of the algorithm through experiments [
39]. Koc C et al. proposed a simulated annealing algorithm based on the branch-and-bound method to improve the efficiency of solving the G-VRP problem [
40]. Jabir E and Zhang S combined vehicle transportation paths and greening to construct a vehicle path optimization model incorporating carbon emission parameters, followed by an improved ant algorithm and a hybrid artificial bee colony algorithm [
41,
42]. Niu Yunyun et al. designed a hybrid taboo search algorithm, which yielded a reduction in the total cost of the open route compared to the closed route, with a significant reduction in CO
2 emission cost and fuel consumption cost [
43]. Bektase et al. innovated the concept of low-carbon transport by including a fixed operating speed and load of the vehicle in the calculation of carbon emissions [
44]. Marcel also studied fixed vehicle speed, an important factor affecting the green vehicle path model, for energy consumption and carbon emissions at a fixed speed [
45]. Kwon Y et al. investigated the problem of optimizing heterogeneous vehicle paths considering carbon emissions and found that the implementation of carbon emissions trading can significantly reduce carbon emissions without increasing costs [
46].
Although the above research has made some progress, there are still some problems, such as poor solution quality, ease of falling into the local optimum and the development of a logistics distribution path with little consideration of environmental factors. It can be found that scholars at home and abroad have made certain achievements in the research of discrete workshop workstation logistics distribution path optimization. Scholars at home and abroad have studied the two issues of low carbon logistics and workshop workstation logistics distribution path optimization separately, yet not many combine the two issues. As national carbon emission governance is becoming more and more regulated, carbon tax policy implementation is coming closer and closer, and manufacturing enterprises must integrate the concept of low carbon into the internal logistics activities of the vehicle in the operation process to reduce the pressure brought by environmental costs. This paper proposes a study on the optimization of shop floor material distribution paths with multiple optimization objectives considering carbon emissions, aiming to help enterprises reduce carbon emission costs based on reducing distribution costs, and achieving customer satisfaction, and realizing the unity of economic benefits and environmental protection. In the analysis of existing workshop material distribution path optimization problems, it has been found that in some workshops, there is a high time penalty cost related to the fact that the distribution trolley cannot deliver the required materials within the time window specified by each workstation, resulting in low service satisfaction at the workstations. Furthermore, unreasonable route planning, which entails the use of more trolleys in the distribution process, increases the distribution distance and distribution costs, etc. Therefore, this paper establishes a multi-objective shop floor material distribution route optimization model based on the cost factors and carbon dioxide emissions generated during the distribution process, taking into account the demand for materials produced at each workstation. Based on this, the example of material distribution within a time window in a smart gas meter workshop owned by an electronic assembly manufacturing K enterprise is analyzed. The results show that the established model can enable the enterprise to more effectively control the carbon emissions and costs generated during development, as well as achieving improved service satisfaction at the workstation and shortening the distribution distance.
This article is structured as follows:
Section 2 provides related work on the shop floor material distribution path optimization model.
Section 3 presents the vehicle path optimization algorithms.
Section 4 presents a discrete assembly manufacturing company workshop, which is taken as an example to verify the correctness of the proposed method. Lastly, the paper ends with
Section 5, which concludes the research outcome with future work.
5. Conclusions
In the process of planning the distribution route for materials on the shop floor, if the carbon emission factor is taken into account, the optimal distribution route within a discrete manufacturing enterprise can not only reduce distribution costs, but also reduce carbon emissions, achieving a win–win situation in terms of economic benefits and environmental protection. As seen in
Table 6, the numbers of vehicles used, the distances traveled, the average loading rates, the carbon emissions, and each associated cost corresponding to the optimal solution paths for both cases are compared and analyzed. In terms of the number of vehicles used, the average loading rate and the penalty cost, the route without carbon emissions and the one with carbon emissions both require seven distribution vehicles, and the penalty cost is 0. The average vehicle load factor without carbon emissions is 82.29%, the total distance traveled is 26.5 km, and the transport cost is RMB 53; the transport cost is 53% and the carbon emission is 145.19 kg. The average vehicle load factor when considering carbon emissions is 86%, the total distance traveled is 24.8 km, the transportation cost is RMB 49.6 and the carbon emission is 108.04 kg. Therefore, the optimal distribution route considering carbon emissions entails a 7.5% lower total distribution cost, 6.4% lower total distance traveled and 25.6% lower total carbon emission than the optimal route without considering carbon emissions. It can be seen that the optimal distribution path considering carbon emissions has more obvious advantages than the optimal distribution path without consideration of carbon emissions. The optimal distribution path considering carbon emissions not only reduces the pollution emitted into the environment, but also helps to reduce the distribution costs of enterprises and improves their market competitiveness.
By comparing and analyzing the results, it is concluded that the path that considers carbon emissions is better. The distribution path planning process should consider not only transportation costs and penalty costs, but also carbon emissions, such that the planned distribution path can be more economical and environmentally friendly. The optimization results can be applied to the actual distribution process of workshop material distribution so as to achieve the objectives of reducing distribution costs, improving service satisfaction, reducing carbon emissions, improving the distribution efficiency of workshop logistics and making the distribution vehicle paths more economical and scientifically defendable.
In this paper, we have used the data obtained from research to solve the distribution path optimization model using MATLAB programming, taking the material distribution in the workshop stations of a discrete assembly manufacturing K company as an example. The optimal distribution path obtained for this company, taking into account carbon emissions, not only reduces distribution costs, but also controls carbon emissions, which has certain relevance to discrete manufacturing enterprises. In reality, there are many factors to be considered in the optimization of the distribution path of the shop floor logistics of a discrete manufacturing enterprise, and this paper makes use of a simplified model, so there are some shortcomings. For example, the distribution vehicles set in this paper are of the same model and have a uniform loading capacity, but in reality, due to the different demands related to distribution, many different models of distribution vehicles with different loading capacities will be used, resulting in changes in fixed costs and transportation costs, which can be increased in subsequent studies of multi-model distribution; at the same time, the driving speed of the vehicle set in this paper is fixed, and only one distribution vehicle is set on each road. In reality, the driving speeds of distribution vehicles are usually directly related to the road conditions, and will not remain unchanged, and the resulting fuel consumption will also vary due to changes in speed. The research process can be further extended by using not only genetic algorithms but also other algorithms, such as ant algorithms and bee colony algorithms. In addition, to compensate for the limitations of various heuristics, a combination of multiple heuristics can be used, for example, a genetic algorithm with 3-OPT local search as a variational operator and a road slope factor can be introduced into the carbon emission model to reduce carbon emissions. The Firefly algorithm can also used in combination with two local search and genetic operators to solve the VRP problem limited by vehicle volume, and fusing a genetic algorithm and fireworks algorithm can design an improved fireworks genetic algorithm, etc. Finally, to compare the effects, multiple heuristic algorithms can be used simultaneously to study the same problem, and then the optimal solution among them can be selected.