A Novel Collaborative Optimization Model for Job Shop Production–Delivery Considering Time Window and Carbon Emission

Abstract

The manufacturing industry is undergoing transformation and upgrading from traditional manufacturing to intelligent manufacturing, in which Internet of Things (IoT) technology plays a central role in promoting the development of intelligent manufacturing. In order to solve the problem that low production efficiency and machine utilization lead to serious pollution emissions in the workshop caused by untimely transmission of information in all links of the production and manufacturing process to whole supply chains, this study establishes an intelligent production scheduling and logistics delivery model with IoT technology to promote green and sustainable development of intelligent manufacturing. Firstly, an application framework of IoT technology in production–delivery supply chain systems was established to improve efficiency and achieve the integration of production and delivery. Secondly, an integrated production–delivery model was constructed, which takes into account time and low carbon constraints. Finally, a two-layer optimization algorithm was proposed to solve this integration problem. Through a case study, the results show this integration production–delivery model can reduce the cost of supply chains and improve customer satisfaction. Moreover, it proves that carbon emission cost is a major factor affecting total cost, and it could help enterprises to realize the profit and sustainable development of the environment. The production–delivery model could also support the last kilometer distribution problem and extension under E-commerce applications.

1. Introduction

With the rapid development of the new generation of information technology, the Internet of Things (IoT) industry has made great progress. Nowadays, IoT technology is penetrating into all fields, especially the manufacturing industry. Internet of Things technology is widely used in production and manufacturing. It combines mechanical machine and big data technology, and uses RFID (Radio Frequency Identification), data acquisition, and automation technology to quickly capture data for analysis, processing, and transmission, so as to digitize manufacturing resources, production process, on-site operation, material management, and quality control. Ultimately, all the machines, systems, processes, and personnel for data production and consumption can be connected more efficiently and flow more smoothly, and better operation can be achieved by improving productivity, flexibility, and quality [1].

The growth of E-commerce platforms has stimulated economic development. After receiving an order, the merchant starts to perform production and delivery tasks. The combination of production and delivery can help to increase the efficiency of supply chains and increase overall production value. In most cases, each customer’s order information is different, including delivery coordinates, expected delivery time, amount of products, categories of products, etc. In this case, facing orders from many customers with different needs, enterprises make overall schedule planning for the production and delivery of each order, so as to achieve the delivery requirements under customer satisfaction, and ultimately maximize the overall profits of enterprises. Therefore, with the support of IoT technology, and with the operation of E-commerce service platforms as a research background, how to solve production–delivery collaborative optimal problems are the research gap in this field.

Due to the changes in application scenarios, including the development of shared economies, the maturity of mobile payment technology, and changes in consumption concepts, traditional production scheduling optimization methods will be difficult to use to meet scheduling problems of enterprises and the delivery problem of customers at the same time. Traditional production and manufacturing mostly focus on pull-type production and push-type production [2]. In this production scenario, most scholars only aim at minimizing the completion time and cost, which can solve practical problems for enterprises. However, in this process, the problem of delivery is not taken into account. In fact, products processed with minimum completion time may need more storage costs, because these products cannot be delivered to customers in time. Therefore, it is of great significance for theory and practice to study the collaborative optimization method of production–delivery. Based on this consideration, this paper puts forward the research method of collaborative optimization of production scheduling–logistics delivery in order to make up for the research gaps in this field and provide methodological guidance for relevant enterprises and scholars.

In this study, a two-layer optimization model was designed for the integration of production and delivery, and the two-layer optimization algorithm was applied to solve the problem. The core factors considered in this study are as follows: How to quantify carbon emissions in the production–delivery process? What objective functions should be considered in this model? How to build a low-carbon sustainable collaborative production–delivery model? Moreover, whether this proposed model could provide practical guidance for E-commerce applications to reduce operation cost and reduce carbon emissions in the current economic market environment, and contribute to the improvement of E-commerce services. In addition, this study used a two-layer collaborative model to optimize the problem of production–delivery in the existing E-commerce platform, maximize customer satisfaction, and contribute to the last kilometer delivery problem of the business platform. This method can provide theoretical and technical guidance for E-commerce enterprises to reduce operating costs, reduce carbon emissions, and improve core competitiveness in the current economic market environment.

The study is organized as follows: Section 2 presents the relevant literature, including the practical application of IoT technology, collaborative research on production and delivery issues, and green manufacturing. Section 3 describes the architecture of the production–delivery model based on IoT technology and designs a two-layer collaborative optimization model. Section 4 gives a two-layer genetic algorithm. Section 5 shows a case study. Section 6 provides the conclusions.

2. Literature Review

With the development of IoT technology and coming information era of “intelligent perception” in manufacturing enterprises, the wide application of production automation and automatic control systems has become an increasingly important issue to improve production efficiency, product quality, and productivity [3,4]. Nowadays, IoT technology is changing the mode of industrial management and operation through combining automation technology, artificial intelligence, and cloud computing from traditional industry to intelligent manufacturing [5]. Zhang et al. [6] developed IoT technology enabled model, realized production planning, and control in intelligent manufacturing, and provided real-time production performance analysis and abnormal diagnosis of production data. Ding and Jiang’s [7] research used RFID technology to track production data, constructed judgment commands for production operations, and realized the configuration and analysis of intelligent workshop. Zhang et al. [8] established a production–delivery model of workshop based on industrial IoT to improve the efficiency of the system.

Taking the E-commerce platform [9] of Jingdong to Home as the research background, based on its logistics system, the integration of production and service from network orders to delivery to destination is achieved by Internet plus technology [10]. Hence, collaborative optimization of production scheduling and logistics delivery has practical significance for promoting supply chain integration. For example: Wang and Cheng [11] established an integrated model considering both production scheduling and product delivery, and developed a heuristics method to achieve minimum delivery time. Chang et al. [12] considered a production–delivery problem in which the objective is to find a collaborative production–delivery schedule to minimize the weighted sum of the total weighted job delivery time and the total delivery cost. Cheng et al. [13] proposed an improved ant colony algorithm with the aim to minimize the total cost for a production–delivery problem. Devapriya et al. [14] developed a heuristic method to obtain the production–delivery sequence. Cheng et al. [15] studied a production–delivery problem with parallel batching machines to minimize the service span. However, these researches usually ignore time window. Li et al. [16] proposed a two-stage hybrid method to solve the integrated production–delivery problem. Jia et al. [17] considered a production–delivery problem and used two hybrid meta-heuristic algorithms based on ant colony optimization to minimize the total weighted delivery time.

However, customers require delivery time window when signing contracts with the widespread usage of JIT (Just In Time) production mode and the increasing attention paid to the delivery time of products, not only for perishable goods with strict time requirements, but also strict time requirements for each kind of product. As timely delivery within the time window will maintain a good reputation and order resources for enterprises, early or delayed delivery will increase additional costs, including inventory cost and operation cost, which would bring losses such as customer order reduction. Therefore, by incorporating time windows into the production–delivery problem, the efficiency of each link in the supply chain and the overall efficiency are both improved. Liang et al. [18] developed an approach with Tabu search and a genetic algorithm for a production–delivery problem, in which time window restrictions are considered. For the production–delivery problem discussed in Reference [19], time window and delivery capacity are constrained to maximize profits. Ullrich and Christian [20] considered time windows for machine scheduling and vehicle routing with the objective to minimize total tardiness. Fu et al. [21] established a mathematical model subjected to delivery time windows, in which the objective is to minimize total setup cost and transportation cost. Kong et al. [22] studied a single-machine integration problem, in which transportation and JIT assembly with production deadlines are studied to maximum production efficiency. Noroozi et al. [23] aimed to maximize the total benefit by weighing the receipt of orders, delivery cost, and tardiness penalty for an integrated production–delivery scheduling problem with order acceptance and batch direct delivery. However, these studies rarely take the cost or other factors related to carbon emissions into account.

Under the trend of green manufacturing, many companies have begun to shift original mode to green and low-carbon production and management [24,25]. On the one hand, green manufacturing relieves environmental pressure [26]. On the other hand, it provides development space for enterprises to reduce costs and waste, and achieve sustainable development. Based on the requirements of cost and time, the minimization of environmental pollution has become one of the vital issues in production process. Lei et al. [27] provides a teaching–learning-based method to minimize total energy consumption and total tardiness for a hybrid flow shop scheduling problem. Zheng and Wang [28] proved the effectiveness of the collaborative multi-objectives fruit fly algorithm proposed for a manufacturing scheduling problem, where the objectives were to minimize the makespan and total carbon emissions. Jiang and Deng [29] built a mathematical model for a low-carbon job shop scheduling problem with the aim to minimize the sum of energy consumption cost and earliness/tardiness cost. Lei et al. [30] proposed a shuffled frog-leaping algorithm to minimize the workload balance and total energy consumption. Zhang et al. [31] constructed a multi-objectives model of a flexible job shop scheduling problem, and developed a two-layers scheduling method based on game theory to reduce makespan, total workload, and energy consumption. Carbon dioxide emission optimization was used in Reference [32] to study time-related vehicle routing and scheduling problems, and a dynamic programming algorithm was developed to determine the optimal vehicle schedule. At the same time, because of the wide use of IoT technology in manufacturing workshops creates large numbers of real-time data in such research, how to achieve real-time data-driven optimization so as to improve energy efficiency and production efficiency becomes a vital issue. Zhu [33] proposed a collaborative logistics delivery scheduling method based on IoT and big data to obtain large amounts of data on logistics delivery resources, so as to establish a logistics delivery roadmap. However, intelligent manufacturing based on the concept of green low-carbon manufacturing and IoT technology is seldom involved in these production–delivery studies.

With the development of supply chain, more and more researchers have studied the impact of supply chain integration on enterprise operation and sustainable development from practical methods and strategic perspectives. Sueyoshi et al. [34] provided the standard to measure the sustainability of enterprises through a new method. By comparing the effectiveness of integrated companies and independent companies, it proved the advantages of supply chain systems in operation and improving the sustainability of enterprises. Liu et al. [35] proposed a comprehensive sustainability analysis method, which integrates life cycle assessment and multi-criteria decision-making processes to make strategic decisions on green supply chain management and realize sustainable development. Macchion et al. [36] put forward the method of sustainable development in supply chain management from the strategic level. Kang et al. [37] were committed to the role of supply chain integration in improving the practice of sustainable development management and performance, providing research reference value for sustainable development and supply chain management research. These studies provide concept guidance and methodological inspiration of sustainable development for the modeling of production–delivery collaborative optimization in integrated supply chains.

Life cycle assessment is used to assess the impact of supply chains on sustainability. Moazzem et al. [38] used the life cycle assessment method to explore the impact of different types of textile supply chains on the environment. Song [39] developed a supply chain carbon footprint analysis method based on life cycle assessment to calculate product carbon footprints and parameters to solve greenhouse gas emissions. Croes and Vermeulen [40] designed a new sustainability measurement method of “bottom-up” and “product-specific LCA (Life Cycle Assessment)” to measure the environmental and social costs of products in an all-around way.

With the development of a low-carbon economy, increasing attention has been paid to the impact of carbon emission policies on supply chains. Pulselli et al. [41] constructed a carbon accounting framework to assess greenhouse gas emissions and provide information for urban policy and construction. Wang and Chen [42] established a three-level carbon accounting model between cities to quantify the emissions of the supply chain, in order to achieve effective carbon emission reduction and alleviate the pressure of global climate change. Hariga [43] assessed the impact of carbon emissions accounting from transportation and storage of refrigerated goods in a multi-stage supply chain consisting of warehouses, distribution centers, and retailers.

Through the above literature research, we found that a product carbon footprint based on life cycle assessment is a practical measurement index, which is actually a quantitative evaluation of carbon footprints. Through this evaluation, enterprises can understand the energy consumption, material consumption, and emissions of products and supply chains in each link and lay a foundation for enterprises to achieve environmental performance management, cost control, and low-carbon design. This provides abundant research materials for this research, which is based on the concept of low carbon, to design a sustainable development model of supply chain, and to achieve the goal of maximizing profits for enterprises.

In the production–delivery integration service process oriented to customer requirements under the existing IoT business model, the problem of global optimality caused by information communication barriers needs further improvement. For example, E-commerce platforms outsource the logistics delivery part to a third party. At this time, although production and delivery can meet customer requirements, it only achieves partial order optimization and cannot achieve global optimization. Thus, this study is devoted to proposing a two-layer production–delivery integration model to solve this kind of problem. With the goal of customer satisfaction and low carbon emissions, the production and distribution of all orders are integrated to ultimately achieve global optimization.

The following work was studied in this paper. Firstly, IoT technology was applied to the whole production–delivery process. Secondly, carbon emissions during production–delivery process and time windows were quantitatively expressed. Then, a two-layer production–delivery collaborative model was constructed to minimize the total cost. Finally, a genetic algorithm was used to solve this two-layer model, in which delivery time was taken as the connecting point. In addition, a production case was selected to show this two-layer model and two-layer optimization method.

3. Two-Layer Collaborative Optimization Model

3.1. IoT-Based Sustainable Architecture

Industry 4.0 is a technological transformation of an industry and a transformation of the industry. Intelligent manufacturing proposed by Industry 4.0 is an information manufacturing process facing the whole life cycle of products and realizing ubiquitous perception [44,45]. As one of the pillar technologies of Industry 4.0 technology, IoT technology can promote better operation of intelligent manufacturing by improving productivity, flexibility, and quality [46]. IoT technology is used to connect all links involved in the production–delivery process, including suppliers, production, products, storage, transportation, and etc. [1]. From raw material production to finished product, delivery is the process from production workshop to delivery vehicle, in which products are stored in an automated warehouse. Automated warehouse integrates the communication system, automatic control system, computer system, and other auxiliary equipment to form a complex automation system. Using the first-class integrated logistics concept and advanced control, bus, communication, and information technology, the warehouse operation is carried out through the coordinated action of the above intelligent equipment, effectively connecting production links and forming an automated logistics system in storage, thus forming a planned and arranged production chain. Aiming at building an intelligent workshop, end-to-end seamless operation is realized in all aspects of design, supply, manufacturing, and service, which prompts that intelligent manufacturing and intelligent logistics are in the process of integration. Hence, how to manage the process of manufacturing and logistics, coordinate production scheduling, and logistics delivery to achieve the integration of intelligent manufacturing and intelligent logistics becomes a major challenge. Based on this, an intelligent manufacturing system combining Industry 4.0 and IoT technology was designed. The schematic diagram of IoT architecture for a production–delivery model is shown in Figure 1.

As shown in Figure 1, the IoT architecture is divided into three layers: the data acquisition layer; production scheduling platform, and the application layer.

Data Acquisition Layer: Real-Time Monitoring with Perception Technology. The data acquisition layer is the first layer, where Internet interconnection of the whole workshop can be realized by IoT technology. Smart sensors are embedded in various machines to gain communication functions, and a wireless local area network (WLAN) is distributed throughout the workshop, connecting the machine and all the products, ultimately realizing real-time monitoring and tracking of the processing status of the machine and products in the whole process. All kinds of production data collected by RFID and other sensor technologies are fed back to the collection and processing ports on the network end through the communication network, thus the control of the production schedule and the implementation and adjustment of production planning can be implemented.

Production Scheduling Platform: Data and Resource Integration. Data processing and integration is the second layer. Supported by high-efficiency computing technologies such as big data and cloud computing, data collected by the network end are processed in real-time and high-speed on the production scheduling platform, including data mining, management, control, and storage intelligently. The material and product information resources are integrated into a large-scale intelligent network through data calculation and analysis, which provides an efficient and reliable technology support platform for production planning and control. The IoT combining connectivity with real-time analysis and cloud services can, thus, increase manufacturing output and efficiency and achieve more flexible manufacturing.

Application Layer: Production–Delivery Collaborative Optimization Model. The application and service of these data is the third layer. The specific delivery amounts and processing sequence of products on the machine are arranged and adjusted timely according to real-time state tracking of the whole process of products and the feedback data from the production scheduling platform. Aiming at multi-variety and small-batch products, this research resolves the integrated problem of workshop production scheduling and logistics delivery and proposes an IoT-based intelligent production–delivery dynamic scheme. It builds a continuously improved and updated scheduling database through the classification and storage of data at large data terminals, which can guide the real-time implementation of production schemes.

Therefore, after building the IoT architecture, we quantified the actual integrated problem of production scheduling and logistics delivery and established a novel two-layer model to reflect the application of IoT intelligent architecture.

3.2. Problem Description

In this study, workshop production scheduling and logistics delivery are integrated as a two-layer system for design and optimization. It was assumed that the sorting and loading time are ignored. The first layer was logistics delivery. It was assumed that vehicles would start from the delivery center and deliver products to required nodes, and then return to the delivery center. The delivery time of products fall within the time window of the due date, that is, to achieve customer satisfaction. By taking the customer’s prescribed due date as the constraint, the delivery route is arranged by minimizing the total cost under minimum carbon emissions in order to achieve green sustainable production and delivery. The second layer was workshop production scheduling. Under the condition of the optimal route in the delivery stage, the aim was to intelligently arrange the processing sequence and processing time of products on the machine with IoT technology in order to minimize the completion time of products. Figure 2 describes the schematic of the production–delivery problem.

Figure 2 shows the complete process from placing an order to delivering it to the customer. Firstly, various received orders are processed, including data collection, data processing, and practical application. Secondly, the application part includes the quantification and modeling of the production–delivery problem. In the production scheduling stage, all kinds of products are processed by the production line consisting of several machines, and the essence of the optimization of production scheduling scheme is to solve the matching problem between the products processing sequence and machine sequence. In the logistics delivery stage, the products are transported by several vehicles from the delivery center to customers within the prescribed due date.

In this study, we considered the constraints of the machine processing, vehicle path, carbon emissions, and other factors when designing the model. This section includes the parameters, 0–1 variables, and model.

3.2.1. Hypothesis

(1)

Each product is processed by multiple processes on machines.

(2)

The opportunity maintenance is carried out on the machine and the processing tasks are not interrupted.

(3)

There is a delivery center, multiple customer demand nodes (referred to later and will be abbreviated as nodes), and multiple vehicles.

(4)

Assume that node $i$ has the need of multiple kinds of product, orders are divided by categories, and products are distributed in batches. The set of nodes in the model is $\{0,1,2,\cdots ,n\}$, where node 0 represents the initial delivery center, the others are all customer demand nodes. $i,j$ denotes the number of nodes, $i,j\in \left\{0,1,2,\cdots ,n\right\},i\ne j$.

(5)

Assuming that the customer’s demand for products remains stable and known.

3.2.2. Parameters

The parameters and 0–1 variables related to the construction of the two-layer production–delivery model, such as machine, processing time, vehicle, time window, and costs, are shown in

Table 1. The basic parameters related to the production–delivery model.

$a$: early penalty cost per unit time	$M$: the number of machines
$b$: delay penalty cost per unit time	$p_{mq}$: power of machine $m$ operating on $q$ file
$C_{carbon\cdot s}$: carbon emissions in the production process	$P$: the number of processes
$C_{carbon\cdot d}$: carbon emissions in the delivery process	$Q_1$: loading weight of vehicles at full load
$C_m$: cost of machine maintenance	$Q_k$: weight of vehicle $k$
$C_{pe}$: penalty cost	$t_{\left[w\right]\left[p\right]\left[m\right]}$: processing time of the process $p$ of the product $w$ on the machine $m$
$C_r$: maintenance cost	$t_{\left[w\right]}$: completion time of product $w$
$C_{start}$: average start-up cost of a single machine	$t_{\left[w\right]}^{*}$: delivery time of product $w$
$C_{v\cdot s}$: average starting cost of a single vehicle	$v_k$: uniform speed of vehicle $k$
$C_{ud}$: transportation cost of unit distance	$W$: the number of products
$C_{ue}$: cost per unit of energy consumed by machines	$X$: actual weight of load
$C_{uf}$: price of unit fuel	$\alpha$: total number of machine
$d_{ij}$: the distance from node $i$ to node $j$	$\beta$: number of vehicles
$d_w^l$: lower limit of time window for product $w$	$\rho$: carbon emissions of unit energy consumption
$d_w^u$: upper limit of time window for product $w$	$\sigma$: carbon emission factor released per unit fuel consumption
$F_0$: fuel consumption per unit distance of vehicle at no load	$\delta$: accelerated penalty coefficient for early delivery
$F_1$: fuel consumption per unit distance of vehicle at full load	$\xi$: accelerated penalty coefficient for late delivery
$F_{us}$: fuel consumption per unit distance

.

3.3. Green Collaborative Optimization Model

A green collaborative optimization model of production–delivery is proposed in order to reduce carbon emissions, the production cost, and delivery cost, and ensure the minimum unsatisfied rate of customer’s due date. This model considers carbon emissions and penalty cost that cannot meet the customer’s prescribed due date as constraints to minimize the total production–delivery cost, so as to realize green and economic production–delivery, which is of great significance for enterprises to achieve green sustainable development.

The objective function is to minimize the total cost of green collaborative production–delivery problem, which is divided into three parts: cost related to carbon emissions, cost related to customer satisfaction with delivery time of product, and cost related to production–delivery operation.

3.3.1. Cost Related to Carbon Emissions

In the production stage, carbon released because of products processing is measured by the energy consumption under processing state. Machines consumes a lot of energy when they are in the processing state, where one part of energy is used to support the processing and operating by doing work; the other part is converted and emitted in the form of carbon dioxide and other pollutants. In the delivery stage, vehicle driving is accompanied by continuous consumption of fuel, and carbon released during the process is related to driving distance and load of vehicle. The fuel consumption per unit distance is related to the load of vehicle. Therefore, the cost related to carbon emissions are composed of two parts: cost of carbon emissions in production process and delivery process.

Carbon emissions from workshop production are measured by the amount of work done by the machine at a certain processing power. Assuming that the stable processing power of the machine is p_mq, at the same time, there is a fixed conversion relationship between the carbon emissions and the energy consumption produced by the work of the machine. The cost related to carbon emissions in the workshop production process are denoted as:

$$C_{carbon\cdot s}=P_{mq}\left({\displaystyle {\displaystyle \sum }_{w\in W}}{\displaystyle {\displaystyle \sum }_{p\in P}}{\displaystyle {\displaystyle \sum }_{m\in M}}{t}_{\left[w\right]\left[p\right]\left[m\right]}\right)\times C_{ue}\times \rho$$

(1)

Cost related to carbon emissions in the delivery process are denoted as:

$$C_{carbon\cdot d}=C_{uf}\left({\displaystyle {\displaystyle \sum }_{k\in K}}{\displaystyle {\displaystyle \sum }_{i\in N}}{\displaystyle {\displaystyle \sum }_{j\in N}}{y}_{ij}^k\times F_{us}\times d_{ij}\right)\times \sigma$$

(2)

where, $C_{uf}$ represents price of unit fuel,$F_{us}$ represents fuel consumption per unit distance,$\sigma$ represents carbon emission factor released per unit fuel consumption. By quantifying the cost of fuel consumption in the delivery process and using the conversion factor of fuel consumption and carbon emissions, we get the cost related to carbon emissions in the delivery process.

The fuel consumption per unit distance varies according to the actual vehicle load, so there is:

$$C_{carbon\cdot d}=C_{uf}\left\{{\displaystyle {\displaystyle \sum }_{k\in K}}{\displaystyle {\displaystyle \sum }_{i\in N}}{\displaystyle {\displaystyle \sum }_{j\in N}}{y}_{ij}^k\times \left(F_0+\frac{F_1-F_0}{Q_1}X\right)\times d_{ij}\right\}\times \sigma$$

(3)

The fuel consumption per unit distance is related to the load of the vehicle, so Formula (4) expresses the calculation of the fuel consumption per unit distance with the dynamic change of the load.

Some scholars [47] have collected relevant statistical data for regression analysis and obtained that the fuel consumption per unit distance $F_{us}$ can be expressed as a linear function depending on the weight of load $X$. Fuel consumption per unit distance is denoted as:

$$F_{us}=F_0+\frac{F_1-F_0}{Q_1}X$$

(4)

Proving process:

Fuel consumption per unit distance at no load $F_0=a\cdot Q_k+c$

Fuel consumption per unit distance at full load $F_1=a\cdot \left(Q_k+Q_1\right)+c$

After a series of formula derivations, the numerical results are as follows:

$$a=\frac{F_1-F_0}{Q_1}$$

(5)

$$c=F_0-\frac{F_1{Q}_k-F_0{Q}_k}{Q_1}$$

(6)

Therefore, fuel consumption per unit distance is:

$$F_{us}=F_0+\frac{F_1-F_0}{Q_1}X$$

(7)

Subject to:

$$t_{\left[w\right]}^{*}=t_{\left[w\right]}+{\displaystyle {\displaystyle \sum }_{k\in K}}{\displaystyle {\displaystyle \sum }_{i\in N}}{\displaystyle {\displaystyle \sum }_{j\in N}}\frac{d_{ij}}{v_k}\times y_{ij}^k$$

(8)

$$t_{\left[w\right]}={\displaystyle {\displaystyle \sum }_{p\in P}}{\displaystyle {\displaystyle \sum }_{m\in M}}{t}_{\left[w\right]\left[p\right]\left[m\right]}$$

(9)

$$q_m^{\prime }={\displaystyle {\displaystyle \sum }_{w\in W}}{\displaystyle {\displaystyle \sum }_{p\in P}}{\displaystyle {\displaystyle \sum }_{m\in M}}{t}_{\left[w\right]\left[p\right]\left[m\right]}$$

(10)

$${\displaystyle {\displaystyle \sum }_{i\in N}}{y}_i^k{q}_i\le Q_1, k=1,2,\dots K$$

(11)

$$y_{ij}^k=\{\begin{array}{l}1, from node \begin{array}{c}i\end{array} to \begin{array}{c}node j \end{array}is responsible by vehicle k\\ 0, other\end{array}$$

(12)

Equations (8)–(12) represents the constraints of the objective model. Equation (8) indicates that the delivery time of product is equal to the sum of processing time in the production workshop and transportation time from the delivery center to each node. Equation (9) represents the calculation of processing time. Equation (10) represents the machine load. Equation (11) indicates that the sum of the loads sent from the delivery center by vehicle $k$ to the demand node in turn shall not exceed the full load of the vehicle. Equation (12) indicates that $y_{ij}^k$ is a 0–1 decision variable.

3.3.2. Cost Related to Customer Satisfaction

It will lead to a loss of potential customers and even funds when the delivery time cannot meet the due date requirements. Therefore, this study introduces the concept of delivery time windows and penalty constraints to optimize the collaborative model of production–delivery.

Assume that the time window specified by product $w$ is $\left[d_w^o,d_w^u\right]$, the equation of penalty cost due to early or delay delivery is denoted as

$$C_{pe}=\{\begin{array}{cc}\left[\left(d_w^e-t_{\left[w\right]}\right)-\frac{d_{ij}^k}{v_k}\right]\times \left(a+\xi \right),& t_{\left[w\right]}+\frac{d_{ij}^k}{v_k}\in \left(0,d_w^e\right)\hfill \\ \hfill \left[\left(d_w^o-t_{\left[w\right]}\right)-\frac{d_{ij}^k}{v_k}\right]\times a,& t_{\left[w\right]}+\frac{d_{ij}^k}{v_k}\in \left(d_w^e,d_w^o\right)\hfill \\ \hfill 0,& t_{\left[w\right]}+\frac{d_{ij}^k}{v_k}\in \left(d_w^o,d_w^u\right)\hfill \\ \hfill \left[\frac{d_{ij}^k}{v_k}-\left(d_w^u-t_{\left[w\right]}\right)\right]\times b,& t_{\left[w\right]}+\frac{d_{ij}^k}{v_k}\in \left(d_w^u,d_w^l\right)\hfill \\ \hfill \left[\frac{d_{ij}^k}{v_k}-\left(d_w^l-t_{\left[w\right]}\right)\right]\times \left(b+\delta \right),& t_{\left[w\right]}+\frac{d_{ij}^k}{v_k}\in \left(d_w^l,\infty \right)\hfill \end{array}$$

(13)

There are three delivery cases: if the delivery time of product $w$ is within $\left[d_w^o,d_w^u\right]$, it will satisfy the customer’s requirements without penalty; if the delivery time is within $\left[0,d_w^o\right]$, it means that the delivery is completed in advance and company will bear the cost related to inventory and cargo storage; if the delivery time is within $\left[d_w^u,\infty \right]$, it means that the delivery is delayed and the company will be liable for at a loss of breaking the contract. Meanwhile, if the delivery time is too early or too late from the appointed time, there will be an accelerated punishment mechanism, that is, the punishment intensity will be increased. The critical values of the general punishment and accelerated punishment mechanism are $d_w^e,d_w^l$, respectively. In addition, the company may face the consequence of liquidated damage and loss of order resources. Therefore, it is assumed that the value of $b$ is greater than that of $a$ so as to reflect the actual situation. Similarly, $\xi$ is greater than $\delta$.

3.3.3. Cost Related to Production–Delivery Operation

The operation cost is spent on ensuring smooth running of production–delivery workshops. In the production stage, the startup cost of machines should be considered, which is equal to the product of the average startup cost of a single machine and total number of machines. In the delivery stage, the vehicle startup cost is equal to the product of the average startup cost of a single vehicle and total number of vehicles. In addition, transportation costs during delivery and maintenance costs of machines should also be considered.

$$C_o=C_{start}\alpha +C_{v\cdot s}\beta +C_{ud}{d}_{ij}+C_r$$

(14)

Therefore, the total cost of the green collaborative optimization model of production–delivery can be shown as:

$$C=C_{carbon\cdot s}+C_{carbon\cdot d}+C_{pe}+C_{start}\alpha +C_{v\cdot s}\beta +C_{ud}{\displaystyle {\displaystyle \sum }_{i\in N}}{\displaystyle {\displaystyle \sum }_{j\in N}}{d}_{ij}+{\displaystyle {\displaystyle \sum }_{k\in K}}{C}_r^k$$

(15)

4. Solution

In order to solve the proposed green collaborative optimization model of production–delivery, this study proposes a two-layer optimization algorithm, which decomposes the model into two associated layers. The first layer is to solve the vehicle delivery problem by developing a genetic algorithm. The second layer is to solve the workshop production scheduling problem by genetic algorithm. With the objective of minimizing the total completion time, a scheduling Gantt chart is generated. That is, the processing sequence and processing time of each kind of product are obtained. The optimal production sequence is generated by taking the minimal total production–delivery cost as the decision objective.

A genetic algorithm is used in this two-layer production–delivery method. The steps of the two-layer genetic algorithm designed in this study are shown in Figure 3.

4.1. Delivery Optimization Layer

A genetic algorithm is an evolutionary algorithm based on the genetic evolution of a natural population. It can be solved by simulating the evolutionary process of genetic selection and natural elimination. The genetic algorithm retains the best solution of the present generation and takes crossover and mutation as random operators. As the evolution algebra tends to be infinite, the genetic algorithm will find the global optimal solution. In the search process, it is not easy to fall into the local optimum and has significant advantages in solving performance and efficiency. The feasible solutions of the problem are regarded as chromosomes, and the chromosomes are coded into symbolic strings. Then the chromosomes are inherited, crossed, and mutated to carry out the genetic evolution of the population. According to the evolutionary rules of survival of the fittest, better groups can be obtained. The brief steps of this genetic algorithm are given as follows:

Step 1 Algorithmic encoding and decoding

0 represents delivery center, and 1–8 represents 8 nodes. 0, 1, 5, 7, 0, 4, 2, 8, 0, 3, 6, and 0 indicate that the vehicle completed three delivery activities from the delivery center. The first time it starts from delivery center it goes through 1, 5, and 7 nodes in turn, then the vehicle returns to delivery center and continues the second delivery, through 4, 2, and 8 nodes in turn, then returns to delivery center for the second time and continues the third delivery, through 3 and 6 nodes in turn, and finally returns to the delivery center. The schematic diagram of chromosome coding and decoding in the delivery stage is described in Figure 4.

Step 2 Constraint handling

For the vehicle routing problem with time windows, the time window constraint is transformed into penalty cost to ensure the search of genetic algorithms to continue. As described in Formula (15), the time window constraint is used as a penalty cost function to solve the total cost.

Step 3 Fitness conversion

The fitness function value reflects the probability of individuals performing genetic operation in the process of inheritance. This study chooses the roulette wheel selection method. The probability of the individual being selected is proportional to its fitness function value, that is, the higher the fitness function value, the greater the probability of individuals being selected; on the contrary, the lower the fitness function value, the smaller the probability of individuals being selected. This can make the genetic algorithm evolve in a better direction, which is very helpful to improve the quality of the solution [48]. In this genetic algorithm, the fitness function of chromosomes is required to be non-negative, because the objective function of the VRP (Vehicle Routing Problem) is positive, and the objective function of this study is to minimize the total cost, so reciprocal of the objective function can be directly taken as the fitness function

$$f_i=\frac{1}{C_{carbon\cdot s}+C_{carbon\cdot d}+C_{pe}+C_{start}\alpha +C_{v\cdot s}\beta +C_{ud}{{\displaystyle \sum }}_{i\in N}{{\displaystyle \sum }}_{j\in N}{d}_{ij}+{{\displaystyle \sum }}_{k\in K}{C}_r^k}$$

(16)

Step 4 Crossover operator and mutation operator

Two-point crossover method was used to generate new chromosomes to find the global optimal solution, which greatly improves the convergence speed [49]. The specific process is given as follows: firstly, two crossing gene points are randomly identified; then the corresponding gene fragments between two crossing points are hybridized; finally, the repetitive gene fragments are eliminated to produce new progeny chromosomes, which represents a new logistics delivery scheme. The genetic crossover is described in Figure 5.

The crossover probability is

$$p_c=\{\begin{array}{r}{p}_{c1}-\frac{\left(p_{c1}-p_{c2}\right)\left(f^{\prime }-f_{avg}\right)}{f_{max}-f_{avg}}, f^{\prime }\ge f_{avg}\\ p_{c1}, f^{\prime }<f_{avg}\end{array}$$

(17)

Mutation operation is an assistant method to generate new individuals, which determines the local search ability of the genetic algorithm. On the one hand, it can improve the local search ability of the genetic algorithm; on the other hand, it can maintain the diversity of the population and prevent premature phenomenon. The genetic mutation is described in Figure 6.

The mutation probability $p_m$ is

$$p_m=\{\begin{array}{r}{p}_{m1}-\frac{\left(p_{m1}-p_{m2}\right)\left(f_{max}-f\right)}{f_{max}-f_{avg}}, f\ge f_{avg}\\ p_{m1}, f<f_{avg}\end{array}$$

(18)

Step 5 Termination

End of calculation. Set the maximum number of iterations and initial parameters of the population evolution. When the iterations of the population evolution reach the maximum number or the optimal solution is found, the calculation will stop and the optimal delivery scheme will be output.

4.2. Production Optimization Layer

Similarly, the genetic algorithm is used to solve the model of the production layer. Through the basic steps of genetic evolution, the optimal production sequence can be obtained as below.

Step 1 Chromosome coding and decoding

The first line of the coding table in Figure 4 shows that three products need to be processed. Number 3 for the first time shows the first process of product 3, and number 3 for the second time shows the second process of product 3. The coding sequence represents the first process of product 3, the first process of product 2, the first process of product 1, the second process of product 3, the second process of product 2, the second process of product 1, etc.

Step 2 Initial population generating

Through the above encoding and decoding results, an initial scheduling scheme is generated randomly in Figure 7, which indicates that the first process of product 3 is processed on machine 1 and the first process of product 2 is processed on machine 2, etc. Initial scheduling scheme diagram shows the processing sequence and processing time allocated by each process of the product on each machine in the initial state.

Step 3 Fitness function setting

This study aims to achieve objective function minimized, thus the reciprocal of objective function is taken as the fitness function.

$$f_i=\frac{1}{{{\displaystyle \sum }}_{w\in W}{{\displaystyle \sum }}_{p\in P}{{\displaystyle \sum }}_{m\in M}{t}_{\left[w\right]\left[p\right]\left[m\right]}}$$

(19)

Step 4 Selection of evolutionary population

To calculate the survival probability of the next generation population based on selection probability, the proportional fitness assignment method is selected to determine the probability of descendants with respect to the probability of fitness value for each individual.

First, according to the individual fitness function, the fitness value of each individual is calculated, expressed as $f_i$, and the fitness function value of all individuals are summed as ${{\displaystyle \sum }}^{}{f}_i$. Then, the ratio of the fitness value of a single individual to the sum of the fitness values of all individuals is calculated to express the probability of its selection, which is $p_i=\frac{f_i}{{{\displaystyle \sum }}^{}{f}_i}$.

Step 5 Crossover operation

By using the method of two-point crossover, chromosomes randomly generate crossover regions, perform crossover operations, and generate new individuals. The process diagram of crossover operation is described in Figure 8.

The crossover probability is used to determine whether the crossover between two individuals is necessary. The adaptive crossover probability calculation method is adopted. Hence, the crossover probability is as follows:

$$p_c=\{\begin{array}{r}{p}_{c1}-\frac{\left(p_{c1}-p_{c2}\right)\left(f^{\prime }-f_{avg}\right)}{f_{max}-f_{avg}}, f^{\prime }>f_{avg}\\ p_{c1}, f^{\prime }<f_{avg}\end{array}$$

(20)

where $p_c$ represents crossover probability, $p_{c1}$ and $p_{c2}$ are random variables within (0,1) to control the cross population. $f^{\prime }$ represents individual fitness value of current population, $f_{max}$ represents maximum fitness value of individual function in the current population, and $f_{avg}$ represents average fitness value of individuals in current population. According to crossover probability, chromosome crossover is determined.

Step 6 Mutation operation

The mutation operation chosen in this study is 2-exchange mutation, which is to randomly select two non-zero elements of a chromosome and exchange their positions to generate new chromosomes. The process of crossover operation is described in Figure 9.

The probability of mutation operation means that a small number of individuals are allowed to perform mutation in order to avoid local optimal solutions. The mutation probability is denoted as:

$$p_m=\{\begin{array}{r}{p}_{m1}-\frac{\left(p_{m1}-p_{m2}\right)\left(f_{max}-f\right)}{f_{max}-f_{avg}}, f>f_{avg}\\ p_{m1}, f<f_{avg}\end{array}$$

(21)

where $p_{m1}$ and $p_{m2}$ are random variable within (0,1) to control mutant population. $f$ represents the individual fitness value of the current population, $f_{max}$ represents the maximum fitness value of the individual function in the current population, and $f_{avg}$ represents the average fitness value of the individual in the current population. According to crossover probability, the chromosome is determined for the mutation operation.

The optimization objective of the two-layer model is to minimize the total production–delivery cost, in which the penalty cost is variable. All kinds of products to be processed will be distributed to different nodes according to various order requirements. The sum of processing completion time of each product and delivery time of product constitutes the delivery time of a specific demand node. According to whether the delivery time of a product falls into the limited time window of this demand node for a product, then decide the production sequence.

The delivery time of a product is presented as:

$$t_{\left[w\right]}^{*}=t_{\left[w\right]}+{\displaystyle {\displaystyle \sum }_{k\in K}}{\displaystyle {\displaystyle \sum }_{i\in N}}{\displaystyle {\displaystyle \sum }_{j\in N}}\frac{d_{ij}}{v_k}\times y_{ij}^k$$

(22)

where $y_{ij}^k$ is a 0–1 decision variable, indicating that the transportation from node $i$ to node $j$ is responsible by vehicle $k$.

In the production stage, different kinds of product correspond to at most $w$ different processing completion times. However, due to different completion time of the products and different requirements of the customers, the arrangement of the production scheduling scheme on the basis of optimized delivery route could support the achievement of the production–delivery collaborative optimization.

5. Case Study

5.1. Numerical Data

A case study for collaborative production–delivery problem is studied. The enterprise’s historical database was analyzed and collated, and it was assumed that the product processing time, customer coordinate points, customer demand for products, expected delivery time window, and corresponding penalty coefficient, and some given constants like unit price, carbon emission conversion coefficient, are known. There are eight machines in the workshop responsible for production tasks of 10 kinds of products.

Table 2. The basic processing time of products.

Q1	Q2	Q3	Q4	Q5	Q6	Q7	Q8	Q9	Q10	Q11	Q12	Q13	Q14	Q15	Q16	Q17
1	53.2	M1	24.03	M2	8.67	M6	61	M7	48.4	M3	98.56	M4	7.96	M8	10.17	M5
2	26.98	M4	82.66	M3	66.08	M5	23.55	M8	9.65	M2	72.85	M1	66.58	M6	69.1	M7
3	25.59	M3	31.16	M4	34.54	M6	11.86	M1	60.93	M7	62.15	M1	24.09	M8	40.78	M5
4	72.19	M7	14.06	M3	18.13	M8	38.41	M5	4.24	M6	20.55	M1	36.07	M2	18.13	M4
5	73.46	M6	74.83	M3	18.52	M2	4.81	M7	6.25	M5	7.94	M8	26.98	M1	37.9	M4
6	70.06	M7	87.31	M4	56.71	M8	39.87	M6	93.21	M3	3.16	M5	80.46	M1	55.63	M2
7	56.72	M3	84.45	M8	60.82	M4	84.76	M2	62.39	M5	97.04	M6	77.07	M7	18.51	M1
8	79.99	M3	68.99	M1	7	M4	9	M2	65.39	M5	62.95	M8	8.22	M7	52.46	M6
9	38.25	M7	5.62	M8	24.02	M6	8.75	M5	26.51	M3	19.83	M2	16.38	M4	74.31	M1
10	54.65	M4	81.33	M5	43.19	M2	40.76	M3	17.7	M6	30.86	M7	49.81	M1	49.3	M8

Note: Q1: Product, Q2: procedure 1, Q3: Machine, Q4: procedure2, Q5: Machine, Q6: procedure3, Q7: Machine, Q8: procedure4, Q9: Machine, Q10: procedure5, Q11: Machine, Q12: procedure6, Q13: Machine, Q14: procedure7, Q15: Machine, Q16: procedure8, Q17: Machine.

shows the processing time of each product on different machines. The parameters related to cost are given in

Table 3. The basic parameter values for cost calculation.

${\mathit{C}}_{\mathit{u}\mathit{d}}$	${\mathit{C}}_{\mathit{u}\mathit{e}}$(Yuan/J)	${\mathit{C}}_{\mathit{u}\mathit{f}}$(Yuan/L)	${\mathit{C}}_{\mathit{r}}$	${\mathit{C}}_{\mathit{s}\mathit{t}\mathit{a}\mathit{r}\mathit{t}}$(Yuan/Machine)
1	$0.22\times {10}^{-6}$	6.13	200	50
${\mathit{C}}_{\mathit{v}\cdot \mathit{s}}$(yuan/vehicle)	${\mathit{F}}_0$(L/100 km)	${\mathit{F}}_1$(L/100 km)	${\mathit{P}}_{\mathit{m}\mathit{q}}$(kw)	${\mathit{Q}}_1$
50	18	25	4.5	25
$\mathit{\alpha }$	$\mathit{\sigma }$	$\mathit{\beta }$	$\mathit{\rho }$
8	3.179	10	0.928

.

The given constants related to total cost solution, for example, transportation cost of unit distance, cost per unit of energy consumed by machines, price of unit fuel, etc., are given in Table 3.

These products need to be processed and delivered to 20 different customers within the time specified by the customer. There are 20 delivery nodes, number 1 represents the delivery center, and numbers 2–21 are the twenty nodes in turn. In the city map of Chongqing, 21 nodes including the delivery center are selected. The distribution of each node is shown in the Figure 10.

The uniform speed of the vehicles was 50 km/h; the maximum driving distance of a single vehicle was 300 km. The coordinate position of each node, demand of each kind of product, specified time window, and early/delay penalty coefficient per unit time is shown in

Table 4. Basic data of each node.

Node	D2	D3	D4	D5	D6
Coordinate position	(81.47, 90.58)	(12.70, 91.34)	(63.24, 9.75)	(27.85, 54.69)	(95.75, 96.49)
Demand	4.38	3.81	7.65	7.95	1.86
Time window	(9:00, 12:00)	(9:00, 12:00)	(9:00, 12:00)	(9:00, 12:00)	(9:00, 12:00)
Early/delay penalty coefficient	(3.51/16.22)	(8.30/31.12)	(5.85/52.85)	(5.49/16.56)	(9.17/26.30)
Node	D7	D8	D9	D10	D11
Coordinate position	(15.76, 97.06)	(95.72, 48.54)	(80.03, 14.19)	(42.18, 91.57)	(79.22, 95.95)
Demand	4.89	4.45	6.46	7.09	7.54
Time window	(12:00, 15:00)	(12:00, 15:00)	(12:00, 15:00)	(12:00, 15:00)	(12:00, 15:00)
Early/delay penalty coefficient	(2.85/45.05)	(7.57/22.90)	(7.53/15.24)	(3.80/53.83)	(5.67/25.99)
Node	D12	D13	D14	D15	D16
Coordinate position	(65.57, 70.60)	(43.57, 3.18)	(84.91, 27.69)	(93.40, 4.62)	(67.87, 9.71)
Demand	2.76	6.79	6.55	1.62	1.19
Time window	(15:00, 18:00)	(15:00, 18:00)	(15:00, 18:00)	(15:00, 18:00)	(15:00, 18:00)
Early/delay penalty coefficient	(7.59/43.14)	(5.40/18.18)	(5.30/26.38)	(7.79/14.55)	(9.34/13.61)
Node	D17	D18	D19	D20	D21
Coordinate position	(75.77, 82.35)	(74.31, 69.48)	(39.22, 31.71)	(65.55, 95.02)	(17.12, 3.44)
Demand	4.98	9.59	3.40	5.85	2.23
Time window	(18:00, 20:00)	(18:00, 20:00)	(18:00, 20:00)	(18:00, 20:00)	(18:00, 20:00)
Early/delay penalty coefficient	(12.90/14.50)	(5.68/35.10)	(4.69/40.18)	(1.19/18.39)	(3.37/12.33)

.

5.2. Result Discussion

5.2.1. Optimal Vehicle Routing Path

Based on data from a known case, it was assumed that each kind of product will be delivered to the 20 nodes, and the optimal route was determined on the basis of minimizing the total cost. According to the coordinates of the nodes,

Table 5. Geographical distance between any two nodes.

	1	2	3	4	5	6	7	8	9	10	11	12	13	14	15	16	17	18	19	20	21
1	0.00	17.42	22.68	18.56	13.45	14.45	37.63	46.48	39.49	41.64	29.40	43.16	40.21	33.59	28.44	25.26	45.80	40.39	45.38	34.80	42.56
2	17.42	0.00	6.18	10.07	5.58	8.89	20.22	29.10	22.17	28.47	12.14	26.07	22.89	18.62	12.71	10.73	29.85	24.26	28.59	18.53	26.28
3	22.68	6.18	0.00	9.14	9.37	14.87	15.54	24.03	18.30	28.92	7.00	20.48	17.69	12.48	6.54	12.45	23.72	18.15	22.75	16.94	24.15
4	18.56	10.07	9.14	0.00	7.03	17.58	23.80	31.53	27.03	37.61	15.47	27.18	25.27	15.68	11.75	20.27	28.08	23.02	28.67	26.06	33.29
5	13.45	5.58	9.37	7.03	0.00	10.80	24.76	33.39	27.15	33.92	16.30	29.81	27.06	20.31	14.99	16.16	32.39	26.95	31.94	24.05	31.77
6	14.45	8.89	14.87	17.58	10.80	0.00	26.45	35.44	27.28	27.20	19.55	33.28	29.63	27.35	21.38	11.37	38.04	32.45	36.15	21.26	28.81
7	37.63	20.22	15.54	23.80	24.76	26.45	0.00	9.01	4.18	23.06	8.54	7.73	3.58	13.54	12.67	16.77	15.23	11.13	11.16	10.47	12.94
8	46.48	29.10	24.03	31.53	33.39	35.44	9.01	0.00	9.15	27.39	17.11	5.33	6.35	18.14	19.82	25.40	12.43	11.89	7.13	17.35	15.60
9	39.49	22.17	18.30	27.03	27.15	27.28	4.18	9.15	0.00	19.58	11.56	10.21	6.45	17.72	16.43	16.62	18.35	14.90	13.65	8.22	8.86
10	41.64	28.47	28.92	37.61	33.92	27.20	23.06	27.39	19.58	0.00	25.48	29.75	26.00	35.06	31.27	17.76	37.93	34.18	33.13	13.35	11.86
11	29.40	12.14	7.00	15.47	16.30	19.55	8.54	17.11	11.56	25.48	0.00	13.96	10.81	10.21	5.83	12.53	18.65	13.13	16.63	12.32	18.47
12	43.16	26.07	20.48	27.18	29.81	33.28	7.73	5.33	10.21	29.75	13.96	0.00	4.16	12.99	15.44	24.31	8.28	6.58	3.48	17.98	18.48
13	40.21	22.89	17.69	25.27	27.06	29.63	3.58	6.35	6.45	26.00	10.81	4.16	0.00	12.88	13.63	20.28	11.96	8.59	7.61	13.88	15.16
14	33.59	18.62	12.48	15.68	20.31	27.35	13.54	18.14	17.72	35.06	10.21	12.99	12.88	0.00	5.98	22.53	12.40	7.54	13.54	21.71	26.29
15	28.44	12.71	6.54	11.75	14.99	21.38	12.67	19.82	16.43	31.27	5.83	15.44	13.63	5.98	0.00	17.08	17.43	11.96	17.14	18.15	24.06
16	25.26	10.73	12.45	20.27	16.16	11.37	16.77	25.40	16.62	17.76	12.53	24.31	20.28	22.53	17.08	0.00	30.61	25.32	27.57	9.91	17.45
17	45.80	29.85	23.72	28.08	32.39	38.04	15.23	12.43	18.35	37.93	18.65	8.28	11.96	12.40	17.43	30.61	0.00	5.60	5.31	25.70	26.76
18	40.39	24.26	18.15	23.02	26.95	32.45	11.13	11.89	14.90	34.18	13.13	6.58	8.59	7.54	11.96	25.32	5.60	0.00	6.12	21.36	23.71
19	45.38	28.59	22.75	28.67	31.94	36.15	11.16	7.13	13.65	33.13	16.63	3.48	7.61	13.54	17.14	27.57	5.31	6.12	0.00	21.46	21.71
20	34.80	18.53	16.94	26.06	24.05	21.26	10.47	17.35	8.22	13.35	12.32	17.98	13.88	21.71	18.15	9.91	25.70	21.36	21.46	0.00	7.80
21	42.56	26.28	24.15	33.29	31.77	28.81	12.94	15.60	8.86	11.86	18.47	18.48	15.16	26.29	24.06	17.45	26.76	23.71	21.71	7.80	0.00

shows the distance between any two nodes.

Assume the maximum number of iterations is 1000, the population size is 200, the probability of crossover operation is 0.8, and the probability of mutation operation is 0.06. Based on this, the optimal delivery route and driven distance for 10 kinds of product are shown in

Table 6. Optimal delivery route for 10 kinds of products.

Products	Optimal Delivery Route	Driven Distance
1	1-12-18-1-14-8-9-15-16-1-5-7-3-10-20-1-6-2-11-17-1-4-13-19-21-1	556.2342
2	1-7-3-14-15-1-5-10-2-11-17-1-20-6-8-19-1-12-18-1-13-4-9-16-21-1	655.7591
3	1-3-7-19-13-1-5-12-1-4-16-9-15-21-1-10-2-11-20-17-1-18-8-6-14-1	636.8254
4	1-20-2-8-14-1-11-6-12-17-1-3-5-9-15-1-7-10-18-19-1-4-16-13-21-1	637.7306
5	1-4-16-9-15-21-1-5-12-18-1-3-7-20-11-17-1-2-6-10-1-14-13-8-19-1	554.6523
6	1-4-8-14-9-1-20-11-6-18-1-7-3-5-19-21-1-13-15-16-1-10-2-12-17-1	670.1354
7	1-20-6-11-21-1-5-12-18-17-1-7-3-14-15-1-9-4-16-13-1-10-2-8-19-1	636.9411
8	1-5-7-3-19-21-1-4-8-17-1-9-15-16-1-20-2-11-12-18-1-10-6-14-13-1	623.0138
9	1-7-14-19-1-2-12-18-1-3-10-8-1-4-9-16-21-1-5-20-6-11-17-1-15-13-1	673.2936
10	1-10-11-18-12-17-1-20-2-15-1-5-3-7-13-21-1-6-8-14-1-4-9-16-19-1	571.8062

.

Through the optimal delivery route, the product demand of each node and the distance between any two nodes, the delivery time of 10 kinds of products to each node is obtained in

Table 7. Delivery time for 10 kinds of products to each node.

Node	D2					D3					D4					D5
Product	1	2	3	4	5	1	2	3	4	5	1	2	3	4	5	1	2	3	4	5
Delivery time	8.43	5.03	9.11	1.81	8.66	6.96	2.31	1.59	6.76	6.34	10.35	12.50	5.33	11.65	1.70	5.68	3.78	3.55	6.95	4.71
Product	6	7	8	9	10	6	7	8	9	10	6	7	8	9	10	6	7	8	9	10
Delivery time	13.16	12.54	9.79	4.44	4.88	7.88	7.14	2.55	5.86	6.52	1.84	9.63	4.60	8.40	10.40	8.07	4.94	1.74	10.80	6.33
Node	D6					D7					D8					D9
Product	1	2	3	4	5	1	2	3	4	5	1	2	3	4	5	1	2	3	4	5
Delivery time	8.25	7.28	13.13	4.51	8.84	6.17	2.00	1.90	9.33	6.65	3.84	7.99	12.42	2.39	11.22	4.02	13.04	6.06	7.49	2.44
Product	6	7	8	9	10	6	7	8	9	10	6	7	8	9	10	6	7	8	9	10
Delivery time	5.68	2.64	12.17	11.70	8.10	7.57	6.83	2.24	2.04	6.83	2.47	13.12	5.23	6.99	8.81	3.18	9.09	6.97	8.94	10.95
Node	D10					D11					D12					D13
Product	1	2	3	4	5	1	2	3	4	5	1	2	3	4	5	1	2	3	4	5
Delivery time	7.06	4.46	8.54	9.79	9.39	8.67	5.27	9.35	4.12	7.11	2.33	10.62	4.14	5.18	5.30	10.85	11.99	2.28	12.47	11.10
Product	6	7	8	9	10	6	7	8	9	10	6	7	8	9	10	6	7	8	9	10
Delivery time	12.59	11.97	11.62	6.44	2.46	5.29	3.03	10.03	12.09	2.97	13.68	5.53	10.31	4.96	3.37	10.58	10.44	12.97	14.00	6.90
Node	D14					D15					D16					D17
Product	1	2	3	4	5	1	2	3	4	5	1	2	3	4	5	1	2	3	4	5
Delivery time	3.47	2.56	13.67	2.75	10.84	4.35	2.68	6.39	7.82	2.77	4.69	13.37	5.73	12.06	2.11	9.04	5.64	10.11	5.35	7.48
Product	6	7	8	9	10	6	7	8	9	10	6	7	8	9	10	6	7	8	9	10
Delivery time	2.83	7.39	12.71	2.31	9.17	10.85	7.51	7.30	13.72	5.13	11.19	10.04	7.64	9.27	11.28	13.84	5.78	5.48	12.47	3.53
Node	D18					D19					D20					D21
Product	1	2	3	4	5	1	2	3	4	5	1	2	3	4	5	1	2	3	4	5
Delivery time	2.46	10.75	12.18	10.47	5.43	11.01	8.13	2.13	10.59	11.37	7.33	6.86	9.60	1.44	6.86	11.44	13.72	6.87	12.77	3.25
Product	6	7	8	9	10	6	7	8	9	10	6	7	8	9	10	6	7	8	9	10
Delivery time	6.33	5.66	10.44	5.09	3.24	8.71	13.26	3.00	2.58	11.83	5.04	2.22	9.42	11.28	4.51	9.14	3.40	3.44	9.62	7.20

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Table 7 presents the arrival time of different products to customers, including product type number and delivery time information, in which the result shows that it is vital to plan the optimal delivery path under the goal of minimizing the cost. In the implementing process, this study takes delivery start time of the product and processing completion time as the connection point to optimize the delivery of product and production scheduling scheme as a whole, which could effectively meet the needs of the customer-driven manufacturing enterprises. In addition, in order to improve operational efficiency and reduce inventory costs, enterprises should take customers’ time requirements for products into account while making production scheduling plans, which plays an important role in the whole production scheduling and machine utilization.

In the process of each product being delivered to 20 nodes by vehicles, the cost consumption is shown in

Table 8. The cost of carbon emissions during delivery process.

Product	Optimal Delivery Route	Cost of Carbon Emissions under Each Path	Cost of Carbon Emissions during Delivery for Each Kind of Product
1	1→12→18→1 1→14→8→9→15→16→1 1→5→7→3→10→20→1 1→6→2→11→17→1 1→4→13→19→21→1	344.8007 482.8529 568.2689 382.7344 443.7455	2222.4024
2	1→7→3→14→15→1 1→5→10→2→11→17→1 1→20→6→8→19→1 1→12→18→1 1→13→4→9→16→21→1	406.2998 666.5079 559.4502 344.8007 704.7106	2681.7692
3	1→3→7→19→13→1 1→5→12→1 1→4→16→9→15→21→1 1→10→2→11→20→17→1 1→18→8→6→14→1	387.9431 300.6794 526.4188 745.9757 616.7211	2577.7381
4	1→20→2→8→14→1 1→11→6→12→17→1 1→3→5→9→15→1 1→7→10→18→19→1 1→4→16→13→21→1	563.1586 529.18 411.856 637.9799 445.4065	2587.5810
5	1→4→16→9→15→21→1 1→5→12→18→1 1→3→7→20→11→17→1 1→2→6→10→1 1→14→13→8→19→1	526.4188 354.5342 530.7168 353.2058 427.0166	2191.8921
6	1→4→8→14→9→1 1→20→11→6→18→1 1→7→3→5→19→21→1 1→13→15→16→1 1→10→2→12→17→1	526.4856 595.3754 643.2829 351.3396 609.0063	2725.4898
7	1→20→6→11→21→1 1→5→12→18→17→1 1→7→3→14→15→1 1→9→4→16→13→1 1→10→2→8→19→1	538.7322 414.2679 406.2998 617.2124 615.2985	2591.8109
8	1→5→7→3→19→21→1 1→4→8→17→1 1→9→15→16→1 1→20→2→11→12→18→11→10→6→14→13→1	540.5835 410.896 357.0779 582.3097 640.9905	2531.8575
9	1→7→14→19→1 1→2→12→18→1 1→3→10→8→1 1→4→9→16→21→1 1→5→20→6→11→17→1 1→15→13→1	422.1617 352.8786 477.7923 457.1433 595.1697 296.3295	2601.4751
10	1→10→11→18→12→17→1 1→20→2→15→1 1→5→3→7→13→21→1 1→6→8→14→1 1→4→9→16→19→1	656.3156 354.4466 392.947 390.6841 510.2755	2304.6688

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With the progress of delivery activities, the load of a truck is getting smaller and smaller. At this time, the fuel consumption per unit distance is also changing with the load. Table 8 shows the cost associated with carbon emissions for each complete process from delivery center then back to it.

At the first stage, the optimal delivery route is obtained by genetic algorithm on the basis of given customer coordinate information. At the second stage, in order to meet the customer’s requirements for delivery time, the optimal production scheduling scheme is solved on the basis of minimizing the total cost of production–delivery to achieve two-stage collaborative optimization. The following is the process of solving the production scheduling scheme.

5.2.2. Optimal Production Scheduling for Satisfying Customer Demand

The basic data of production are as follows: the number of population is 200, the maximum number of iterations is 300, the initial crossover probability p_c = 0.9, and the mutation probability p_m = 0.08. The total completion time is calculated to be 726.01 s. In Figure 11, the Gantt chart of products processing is given and the processing completion time of 10 kinds of products is calculated and shown in Table 5.

In

Table 9. Processing completion time of 10 kinds of products.

Product Type	1	2	3	4	5
Processing Completion Time	549 s	684 s	604 s	407 s	626 s
Product Type	6	7	8	9	10
Processing Completion Time	689 s	726 s	667 s	708 s	612 s

and Figure 11, it can be seen that the minimum completion time of this batch of products is the final processing completion time of the seventh product, i.e., the completion time is 726 s. The fourth product is processed at the earliest, with a processing time of 407 s. Moreover, it can be found that machine’s utilization rate determines the maximum completion time, and machine idleness in production process is inevitable. Thus, machine idleness should be shortened as much as possible to shorten the minimum completion time in real situations.

The results of all costs at delivery and production stages are shown in

Table 10. Specific cost result.

A1	A2	A3	A4	A5	A6	A7
1	0.509	101.04	2222.4024	51.43	1556.2342	3830.0666
2	0.635	101.04	2681.7692	64.16	1655.7591	4401.6883
3	0.561	101.04	2577.7381	56.68	1636.8254	4271.2435
4	0.378	101.04	2587.5810	38.19	1637.7306	4263.5016
5	0.581	101.04	2191.8921	58.70	1554.6523	3805.2444
6	0.639	101.04	2725.4898	64.56	1670.1354	4460.1852
7	0.674	101.04	2591.8109	68.10	1636.9411	4296.852
8	0.619	101.04	2531.8575	62.54	1623.0138	4217.4113
9	0.657	101.04	2601.4751	66.38	1673.2936	4341.1487
10	0.568	101.04	2304.6688	57.39	1571.8062	3933.865

A1: Product type; A2: Cost of carbon emissions unit product processing; A3: Demand quantity of products; A4: Cost of carbon emissions during delivery; A5: Cost of carbon emissions during production; A6: Cost of operation; A7: Total cost.

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According to the cost data in Table 10, the cost related to carbon emission accounts for more than 50% or even 60% of the total cost. It is shown that the optimization of carbon emission contributes to the cost reduction in the optimization of sustainable scheduling. While relieving the environmental pressure, it reduces the cost for the enterprise and promotes its sustainable development.

In the study of the integration problem of production and delivery, this study aims to propose such a novel solution idea: under the condition of meeting the minimum cost in the delivery route process, the optimal production scheduling scheme can be realized to meet customer’s requirements for delivery time within the delivery time window, and the collaborative optimization of production and delivery can be finally realized. Through the application of the case part, it was found that low carbon production and delivery can be realized by adjusting production sequence, so as to reduce the pressure on the environment and achieve sustainable development under the concept of low carbon economy. Finally, cost was taken as the optimization objective to maximize the profits of enterprises and occupy the core competitiveness of the market.

5.2.3. Comparison and Analysis

In order to further illustrate the superiority and practicability of the proposed method, this paper used the method from Reference [50] to solve the problem in this paper. Reference [45] presented the important role of production scheduling cost in enterprises, and constructed a multi-objective production scheduling optimization agent model based on the genetic algorithm. Among them, the Gantt chart of the optimal production scheduling based on Reference [45] is shown in Figure 12.

According to the results of operation, although the production scheduling optimization method designed in Reference [45] can meet the needs of production scheduling scheme formulation, in terms of the effective working time of the machine and the completion time of each product, the results are not as good as those obtained by the method designed in this study. Among them, the main reason for this problem is that Reference [45] does not take the delivery of products into account in production scheduling, which is prone to the production scheduling of the workshop and logistics delivery of the warehouse cannot be well coordinated, which is not conducive to the development of the whole enterprise. Because when the production cost is minimized, it may lead to the increase of inventory cost, which will lead to the increase of operating cost of the whole enterprise. On the contrary, coordinating production scheduling, and delivery may make the operation cost of enterprises smaller.

The numerical results obtained by the two-layer collaborative model in this study were compared with those in Reference [45]. It was found the model has a significant optimization effect in solving this kind of problem. Data comparison among the total cost, the cost of carbon emissions during production, and the cost of carbon emissions during delivery are shown in

Table 11. Comparison results between Reference [45] and this study.

Performance Measure	The Optimal Solution		Optimization Ratio
	Reference [45]	This Study
Total cost	48,959.3526	41,821.2066	14.58%
Cost of carbon emissions during production	649.57	588.13	9.46%
Cost of carbon emissions during delivery	28,120.7395	25,016.6849	11.04%

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It can be seen in Table 11 that the optimal solution is quite different. The optimal solution in this study reduces the total cost by 14.58%, in which the cost of carbon emissions during production is reduced by 9.46% and the cost of carbon emissions during delivery is reduced by 11.04%. Compared with the method used in Reference [45], the results obtained by this proposed model are more superior, which could greatly support the production–delivery process in a real situation.

Through the research in this paper, it was found that the inconsistency between production scheduling and logistics delivery may be a key factor affecting the inventory cost of enterprises. Therefore, this paper calls on enterprises to consider the link of product delivery as much as possible when formulating production scheduling schemes, so as to minimize the overall operating cost of enterprises. The production scheduling–logistics delivery collaborative optimization model designed in this paper can provide a better way for enterprises to achieve this goal.

In the study of the integration problem of production and delivery, this study aimed to propose a novel solution idea: under the condition of meeting the minimum cost in the delivery route process, the optimal production scheduling scheme can be realized to meet customer’s requirements for delivery time within the delivery time window, and the collaborative optimization of production and delivery can be finally realized.

Through the application of the case part, it is found that compared with Reference [45], the cost related to carbon emissions and total cost in the production and delivery process are reduced in a certain proportion 10–15%. It shows that low carbon production and delivery can be realized by adjusting production sequence, so as to reduce the pressure on the environment and achieve sustainable development under the concept of a low carbon economy. Finally, cost is taken as the optimization objective to maximize the profits of enterprises and occupy the core competitiveness of the market.

6. Conclusions

Under the background that the modern manufacturing industry tends to be integrated, intelligent, and agile, this study focuses on the problem of high-investment, high-consumption, high-pollution, low-efficiency, its inability to respond to individualized order quickly and accurately, and the weak timeliness of delivery in traditional manufacturing. A two-layer production–delivery collaborative optimization model considering delivery time window is proposed, and carbon emissions in the whole production–delivery process are optimized for green sustainable development. Firstly, as widespread application of big data, IoT technology, cloud computing, and other technologies in industry will be the development trend of the future, this study built an IoT technology architecture for production–delivery research. Secondly, quantifying the energy consumption of machines and fuel consumption of vehicles as carbon emissions during whole production–delivery process, time window constraint and carbon emissions were transformed into two cost functions, respectively, and the total cost was minimized to establish a two-layer production–delivery optimization model, so as to implement a low-carbon and economical production–delivery process. Finally, taking delivery time as the connection point, a two-layer optimization algorithm was developed. The computational results of a case study show the efficiency and effectiveness of this proposed sustainable collaborative model, which provides a theoretical basis and practical guidance for the integration optimization of production and delivery of E-commercial platforms. In the actual platform, in order to meet the potential demand of more and more customers for the integration and instantaneity of production and delivery, E-commerce platforms are required to continuously optimize the service mode of the logistics and delivery sector and provide more customers with logistics and delivery services matching online transactions in a timely and efficient manner.

In future work, the impact of improving product quality, reducing rejection rates, and improving productivity on green and sustainable manufacturing will be studied in depth. Furthermore, there is also the extension on group production modes. According to process similarity, function similarity or other characteristics, the scheduling model established by classifying and processing workpieces could meet more real situations, which would enrich the related scheduling research.