Joint Optimization of Inventory and Schedule for Coal Heavy Rail Considering Production–Transportation–Sales Collaboration: A Spatio-Temporal-Mode Network Approach (2024)

1. Introduction

Coal is a crucial energy resource in China, integral to industrial production and residential power generation. Ensuring a secure coal supply is a vital aspect of China’s energy security. According to statistics, China’s annual consumption of coal exceeds 3 billion tons, accounting for 56% of disposable energy consumption, making it one of the most important energy resources. Given the uneven distribution of coal resources across the country, a long-distance transportation pattern has emerged: “coal transportation from the north to the south and from the west to the east”. However, this process is plagued by high transportation costs and price conflicts between coal supply and demand. Specifically, the unit distance logistics cost for coal in China is 10–15 times higher than in the U.S., compelling coal companies to seek ways to reduce transportation costs. Addressing the demand for coal supply, minimizing the costs associated with coal stockpiles, reducing heavy-duty transportation expenses, and enhancing market profits and corporate earnings are interconnected challenges that must be tackled.

In the face of increasing future uncertainty, large-scale coal enterprises must leverage the advantages of an integrated production, transportation, and sales supply model to gain a competitive edge in the market post-restructuring and integration. These enterprises need to develop effective inventory and scheduling plans to enhance the coordination and refinement of each link in the coal supply chain, from production to transportation to sales, ultimately maximizing overall supply chain benefits. Balancing the paradox between inventory levels and transportation efficiency is a critical aspect of supply chain synergy. As coal storage and distribution bases continue to be developed, it is essential to balance the coal consumption needs of small, high-frequency demands with low-frequency, large-quantity transportation costs. Effectively coordinating the cost relationships across multiple links in the coal supply chain, including inventory costs at various levels and transportation expenses, is increasingly important. Additionally, managing the upstream and downstream inventory relationships has become crucial to ensuring a smooth and efficient supply chain.

The purpose of this paper is to advance the integrated development of production, transportation, and sales in the coal industry by considering inventory and transportation costs through the lens of supply chain management. This study aims to formulate a refined coal transfer scheme within an integrated transportation system distinguishing between the internal and external operations of the enterprise under a multilevel supply-chain node structure. The issue is framed as a transportation optimization problem within the context of coal production, transportation, and sales integration. To capture the complexities of the coal market, such as the synergy of multiple transportation modes, supply–demand matching, flow distribution, and storage and trans-shipment at distribution bases, we first constructed a transportation optimization model. This model accounts for the inventory at multiple levels within the coal supply chain, aiming to minimize the total cost of the transportation system. Subsequently, we developed a transportation optimization model that considers the benefit of the integration of coal production, transportation, and sales. This model seeks to maximize the overall benefit of the coal supply chain by optimizing the transportation plan. Finally, we constructed a model focused on maximizing the revenue of the integrated coal production, transportation, and sales framework. By solving this optimization model, we obtained a transportation plan to enhance the overall revenue of the coal supply chain.

The remaining sections of this paper are organized as follows: Section 2 presents a review of the relevant literature. Section 3 details the modeling and solution of the transportation optimization model which considers the inventory of multilevel nodes within the coal supply chain. The modeling is based on the spatio-temporal network of coal transportation and aims to balance inventory cost and transportation cost within an integrated coal transportation network. This section explores the optimal transportation paths and modes, capacity allocation, and coal storage durations at distribution bases, and validates the model using Gurobi. Comparisons are made to determine the significance of considering inventory costs and refining the transportation scheme to an hourly level. Section 4 provides a case study, using coal transported to East China by the CHN ENERGY Investment Group as an example. This section validates the model by solving the optimal transportation paths, volumes, inventory levels, storage durations, and transit situations. A sensitivity analysis is conducted on factors such as the ratio of self-produced to purchased coal, coal prices, and transportation rates. Recommendations for a trans-shipment scheme under the integrated production, transportation, and sales framework are proposed, offering valuable insights for the energy industry’s integrated supply chain. Section 5 concludes the paper with a summary of the research findings, highlights the study’s limitations, and suggests directions for future research.

2. Literature Review

The qualitative analysis of coal transportation in foreign countries primarily addresses the challenge of limited coal transportation capacity. Todd [1] analyzed the production, consumption, inter-regional transportation capacity, and port throughput of coal in each region of China and proposed the enhancement of the port and railroad connectivity infrastructure. Todd [2] further examined the demand for coal in China and evaluated the level of railroad capacity allocation, and concluded that railroads need to address coal supply and demand matching by constructing new lines and expanding the capacity of existing ones. Keith [3] discussed the important role of heavy railroads in South Africa’s mineral exports and offered recommendations on maintaining railroad network capacity to meet the growing demand for coal and iron ore transportation through upgrades and management improvements. Eikhoff [4] analyzed the distribution of coal resources and traffic flow in Germany, suggesting ways to sustain railroad network capacity under stringent environmental constraints to accommodate increased coal and iron ore transportation demands. Wang et al. [5] focused on the relationship between city distribution and rail freight transportation in China using quantitative research methods. Studies on the causes of unachievable coal transport volume targets utilized descriptive qualitative and quantitative analysis [6]. For forecasting and analyzing coal traffic on the Daqin Railway, a qualitative analysis method was employed to predict railway freight volume [7]. The location selection of railway logistics centers for eastward coal transportation involved both qualitative and quantitative methods [8]. Furthermore, the impact of COVID-19 on China’s coal imports was qualitatively analyzed, highlighting its effects on transportation and domestic coal production [9].

The qualitative analysis of coal transportation in China mainly focuses on addressing the issue of insufficient capacity in railroad coal transportation channels. Research on coal storage and distribution bases for coal transit and storage has also been increasing. Wang C [10] argued that, given the spatial layout of China’s coal production places and main consumption places, the development of dedicated coal transportation corridors is necessitated based on statistical data on China’s coal industry. This research discussed the enhancement of multimodal transportation to improve the possibility of long-distance and multilink coal transportation. Given coal’s importance as a fuel for power generation, ensuring a stable coal supply is essential. However, rising coal consumption has accentuated the issues of insufficient transportation capacity and port throughput. Consequently, research has increasingly focused on the construction and optimization of coal storage and distribution bases to mitigate these challenges.

Due to the characteristics of long-distance and multilink transportation, coal transportation often involves multiple modes of transportation. Leveraging the advantages of integrated transportation can help reduce costs and improve efficiency, and there has been an increasing amount of research on multimodal transportation transfer schemes. Osleeb [11] et al. optimized the U.S. coal logistics system based on railroad and coastal transportation networks by constructing a mixed-integer programming model to minimize the total cost of production, transportation, and transit for different coal types and transportation modes. Mishra [12] put forward the importance of multiple mode connectivity across multiple transportation modes. He developed a series of connectivity indicators for points, road sections, and regions, and used these indicators to quantify and evaluate connectivity in the establishment of a multimodal transportation hub selection model, validating the model with practical examples. Nitidetch [13] combined qualitative and quantitative analyses, combining the hierarchical analysis method (AHP), the data envelopment analysis method (DEA), and the Technique for Order Preference by Similarity to Ideal Solution (TOPSIS). This approach harmonizes conflicting criteria to select the most appropriate alternatives and provide multimodal transportation routes. The effectiveness of this method was verified through real-world transportation route selection cases.

Some studies focus on coal supply chain networks, addressing multisupplier and multi-power-plant transfer optimization problems primarily by constructing mixed-integer programming models to determine optimal path selection and flow allocation. Osleeb [14] explored the issue of coal transportation network reuse at the New England port, firstly constructing an integer planning model to minimize the total cost. This model was later extended to a multiobjective optimization model, balancing the cost and efficiency of coal transportation, and validated through real case studies. The optimization model of multiobjective planning was extended to consider the optimization model of multiobjective planning, and a proposal for balancing the cost and efficiency of coal transportation was made through a real case study [9]. Ash [15] examined the practical problem of transporting coal from western Canada to power stations in eastern Canada, using a simulation model to evaluate potential paths. This research provides a reference for strategic decision making regarding coal transportation, though it requires a substantial database to reflect real-world conditions accurately. Quelhas [16] applied a multiperiod generalized network flow model to optimize the overall efficiency of energy supply schemes, considering the substitution effects of coal and natural gas, and analyzed the economic efficiency of energy movement from coal and natural gas suppliers to power load centers, which enriched the perspective of analyzing the energy problem. Yucekaya [17] investigated the coal transportation path selection problem involving multiple suppliers and types of coal, establishing a mixed-integer model for optimal path selection. Shih studied the procurement and transportation problem of an electric utility company with multiple power plants and suppliers, considering procurement, transportation, and inventory cost. Shih’s mixed-integer programming model aimed to minimize total costs, effectively optimizing transportation for multiple suppliers and demand points. Chang [18] focused on determining the shortest path of a coal and power transportation network by connecting the coal source and coal consumption places to form a minimum spanning tree solved using a shortest-path routing algorithm.

Various studies have been conducted to analyze and improve the route optimization of coal multimodal transport, considering factors such as coal transportation direction and source locations in transfer areas [19]. The impact of air pollution caused by dust emissions during coal storage, transfer, and transportation has also been a significant concern, prompting the application of robust optimization techniques in designing air-quality monitoring networks [20]. Furthermore, models utilizing genetic algorithms have been proposed for optimizing coal procurement and transportation decisions, particularly for thermal power plants [21]. Moreover, research has been conducted on optimizing coal truck flow in open-pit mines, emphasizing the importance of efficient coal mining, transportation, and processing operations [22]. Overall, the optimization of coal transfer and transportation processes is essential for improving efficiency, reducing costs, and minimizing environmental impacts in the coal industry. Most current studies on coal transfer optimization focus on the selection of transport paths and flow distribution, including the selection of transport modes. These studies typically consider constraints such as the capacity of nodes and arcs in the coal transport network, supply and demand capacity, and inventory capacity. The objective functions often aim to minimize total transport costs or maximize total returns. This has led to the development of a relatively mature theory of transfer optimization models which analyze the price of coal in different periods, transportation rates, inventories, and other factors in the trans-shipment scheme.

3. Methodology

3.1. Problem Statement

In this section, we examine the three-level coal supply chain network of coal sources, coal storage and distribution bases, and consumption sites. A coal storage and distribution base serves as a critical hub for centralized coal warehousing, transportation, and deployment, addressing the issue of long transportation distances for coal supplied from a coal source. These bases are strategically located with respect to coal production and distribution areas, consumption concentration, major railroad transportation nodes, and key receiving and discharging ports. The layout and abstraction of this transportation network are illustrated in Figure 1. Large-scale coal enterprises generally have self-built railroad lines connecting coal mines to demand points, with railroad transportation being the primary mode of transport. Coal is typically transported southward through ports, with a small portion handled by short-distance road transportation. At the consumption point, coal consumption can be predicted per unit hour. The total cost of the whole system includes inventory costs, transportation costs, transit costs, and arrival-time penalty costs across the three nodes of the coal supply chain. For different transportation demands, the coal requirement at a demand point can be met either directly from the coal source or from the coal storage and distribution base. Therefore, different transportation schemes and modes, as well as path selections, directly impact the transportation cost and arrival time, resulting in varying inventory costs. The entire coal collection and transportation system needs to consider minimizing overall costs while continually optimizing the transportation scheme. The transportation optimization problem is studied in this section to simplify the complex coal transportation problem into a path integer planning problem within a three-level supply chain system, comprising multiple coal sources, multiple storage and distribution bases, and multiple coal consumption places. The objective is to minimize the total system cost while considering capacity constraints and inventories at each node. Ultimately, an optimized scheme for coal path selection and flow distribution is obtained, taking into account multilevel node inventories.

A spatio-temporal network can more clearly and accurately represent the spatio-temporal displacement of coal flow and vehicle flow in a network, as shown in the figure below. The transport spatio-temporal network diagram contains a number of coal sources ( $o$ ), coal storage and distribution bases ( $s$ ), and coal consumption places ( $d$ ). The coal can be transported directly from the source to the coal consumption place, for instance, by transporting the coal through the transport arc $(o_{4}, {d_{1}, T}_{1}, T_{3})$ , which departs from $o_{4}$ at the moment $T_{1}$ and arrives at $d_{1}$ at the moment $T_{3}$ . It can be stored for a certain period of time at the storage and distribution coal base and then transported to the coal consumption place. It can also be stored in the storage and distribution base for a certain period of time and then transported to the coal consumption place, for example, it can first be transported to the storage and distribution base through the transport arc $(o_{3}, {s_{1}, T}_{1}, T_{2})$ , then stored in the storage arc $(s_{1}, {s_{1}, T}_{2}, T_{3})$ , and then transported to the coal consumption place through the transport arc $(s_{1}, {d_{3}, T}_{3}, T_{4})$ . Taking this graph network as a prototype, the coal transfer optimization model is established, as shown in Figure 2.

For more complex problems in practical applications, two-dimensional spatio-temporal networks can be further expanded into three-dimensional spatio-temporal state networks by adding state dimensions such as speed, capacity, and mode of transport. A three-dimensional spatio-temporal state network can provide a clearer description of the problem, and the problem can be modelled and solved by adding the required attributes. This paper studies the coal transport mode and path selection problem under the long-distance transport system of the coal supply chain, so the transport mode is added to the spatio-temporal network as the third dimension, and the coal transport nodes at the fixed departure moments of railway transport and waterway transport are taken as the spatio-temporal points so as to construct a three-dimensional spatio-temporal network of time–space–transport mode and to describe and study the problem.

On the basis of the physical network, the time dimension and transport-mode selection dimension are added to construct the time–space–transport-mode three-dimensional spatio-temporal network $G (N, A, M)$ , where $N$ denotes the set of spatio-temporal points, $A$ denotes the set of spatio-temporal arcs, and $M$ denotes the set of transport modes. $i, j$ denotes the serial number of the physical network node, $t_{s}, t_{A}$ denotes the time serial number, and $m, n$ denotes the transport-mode serial number.

A simple three-bit spatio-temporal network schematic is shown in Figure 3, including three transport modes—road, railway, and water transport. This paper explores the spatio-temporal network and finds that the main nodes are the following two:

(1): Departure node: $(i, t_{p s}, m)$ indicates that coal starts to be transported from point $i$ at the moment $t_{p s}$ by transport mode $m$ . There are also departure points $(i_{1}, t_{2}, m_{3})$ , $(i_{1}, t_{2}, m_{2})$ , etc., in the diagram.
(2): Arrival node: $(j, t_{p a}, m)$ arrives at node $j$ at the moment $t_{p a}$ by transport mode $m$ , and there are other departure points in the graph, such as $(i_{3}, t_{3}, m_{3})$ , $(i_{3}, t_{3}, m_{2})$ , and so on.

The spatio-temporal arc connecting the spatio-temporal nodes $(i, t_{p s}, m)$ and $(j, t_{p a}, m)$ is denoted as $(i, j, t_{p s},, t_{p a}, m, m)$ , which indicates that it enters into the spatial arc $(i, j)$ at the moment $t_{p s}$ with mode of transport $m$ and ends with mode of transport $m$ at the moment $t_{p a}$ . According to the transport process under the integrated coal transport system, the spatio-temporal arcs of the spatio-temporal state network in this paper mainly include the following kinds:

(1): Transport arc: $(i, j, t_{p s},, t_{p a}, m, m)$ denotes the transport arc, such as the arc from the space–time node $(i_{1}, t_{2}, m_{2})$ to $(i_{3}, t_{3}, m_{2})$ , i.e., the $m$ transportation mode is used to depart from $i_{1}$ at the moment $t_{2}$ and arrive at node $i_{3}$ at the moment $t_{3}$ .
(2): Transit arc: $(j, j, t_{f s}, t_{f f}, m, n)$ denotes the transit arc, $(i_{3}, i_{3}, t_{3}, t_{4}, m_{2}, m_{3})$ denotes that the $m_{2}$ transport mode arrives at the $i_{3}$ point at the moment $t_{3}$ and starts the transport mode transit to $n$ , and the transport mode transit is completed at the moment $t_{4}$ .
(3): Waiting arc: $(j, j, t_{w s}, t_{w f}, n, n)$ represents the waiting arc. Due to the transport mode, it is often necessary to wait for the next train to start or for the next class of routes to start, and this waiting for the start of the state that node $j$ transit is completed waiting for the departure of the waiting arc. $(i_{3}, i_{3}, t_{4}, t_{5}, m_{3}, m_{3})$ means that after completing the transit at point $i_{3}$ at time $t_{4}$ , the departure is waited for at time $t_{5}$ .
(4): Storage arc: $(s^{t}, s^{t + 1})$ denotes a storage arc, which indicates that coal is stored at the same location for a period of time at different time intervals, and $(s^{t}, s^{t + 1})$ indicates that coal is stored for 1 unit of time at the point $s$ . The role of the coal storage and distribution base is to carry out coal transit storage, and the nodes of the storage arc are only at the coal storage and distribution base. Due to the long distance of coal transport and the long time limit for its arrival, there is a coal storage and distribution base in the coal transport network to ensure a certain amount of coal stockpile, and the storage arc indicates that the coal starts to be stored at the storage and distribution base $m$ at the moment $t$ , that it is stored for one period of time, and that it can be stored for more than one period of time in the coal storage and distribution base.

The essence of the model is a train spatio-temporal flow organization model considering the storage of coal, which consists of two main parts, i.e., train spatio-temporal flow optimization and storage optimization. Both are composed of corresponding objective functions and constraints, as well as the constraints associated with the two. The overall structure of the model is shown in Figure 4.

3.2. Notations

In this paper, we abstract and mathematically model the transport organization optimization problem by considering the inventory cost of multilevel supply chain nodes. The relevant notations are defined below.

Sets	$G (N, A, M)$	Three-dimensional space–time network
	$N$	A collection of spatio-temporal network nodes, $(i, t_{p s}, m), (j, t_{p a}, m), (j, t_{f s}, m),$ $(j, t_{f f}, m), (j, t_{w s}, n), (j, t_{w f}, n) \in N$
	$A$	The set of arcs $(i, j) \in A_{p n}$ , $(i, j, t_{p s}, t_{p a}, m, m) \in A_{t p}, (j, j, t_{w s}, t_{w f}, n, n) \in A_{w}, (j, j, t_{f s}, t_{f f}, m, n) \in A_{t f}$ denote the physical network transport arcs, the transport arcs in spatio-temporal networks, the waiting arcs, and the transit arcs, respectively
	$M$	A collection of modes of transport in spatio-temporal networks, $m_{1}, m_{2}, m_{3} \in M$ , $m_{1}$ —railway transport, $m_{2}$ —waterway transport, $m_{3}$ —road transport. $m, n$ indicate different modes of transport
	$T$	Moments in the transport space–time network, $t_{p s}, t_{p a}, t_{f s}, t_{f a}, t_{w s}, t_{w f} \in T$ . The time slot is 15 min
	$T T$	Moment where coal is consumed, time period 1 h
	$K$	The set of all coal batches, $k \in K$ . Each coal batch contains the following information: OD pairs, the amount of coal shipped in that batch, and the arrival time window
	$V_{j}^{-}$	The set of successor nodes of node $j$ , $j \in N$
	$V_{j}^{+}$	The set of successor nodes of node $i$ , $j \in N$
	$F$	Collection of transit nodes
	$S$	Aggregation of coal storage and distribution bases
Arcs	$(i, j)$	Physical network transport arc
	$(i, j, t_{p s}, t_{p a}, m, m)$	Transport arc
	$(j, j, t_{f s}, t_{f f}, m, n)$	Intermediate arc
	$(j, j, t_{w s}, t_{w f}, n, n)$	Waiting arcs, due to the transit of transport modes, often need to wait for the next train to start or the next route to start, i.e., waiting arcs for node $j$ wait for departure after the completion of transit
	$(s, s, t, t + 1)$	Storage arc
Parametrics	$h_{m a x d}$	Maximum stockpile capacity (in tons) where coal is consumed
	$o^{k}$	Source of coal for lot k coal
	$d^{k}$	Consumption of coal from lot k
	$q^{k}$	Weight of coal from lot k, in tons
	$[t_{E}^{k}, t_{L}^{k}]$	Time window in which the k-th instalment of coal must be delivered to the place of coal consumption
	$c_{a h}$	Time unit and coal storage unit and distribution base storage costs (in CNY/hour∙ton)
	$c_{b h}$	Cost of storage per unit of time per unit of coal consumed (in CNY/hour∙ton)
	$c_{(i, j, t_{p s}, t_{p a}, m, m)}$	Transport arc $(i, j, t_{p s}, t_{p a}, m, m)$ cost per unit weight per unit distance (in CNY/ton∙km)
	$E_{(i, j . t_{A}, t_{S}, m, m)}$	Transport arc $(i, j, t_{p s}, t_{p a}, m, m)$ capacity, (in tons)
	$T_{(i, j . t_{A}, t_{S}, m, m)}$	Transport arc $(i, j, t_{p s}, t_{p a}, m, m)$ transport time (in units of one time slot, i.e., 15 min)
	$c_{(j, j, t_{f s}, t_{f f}, m, n)}$	Transit arc $(j, j, t_{f s}, t_{f f}, m, n)$ transit cost per unit weight (in CNY/hour∙ton)
	$T_{(j, j, t_{f s}, t_{f f}, m, n)}$	Transit arc $(j, j, t_{f s}, t_{f f}, m, n)$ transit time (in time slots) from transport mode m to n
	$t_{s (i, t_{p s}, m)}$	Moments corresponding to spatio-temporal nodes $(i, t_{p s}, m)$ from node $i$
	$t_{a (i, t_{p s}, m)}$	The moment corresponding to the spatio-temporal node $(j, t_{p a}, m)$ arriving at node $j$
	$t_{f (j, t_{f f}, n)}$	The spatio-temporal node $(j, t_{f f}, n)$ corresponding to the moment when the transit is completed at node $j$
	$t_{s (j, t_{p s}, n)}$	The spatio-temporal node $(j, t_{p s}, n)$ corresponding to the moment of departure from node $j$
	$p_{d}$	Rate of coal consumption per unit hour at demand point $d$ at $t t$ (in tons per hour)
Decision Variables	$x_{(i, j, t_{p s}, t_{p a}, m, m)}^{k}$	0–1 decision variable, which is 1 if the k-th shipment chooses transport arc $(i, j, t_{p s}, t_{p a}, m, m)$ for transport and 0 otherwise
	$y_{(j, j, t_{f s}, t_{f f}, m, n)}^{k}$	0–1 decision variable, whose value being 1 indicates that the k-th batch of goods is transiting at node $j$ by choosing $(j, j, t_{f s}, t_{f f}, m, n)$ ; if $m = n$ , this means switching between the same mode of transport; $m$ means switching between different modes of transport, otherwise it is zero
	$h_{(s, s, t, t + 1)}^{k}$	0–1 decision variable, which is 1 if the k-th shipment is stored at moment $t$ at node $n$ and has a value of 0 otherwise
	${O p}^{k}$	0–1 decision variable, which is 1 if the k-th coal shipment is made and has a value of 0 otherwise
	$h_{d}^{t t}$	Intermediate variable, integer variable, and stock at demand point $d$ at moment $t t$ , where $h_{d}^{0}$ is the initial stock at demand point $d$ . Consideration of stock at the demand point is given in units of hours

In order to solve the coal transfer optimization problem with multiple coal sources and multiple demand places, the coal sources and coal demand places are combined with each other to form the supply–demand relationship of $k$ batches of coal, and the decision variables $x_{(i, j, t_{p s}, t_{p a}, m, m)}^{k}$ , $y_{(j, j, t_{f s}, t_{f f}, m, n)}^{k}$ , and $h_{(s, s, t, t + 1)}^{k}$ denote that the supply and demand relationship for each batch of coal is not the same as the supply–demand relationship, and the decision variables ${O p}^{k}$ indicate that each batch of coal is sent out or not. For coal path selection, including the transport arc, transit, and storage time, the decision variable ${O p}^{k}$ , which indicates whether the k-th batch of coal is actually sent out or not, is introduced, and the lower cost part of the OD pair is chosen. The optimization model is thus solved to obtain the matching and transport paths of the coal source and coal demand with the lowest cost to satisfy the coal demand at all demand points.

3.3. Model Assumptions

Before constructing the transportation organization optimization model considering the inventory cost of multilevel supply chain nodes, the following assumptions were made about the situation related to the transfer:

(1): It was assumed that the rate of coal consumption per unit time of power plants and coal chemical plants is fixed and can be known in advance and that there also exists a class of coal consumption places, which are sold directly without considering their inventory changes, and that coal can only be provided by coal source and coal storage and distribution bases and cannot be trans-shipped between coal consumption places.
(2): Assuming that the transportation process of the coal industry chain includes the production, transportation, and sale of coal resources, coal can be transported directly from the coal source to the coal consumption place, or it can be stored for a period of time by the storage and distribution base and then transported to the coal consumption place.
(3): It was assumed that coal is mined and processed internally, that there is no inventory cost at the coal source, that the total coal production can meet the demand of the coal consumption place, and that there is no outsourcing of coal.
(4): The same batch of coal can only be transited at the transportation nodes for a given transportation mode, and each node is transited at most once.
(5): During the decision-making cycle, the structure of the integrated coal transportation network and the train schedule are known and do not change.
(6): Since this paper considers the coal demand refined to the hour, to simplify the problem, OOD pairs of alternative sets are used, i.e., according to the actual supply and demand situation input, possible transportation of k batches of coal is determined after cost comparison to choose whether the batch of coal is issued or not, and if the batch of coal is issued, the corresponding coal source for transportation to the location of coal consumption is determined.

3.4. Construction of Spatio-Temporal-Mode Network for Coal Heavy Rail

The steps for constructing the spatio-temporal network are as follows:

(1): Set the relevant parameters for each batch of coal $k \in K$ .

Add the start point, $i = o^{k}$ , and the end arrival point, $d^{k}$ , for $k$ batches of coal, while each batch of coal is assigned a time window for the earliest dispatch time and the latest arrival time, $[t_{e}^{k}, t_{l}^{k}]$ , and a weight, $q^{k}$ .

(2): Add running arc segments $(i, j, t_{p s}, t_{p a}, m, m)$ .

An interval running arc represents the process of coal being sent from station $i$ at the moment $t_{p s}$ , transported by transport mode $m$ , and arriving at station $j$ at the moment $t_{p a}$ , and the transport arc is determined by the departure and arrival moments of the trains running through the stations, among which the railway transport and shipping are determined by the timetable, and the road transport is relatively more flexible in terms of the departure time, so when generating the transport arc segment, it generates the road transport arc that departs at each time slot, and each time slot is 15 min.

(3): Add the transit arc $(j, j, t_{f s}, t_{f f}, m, n)$ .

The transit arc represents the process of coal being transported to transit node $j$ by transport mode $m$ at the time $t_{f s}$ and then waiting for the next train of transport mode $n$ to be sent out from the station at the time $t_{f f}$ after the completion of the transit operation. Introducing the transit succession time window, $[t_{f}^{l h s}, t_{f}^{r h s}]$ , which needs to be satisfied for any batch of coal, ensures the minimum duration of the transit operation of different transport modes, $t_{f}^{l h s}$ , and also restricts the maximum residence time of coal in the station, $t_{f}^{r h s}$ . When the transport modes of the front and rear transport arcs are different at transit node $j$ and the transit time constraint is satisfied, then the transit operation will be carried out at that point and the next train of transport mode n is sent from the station at $t_{f f}$ . Then, a trans-shipment operation is performed at that point.

(4): Add storage arc segments $(s, s, t, t + 1)$ .

Due to the long distance of coal transport, the time limit for transport is high. In the coal transport network, there is a coal storage and distribution base to ensure a certain amount of coal stockpiling. The storage arc indicates the coal in the coal storage and distribution base $m$ at moment $t$ for a given time period. Coal can be stored for more than one time period in a coal storage and distribution base.

3.5. A Simultaneous Model for Inventory and Schedule Optimization Considering Production, Transportation, and Sales

The optimization objective of this model is to minimize the cost generated by the coal logistics system as a whole, which is composed of three parts: the first one is the transportation cost, the second one is the transit cost, and the third one is the inventory cost. Coal is transported from the coal source to the consumer end of deployment. The main modes of coal transport are railroad transport and waterway transport. The end of a railroad line is connected to a factory, or other consumer places can be reached by road, which constitute a small part of the overall transport network. The main routes are as follows: (1) coal source—railway transportation—port—water transportation—consumption area—neighboring power plants; (2) coal source—direct railway transportation—consumption area—neighboring power plants. For transport mode (1), the overall transport cost includes the cost of railroad and water transport, but also includes the cost of transit at the port. The advantage of this mode is that the cost of sea transport is lower, which can greatly save on the cost of transport. For transport mode (2), the organization is relatively simple compared with sea transport; railroad transport is faster, and it can avoid the additional cost of transit due to the rail and sea transit at a port. The ends of these two modes of transportation are specific power plants and coal chemical plants radiating from the consumption area to which coal is often transported by road due to the limited coal demands. Therefore, a trail comparison for the two transportation modes needs to analyze and consider the comprehensive cost consumption of the two transportation modes. In addition, in order to respond faster to the demand of the consumption place and ensure supply, the storage and distribution base becomes an important node of storage and transit in the coal transportation network, and the coal source, the storage and distribution base, and the consumption place will all incur a certain amount of the inventory costs, which are also a component of the total cost of the coal logistics system. With the application of fine management ideas, the fine supply chain has become a method to enhance the competitive advantage of enterprises, further refining decision making from day-by-day optimization, and enterprises need to measure transfer and inventories in a more refined way. Therefore, this paper adopts the modeling method of spatio-temporal networks for optimization of the formulation of a coal transportation plan. Each time period is set as 15 min, and a time factor is introduced when considering the cost. The optimization objective includes a penalty cost, both an inventory cost of coal arriving at a consumption place in advance and a shortage cost of coal arriving at the consumption place late, so as to ensure the accurate supply of coal at the consumption place.

(1) Transport costs are represented as follows:

$Z_{1} = \sum_{k \in K} \sum_{(i, j, t_{p s}, t_{p a}, m, m) \in A_{t p}} O p^{k} \cdot {(q^{k} \cdot d}_{(i, j, t_{p s}, t_{p a}, m, m)} \cdot c_{(i, j, t_{p s}, t_{p a}, m, m)} \cdot x_{(i, j, t_{p s}, t_{p a}, m, m)}^{k} + c_{(i, j, t_{p s}, t_{p a}, m, m)})$

(1)

(2) Transit costs, the costs of transit for changes in the mode of transport, are represented as follows:

$Z_{2} = \sum_{k \in K} \sum_{(j, j, t_{f s}, t_{f f}, m, n) \in A_{t f}} c_{(j, j, t_{f s}, t_{f f}, m, n)} \cdot y_{(j, j, t_{f s}, t_{f f}, m, n)}^{k} O p^{k} \cdot q^{k}$

(2)

(3) Inventory costs of coal storage and distribution bases are also considered. A coal storage and distribution base can be used for long-time storage of coal, and, relative to coal storage in a consumption place, warehouse inventory capacity is larger. Centralized storage inventory costs are lower, and the storage and distribution base inventory cost is written as follows:

$Z_{4} = \sum_{s \in S} \sum_{k \in K} \sum_{t \in T} c_{a h} \cdot q^{k} \cdot O p^{k} \cdot h_{(s, s, t, t + 1)}^{k}$

(3)

(4) Regarding the inventory cost at the place of production and processing of coal for consumption, the place of consumption of this type of coal tends to have a certain coal inventory capacity, and the rate of coal consumption in the production and processing process is known, such that the cost of the coal inventory at a place is written as follows:

$Z_{4} = \sum_{t t \in T T} c_{b h} \cdot q^{k} \cdot O p^{k} \cdot 1 / 2 \cdot (\sum_{t_{p s} = 4 t t - 3}^{4 t t} x_{(j^{'}, i, t_{p a}, t_{p s}, m, m)}^{k} \cdot q^{k} + h_{d}^{t t - 1} - h_{d}^{t t})$

(4)

(5) A penalty cost is set in order to ensure the timely supply of coal. A coal demand time window ${(t}_{E}^{k}, t_{L}^{k})$ is also set, so that if the coal arrives earlier than the time window, a storage cost is incurred, and if it arrives later than the time window, a late penalty cost is incurred:

$Z_{3} = \sum_{k \in K} c_{h} \cdot q^{k} \cdot O p^{k} \cdot \max {t_{E}^{K} - t_{a r}, 0} + \sum_{k \in K} c_{p} \cdot q^{k} \cdot O p^{k} \cdot \max {t_{a r} - t_{L}^{K}, 0}$

(5)

(6) The total coal transport system costs are written as follows:

$Z_{5} = Z_{1} + Z_{2} + Z_{3} + Z_{4}$

(6)

The constraints of the model include the following:

(1) Transport service selection: The k-th batch of coal from node $i$ to $j$ can be transported by only one transport mode in one time zone or not, i.e., at most one transport arc can be selected in each transport arc.

$\sum_{(i, j, t_{p s}, t_{p a}, m, m) \in A_{t p}} x_{(i, j, t_{p s}, t_{p a}, m, m)}^{k} \leq 1, \forall k \in K, \forall (i, j) \in A_{p n}$

(7)

(2) Limit constraint on the number of transits: This indicates that node $j$ performs at most one transit, i.e., it selects at most one transit arc.

$\sum_{\begin{array}{l} (j, j, t_{f s}, t_{f f}, m, n) \in A_{t f} \\ | j = f \end{array}} y_{(j, j, t_{f s}, t_{f f}, m, n)}^{k} \leq 1, \forall k \in K, \forall f \in F$

(8)

(3) Transit and transport variable coupling constraint: If the mode of transport of coal imported and exported from point $j$ changes, then transit has taken place at point $j$ .

$1 + M \cdot (\sum_{(i, t_{p s}, m) \in V_{j}^{-}} x_{(i, j, t_{p s}, t_{p a}, m, m)}^{k} + \sum_{(i^{'}, t'_{p a}, n) \in V_{j}^{+}} x_{(j, i^{'}, t'_{p s}, t'_{p a}, n, n)}^{k} - 2) \leq y_{(j, j, t_{f s}, t_{f f}, m, n)}^{k}, \forall k \in K, \forall j \in F, m \neq n$

(9)

(4) Coupling constraints obtain between transport variables and actual coal issued variables:

$O p^{k} \leq \sum_{\begin{matrix} (i, j, t_{p s}, t_{p a}, m, m) \in A_{t p} \\ | i = o^{k} \end{matrix}} x_{(i, j, t_{p s}, t_{p a}, m, m)}^{k}, \forall k \in K$

(10)

(5) The demand for coal at the place of coal consumption fluctuates within a certain range, and the amount of coal that actually arrives by the specified time is within this range:

$\sum_{k \in K} \sum_{\begin{array}{l} (i, j, t_{p s}, t_{p a}, m, m) \in A_{t p} \\ j = d^{k} \end{array}} x_{(i, j, t_{p s}, t_{p a}, m, m)}^{k} {\cdot q}^{k} \cdot O p^{k} \leq q_{d m a x}$

(11)

$\sum_{k \in K} \sum_{\begin{array}{l} (i, j, t_{p s}, t_{p a}, m, m) \in A_{t p} \\ j = d^{k} \end{array}} x_{(i, j, t_{p s}, t_{p a}, m, m)}^{k} {\cdot q}^{k} \cdot O p^{k} \geq q_{d m i n}$

(12)

(6) Network arc capacity constraints: For any arc in an integrated transport network, there are certain capacity constraints on the amount of throughput allocated to a particular arc, especially for railways:

$\sum_{k \in K} {x_{(i, j, t_{p s}, t_{p a}, m, m)}^{k} \cdot q}^{k} \cdot O p^{k} \leq u_{(i, j, t_{p s}, t_{p a}, m, m)}, \forall (i, j, t_{p s}, t_{p a}, m, m) \in A_{t p}$

(13)

(7) According to the multicommodity flow model, it is necessary to realize the flow balance of the origin node, the intermediate node, and the final destination node, which are the coal source, the intermediate node, and the coal consumption place in this model, and it is also necessary to consider the flow balance of the coal storage and distribution base due to the consideration of the storage of coal by the coal storage and distribution base. The coal source place flow balance is written as follows:

$\sum_{\begin{matrix} (i, j, t_{p s}, t_{p a}, m, m) \in A_{t p} \\ | i = o^{k}, (j, t_{p a}, m) \in V_{i}^{+} \end{matrix}} x_{(i, j, t_{p s}, t_{p a}, m, m)}^{k} - \sum_{\begin{matrix} (j^{'}, i, t_{p a}^{'}, t_{p s}, m, m) \in A_{t p} \\ | i = o^{k}, (j^{'}, {t^{'}}_{p a}, m) \in V_{i}^{-} \end{matrix}} x_{(j^{'}, i, t_{p a}^{'}, t_{p s}, m, m)}^{k} = 1, \forall k \in K$

(14)

(8) Coal storage and distribution base flow balance: The inflow and outflow of coal from the coal storage and distribution base is both the transfer of coal from the coal source and the export of coal to the downstream consumption place, with the remaining coal being saved in stockpiles:

$\sum_{\begin{matrix} (i, j, t_{p s}, t_{p a}, m, m) \in A_{t p} | \\ i = s, (j^{'}, {t^{'}}_{p a}, m) \in V_{i}^{-} \end{matrix}} x_{(j', i, t_{p a}^{'}, t_{p s}, m, m)}^{k} - \sum_{\begin{matrix} (i, j, t_{p s}, t_{p a}, m, m) \in A_{t p} | \\ j = s, (j, t_{p a}, m) \in V_{i}^{+} \end{matrix}} x_{(i, j, t_{p s}, t_{p a}, m, m)}^{k} + f_{(s, s, t - 1, t)}^{k} - f_{(s, s, t, t + 1)}^{k} = 0, \forall k \in K, \forall s \in S$

(15)

(9) Intermediate node equilibrium: Nodes of the road network that are neither the starting point nor the end point of coal transport and that are not transit bases do not have coal storage capacity, and the total amount of inflows must be equal to the total amount of outflows:

$\sum_{\begin{matrix} (i, j, t_{p s}, t_{p a}, m, m) \in A_{t p} | \\ i \neq o^{k}, i \neq s, j \neq d^{k}, (j, t_{p a}, m) \in V_{i}^{+} \end{matrix}} x_{(i, j, t_{p s}, t_{p a}, m, m)}^{k} - \sum_{\begin{matrix} (j^{'}, i, t_{p a}^{'}, t_{p s}, m, m) \in A_{t p} | \\ (j^{'}, {t^{'}}_{p a}, m) \in V_{i}^{-} \end{matrix}} x_{(j^{'}, i, t_{p a}^{'}, t_{p s}, m, m)}^{k} = 0, \forall k \in K$

(16)

(10) The coal consumption ground flow balance is written as follows:

$\sum_{\begin{matrix} (i, j, t_{p s}, t_{p a}, m, m) \in A_{t p} | \\ i = d^{k}, (j, t_{p a}, m) \in V_{i}^{+} \end{matrix}} x_{(i, j, t_{p s}, t_{p a}, m, m)}^{k} - \sum_{\begin{matrix} (j^{'}, i, t_{p a}^{'}, t_{p s}, m, m) \in A_{t p} | \\ (j^{'}, t'_{p a}, m) \in V_{i}^{-} \end{matrix}} x_{(j^{'}, i, t_{p a}^{'}, t_{p s}, m, m)}^{k} = - 1, \forall k \in K$

(17)

(11) Coal consumption site stockpiling: Considering the stockpiling of coal consumption sites in hourly units and the period of transport to be fifteen minutes, then $t t = 4 t$ ; for coal consumption sites, such as power plants and coal chemical plants, the inflow is the amount of coal arriving and the stockpile of the previous period, and the outflow is the coal used for production and consumption at a fixed rate, and the remaining part of the balance is the stockpile for the next period.

$h_{d}^{t t} + \sum_{t_{p s} = 4 t t - 3}^{4 t t} x_{(j', i, t_{p a}, t_{p s}, m, m)}^{k} \cdot q^{k} - p_{d} - h_{d}^{t t + 1} = 0, \forall k \in K, \forall t t \in T T$

(18)

(12) Physical arrival time and the main time-consuming operations of the coal transport system, transport time, storage time, transit time, and waiting time, are written as follows:

$t_{a r}^{k} = \sum_{(i, j, t_{p s}, t_{p a}, m, m) \in A_{t p}} x_{(i, j, t_{p s}, t_{p a}, m, m)}^{k} \cdot T_{(i, j, t_{p s}, t_{p a}, m, m)} + \sum_{s \in S} \sum_{t \in T} f_{(s, s, t, t + 1)}^{k} + \sum_{(j, j, t_{f s}, t_{f f}, m, n) \in A_{t f}} y_{(j, j, t_{f s}, t_{f f}, m, n)}^{k} \cdot T_{(j, j, t_{f s}, t_{f f}, m, n)}, \forall k \in K$

(19)

(13) The following are decision variable constraints:

$x_{(i, j, t_{p s}, t_{p a}, m, m)}^{k} \in [0, 1]$

(20)

$y_{(j, j, t_{f s}, t_{f f}, m, n)}^{k} \in [0, 1]$

(21)

$h_{(s, s, t, t + 1)}^{k} \in [0, 1]$

(22)

$O p^{k} \in [0, 1]$

(23)

In summary, the optimization model of coal transfer considering the inventory costs of multilevel supply chain nodes can be derived, and the minimum total cost of a coal transport system can be established as follows:

$\begin{array}{l} \min Z = \sum_{k \in K} & \sum_{(i, j, t_{p s}, t_{p a}, m, m) \in A_{t p}} O p^{k} \cdot c_{(i, j, t_{p s}, t_{p a}, m, m)} \cdot x_{(i, j, t_{p s}, t_{p a}, m, m)}^{k} \cdot {q^{k} \cdot d}_{(i, j, t_{p s}, t_{p a}, m, m)} \\ + \sum_{k \in K} \sum_{(j, j, t_{f s}, t_{f f}, m, n) \in A_{t f}} c_{(j, j, t_{f s}, t_{f f}, m, n)} \cdot y_{(j, j, t_{f s}, t_{f f}, m, n)}^{k} O p^{k} \cdot q^{k} \\ + \sum_{k \in K} c_{h} \cdot q^{k} \cdot O p^{k} \cdot \max {t_{E}^{K} - t_{a r}, 0} + \sum_{k \in K} c_{p} \cdot q^{k} \cdot O p^{k} \cdot \max {t_{a r} - t_{L}^{K}, 0} \\ + \sum_{s \in S} \sum_{k \in K} \sum_{t \in T} c_{a h} \cdot q^{k} \cdot O p^{k} \cdot h_{(s, s, t, t + 1)}^{k} \end{array}$

(24)

$\begin{array}{l} \min Z = \sum_{k \in K} & \sum_{(i, j, t_{p s}, t_{p a}, m, m) \in A_{t p}} O p^{k} \cdot c_{(i, j, t_{p s}, t_{p a}, m, m)} \cdot x_{(i, j, t_{p s}, t_{p a}, m, m)}^{k} \cdot {q^{k} \cdot d}_{(i, j, t_{p s}, t_{p a}, m, m)} \\ + \sum_{k \in K} \sum_{(j, j, t_{f s}, t_{f f}, m, n) \in A_{t f}} c_{(j, j, t_{f s}, t_{f f}, m, n)} \cdot y_{(j, j, t_{f s}, t_{f f}, m, n)}^{k} O p^{k} \cdot q^{k} + \sum_{k \in K} c_{h} \cdot q^{k} \cdot O p^{k} \cdot \max {t_{E}^{K} - t_{a r}, 0} \\ + \sum_{k \in K} c_{p} \cdot q^{k} \cdot O p^{k} \cdot \max {t_{a r} - t_{L}^{K}, 0} + \sum_{s \in S} \sum_{k \in K} \sum_{t \in T} c_{a h} \cdot q^{k} \cdot O p^{k} \cdot h_{(s, s, t, t + 1)}^{k} \end{array}$

(25)

The corresponding constraints are established as follows:

$\begin{array}{l} s . t . & \sum_{(i, j, t_{p s}, t_{p a}, m, m) \in A_{t p}} x_{(i, j, t_{p s}, t_{p a}, m, m)}^{k} \leq 1, \forall k \in K, \forall (i, j) \in A_{p n} \\ \sum_{\begin{array}{l} (j, j, t_{f s}, t_{f f}, m, n) \in A_{t f} \\ | j = f \end{array}} y_{(j, j, t_{f s}, t_{f f}, m, n)}^{k} \leq 1, \forall k \in K, \forall f \in F \\ 1 + M \cdot (\sum_{(i, t_{p s}, m) \in V_{j}^{-}} x_{(i, j, t_{p s}, t_{p a}, m, m)}^{k} + \sum_{(i^{'}, t'_{p a}, n) \in V_{j}^{+}} x_{(j, i^{'}, t'_{p s}, t'_{p a}, n, n)}^{k} - 2) \leq y_{(j, j, t_{f s}, t_{f f}, m, n)}^{k}, \forall k \in K, \forall j \in F, m \neq n \\ O p^{k} \leq \sum_{\begin{matrix} (i, j, t_{p s}, t_{p a}, m, m) \in A_{t p} \\ | i = o^{k} \end{matrix}} x_{(i, j, t_{p s}, t_{p a}, m, m)}^{k}, \forall k \in K \\ \sum_{k \in K} \sum_{\begin{array}{l} (i, j, t_{p s}, t_{p a}, m, m) \in A_{t p} \\ j = d^{k} \end{array}} x_{(i, j, t_{p s}, t_{p a}, m, m)}^{k} {\cdot q}^{k} \cdot O p^{k} \leq q_{d m a x} \\ \sum_{k \in K} \sum_{\begin{array}{l} (i, j, t_{p s}, t_{p a}, m, m) \in A_{t p} \\ j = d^{k} \end{array}} x_{(i, j, t_{p s}, t_{p a}, m, m)}^{k} {\cdot q}^{k} \cdot O p^{k} \geq q_{d m i n} \\ \sum_{k \in K} {x_{(i, j, t_{p s}, t_{p a}, m, m)}^{k} \cdot q}^{k} \cdot O p^{k} \leq u_{(i, j, t_{p s}, t_{p a}, m, m)}, \forall (i, j, t_{p s}, t_{p a}, m, m) \in A_{t p} \\ \sum_{\begin{array}{l} (i, j, t_{p s}, t_{p a}, m, m) \in A_{t p} \\ | i = o^{k}, (j, t_{p a}, m) \in V_{i}^{+} \end{array}} x_{(i, j, t_{p s}, t_{p a}, m, m)}^{k} - \sum_{\begin{array}{l} (j^{'}, i, t_{p a}^{'}, t_{p s}, m, m) \in A_{t p} \\ | i = o^{k}, (j^{'}, {t^{'}}_{p a}, m) \in V_{i}^{-} \end{array}} x_{(j^{'}, i, t_{p a}^{'}, t_{p s}, m, m)}^{k} = 1, \forall k \in K \\ \sum_{\begin{matrix} (i, j, t_{p s}, t_{p a}, m, m) \in A_{t p} | \\ i \neq o^{k}, i \neq s, j \neq d^{k}, (j, t_{p a}, m) \in V_{i}^{+} \end{matrix}} x_{(i, j, t_{p s}, t_{p a}, m, m)}^{k} - \sum_{\begin{array}{l} (j^{'}, i, t_{p a}^{'}, t_{p s}, m, m) \in A_{t p} | \\ (j^{'}, {t^{'}}_{p a}, m) \in V_{i}^{-} \end{array}} x_{(j^{'}, i, t_{p a}^{'}, t_{p s}, m, m)}^{k} \\ \sum_{\begin{matrix} (i, j, t_{p s}, t_{p a}, m, m) \in A_{t p} | \\ i = d^{k}, (j, t_{p a}, m) \in V_{i}^{+} \end{matrix}} x_{(i, j, t_{p s}, t_{p a}, m, m)}^{k} - \sum_{\begin{array}{l} (j^{'}, i, t_{p a}^{'}, t_{p s}, m, m) \in A_{t p} | \\ (j^{'}, t'_{p a}, m) \in V_{i}^{-} \end{array}} x_{(j^{'}, i, t_{p a}^{'}, t_{p s}, m, m)}^{k} = - 1, \forall k \in K \\ t_{a r}^{k} = \sum_{(i, j, t_{p s}, t_{p a}, m, m) \in A_{t p}} x_{(i, j, t_{p s}, t_{p a}, m, m)}^{k} \cdot T_{(i, j, t_{p s}, t_{p a}, m, m)} + \sum_{s \in S} \sum_{t \in T} f_{(s, s, t, t + 1)}^{k} + \\ \sum_{(j, j, t_{f s}, t_{f f}, m, n) \in A_{t f}} y_{(j, j, t_{f s}, t_{f f}, m, n)}^{k} \cdot T_{(j, j, t_{f s}, t_{f f}, m, n)}, \forall k \in K \\ x_{(i, j, t_{p s}, t_{p a}, m, m)}^{k} \in [0, 1] \\ y_{(j, j, t_{f s}, t_{f f}, m, n)}^{k} \in [0, 1] \\ h_{(s, s, t, t + 1)}^{k} \in [0, 1] \\ O p^{k} \in [0, 1] \end{array}$

(26)

4. Numerical Experiments

4.1. Experimental Background and Design

The object of this section of the study is to present a comprehensive overview of the transportation network that transports coal from the Zhunger mining area and the Yushen mining area from west to east to North China. In order to facilitate problem solving, some simplifications were made regarding the coal transportation network of the CHN ENERGY Investment Group, and, considering the line succession of the State Railway Group, a comprehensive transportation network integrating highway transportation, State Railway’s own railroads, and State Railway transportation was formed. Fifteen important network nodes were selected to be the arc segments of the coal transportation network and constitute the line network shown in Figure 5. The nodes of the coal transportation network studied in this section are numbered, and the node numbers are shown in Table 1.

The distance between each transportation node was obtained according to Gaode Map, the Railway Freight Mileage Table, the Train Ticket Network, and the Ship News Network. The distance between each transport node railroad, as well as the road transport, the transport times, and the railroad capacity are shown in Table 2. Railroad, road, and waterway transport speeds were assumed to be constant at 90 km/h, 85 km/h, and 40 km/h. China’s road transport capacity is small and departures are more flexible, so we did not consider departures for the road transport schedule. Given the different modes of transport rates, there are big differences in the transportation rates of different transportation modes, and there are differences in the rates and the numbers of trips along the CHN ENERGY Investment Group’s own railroad and the national railway. The tariff of the national railway is CNY 0.16–0.18/t·km, while the Haogi railroad, as an important north–south coal transportation corridor in China, has a tariff of CNY 0.13/t·km, and the number of daily train trips is as high as 10 trains/day. According to the annual report of the CHN ENERGY Investment Group for 2021, the unit tariff for its own railroad was CNY 0.066/t·km, the tariff for road transportation was roughly in the range of CNY 0.08–0.6/t·km, the average tariff for short-distance roads (less than 50 km) was CNY 0.65/t·km, and the average tariff for middle-distance roads (50 km–200 km) was CNY 0.35/t·km. The average transportation price was CNY 0.35/ton-kilometer, and the average transportation price for long-distance roads (more than 200 km) was CNY 0.25/t·km. Compared with other modes of transportation, the cost of waterway transportation of coal was the lowest; for example, the unit freight rate of coal transported from Huanghua Port to Shanghai Port by waterway was CNY 0.03/t·km, which was much lower than that of other modes of transportation. The freight rate per ton of coal was measured according to the freight rate announced by the national railway.

Since this paper considers the integrated coal transportation system, if the transportation mode changes before and after a transit node, the transit of the transportation mode is carried out at the node. The transit cost and the transit time generated during the transit period are shown in Table 3. Since the coal storage and distribution base has professional coal handling transit facilities as well as an industrial cluster effect, the transit cost in the coal storage and distribution base saves 2 CNY/ton.

One of the specific considerations regarding the cost of coal inventories is shown in Figure 6. The places of coal consumption are generally power plants, coal chemical plants, etc., so the consumption of coal has definite and continuous characteristics, in line with the deterministic storage problem, i.e., the consumption of goods is continuous and occurs at a constant, known rate. For this type of problem, an inventory curve diagram consists of a series of right triangles. There also exists a demand for direct sale of coal where coal is consumed, when there is no need to consider its inventory cost and it is simply shipped on time.

$\bar{Q} = \frac{1}{t_{b} - t_{a}} \int_{a}^{b} Y_{(t)} d t = - \frac{1}{2} k (t_{b} - t_{a}) = \frac{1}{2} Q$

(27)

From the above analysis, it can be concluded that the inventory cost (I) can be expressed by Equation (28) i.e., half the unit of the inventory cost is multiplied by the receiver’s maximum inventory.

$I = \frac{1}{2} Q \cdot q$

(28)

The research object of this paper is the coal transfer problem with multiple coal source locations and multiple coal consumption locations. This paper considers coal demand that is refined to the hour, and to simplify the problem, an alternative set of OD pairs is introduced, i.e., according to the actual supply and demand situation input, k batches of coal may be transported, as shown in Table 4, and after the cost comparison to choose whether or not to issue the batch of coal, if the batch of coal is issued, then the corresponding coal source location determines the coal consumption location for the transport.

This section takes the transportation of the CHN ENERGY Investment Group to North China as the research object and simulates the coal supply chain of three coal sources, one coal storage and distribution base, and three coal consumption places in total, including the integrated coal transportation system of railway and road transportation, which belongs to the transportation optimization problem with uncertain supply and demand, and includes different kinds of coal consumption places, among which a power plants and a coal chemical plant belong to coal-using enterprises with fixed consumption rates, and their stockpiles can be expressed by Equation (28). For Beijing, a coal-consuming place that only sells coal, stockpiles are not considered. In order to achieve the purpose of improving the utilization rate and efficiency of the equipment in the production process, both the power plant and the coal chemical plant adopt a system in which workers work in shifts to carry out 24 h production operations. According to the general production characteristics of the thermal power generation industry and the coal chemical industry, a power plant consumes 8000 tons of coal per day and a coal chemical plant consumes 12,000 tons of coal per day, which is converted into unit hourly rates of coal consumption of 320 tons per hour and 500 tons per hour, respectively. This translates into unit hourly coal consumption rates of 320 tons/hour and 500 tons/hour, respectively. This paper considers the transit storage function of coal storage and distribution bases, which have lower inventory costs and larger inventory capacities compared with coal consumption places. A coal storage and distribution base can give full play to the role of collection and evacuation. Coal with a load capacity of 10,000 tons is transported in large columns to a coal storage and distribution base, and then the coal storage and distribution base runs small running trains according to the hourly demand of the coal consumption place so as to achieve a balance between the inventory cost and the transport cost, and the cost of inventory is 0.5 million t/hour for each time period at the storage and distribution base. The inventory cost of the coal storage and distribution base is CNY 0.012/ton, i.e., the inventory cost of coal in the coal storage and distribution base is CNY 0.048/ton∙hour, which is much lower than the inventory cost of CNY 0.3/ton∙hour in the place of coal consumption. For the demand of coal consumption places, such as raw coal sales, it is only necessary to satisfy the transport time limit and demand quantity. For example, in the calculation example in this section, the demand range of coal in Beijing on the same day is set to be [6000, 9000], the expected arrival time window is [17:00–19:00 on the same day], the demand range of coal on the next day is set to be [7000, 10,000], the expected arrival time window is [11:00–13:00 on the next day], the expected arrival time window is [11:00–13:00 on the next day], the penalty cost for early arrival is CNY 0.075/ton, and the penalty cost for late arrival is CNY 0.03/ton.

4.2. Results

All experiments in this paper were run on a computer configured with an AMD Ryzen 7 5800H 3.20 GHz, based on the GUROBI 9.5.0 solver, using Python to call gurobi for solving and deriving the results of the arithmetic optimization.

Under the consideration of transportation cost only, the transfer scheme to meet the demand of all coal consumption places is shown in Table 5, with a total cost of CNY 3,149,321 and a total of 46,000 tons of coal issued. This coal transfer scheme ensures that coal arrives within the desired time window when it is transported to the direct sales place in Beijing (node 6) and the production and processing places, such as the Dingzhou power plant (node 11) and the Cangzhou coal chemistry plant (node 13). Coal consumption places also ensure that coal is supplied on time, making reasonable use of their inventories, coal transit at coal storage and distribution bases, etc., so there is no shutdown of production due to lack of stock.

From the point of view of the choice of transport mode, as the transport costs of the State Energy Group’s own railway and the national railway and road transport costs rise in order, their priorities are reversed. For instance, regarding transportation from the coal source Batuta (node 3) to the Dingzhou power plant (node 11) or the China Resources coal chemical plant (node 13), there are multiple transport trails and the minimization of the total cost in the model ensures that coal is selected for transport by the train with a smaller transport cost. Under the condition of sufficient railway capacity, priority is given to the Baoshen Railway, the Shenshuo Railway, and the Shuo Huang Railway (transport path 3-7-8-9-10-11) for transport. Road transport is used as a supplement to railway transport, waterway transport, and other modes of transport with a fixed frequency, e.g., the capacity from Dingzhou West (node 10) to the Dingzhou power plant (node 11) is low, and the frequency of railway transport is one train a day. Since railway transport is cheaper than road transport, railway transport is given priority, and when it is possible to carry out railway transport, coal will be transported to the Dingzhou power plant (node 11) directly, or it will be transported using road transport but with increased transit costs and higher transport costs.

From the perspective of the relationship between transport and inventory, because the unit inventory costs of coal consumption places are higher than those of storage and distribution bases, coal consumption places that are close to storage and distribution bases will store coal in these bases, especially if they have inventory capacity and production operations, as the storage and distribution bases can not only save inventory costs but also play a role in transit storage, and coal consumption places want to have small quantities of coal and use road transport, which has higher transit costs. A coal-consuming place wants to transport coal in smaSll quantities and multibatch modes, which achieves a balance between transport and inventory, and coal storage and distribution bases can guarantee stable coal supply, which verifies the cost-saving effect of the coal storage and distribution base. The 3rd-7th batch transfer scheme refers to the fact that coal is loaded at Daliuta (node 7), the source of coal; a 10,000-ton heavy-duty coal transport train is run to the coal storage and distribution base; and then replenishment is carried out promptly according to the change in the hourly coal stockpile at the Dingzhou power plant (node 11), which has a lower total cost compared to shipment from the source of coal.

4.3. Discussion

(1): Comparison of whether or not to consider coal storage and distribution bases

This section compares the solutions with and without coal storage and distribution bases, where the distribution solution without coal storage and distribution bases is the traditional solution of coal storage and logistics. This section of the transfer cycle for two days under the integrated transport system of public-railway coal transport research considers transfer optimization to determine whether to take into account the storage and distribution of coal base inventory factors. Using the gurobi solution to obtain the coal transfer scheme, at the coal consumption place of Beijing (node 6), with a direct sale, there is no inventory. At the Dingzhou power plant (node 11) and the China Resources Group coal chemical plant (node 13), there is a steady rate of coal consumption during production and processing. The source of coal consumption is coal stockpiles and coal transported in the previous time period, and the coal outflow is the production of coal for consumption and the remaining part of the savings for the stockpile. Therefore, this section only considers the comparison of the stockpiles transported to the Dingzhou power plant (node 11) and the CRG coal chemical plant (node 13). A comparison of the different parts of the two transfer schemes is shown in Table 6.

In terms of the transfer program, without considering the role of the storage and distribution base in transit storage, coal needs to be loaded and shipped from the coal source to the coal consumption place. With a longer transport time, each time the amount of inventory change is the amount of coal shipped for that batch, there is a higher cost of inventory at the coal consumption place. Considering the transfer scheme for coal storage and distribution bases, it is possible to run 10,000-ton heavy-duty coal trains to the coal storage and distribution bases and then send them to the coal consumption places in small batches, which gives full play to the role of the coal storage and distribution bases in transit storage and guarantees coal supply, reducing the pressure on the stockpiles of the coal consumption places.

Coal sources and coal consumption places that are closer to each other, such as Datong and Beijing, can be reached on the same day by road transport, as well as OD pairs covered by their own railway transport network, such as Daliuta and the Dingzhou power plant. The Shenshuo and ShuoHuang lines, as important coal transport corridors of the NNPC Group, have many trains running daily, including 10,000-ton and 20,000-ton heavy-duty trains, which are able to meet the coal demand of coal consumption places in the morning of the same day. Storage and distribution coal bases have less impact on supply and demand in these two cases. In the case of OD pairs that cannot meet the demand for coal on the same day, it is cheaper to centralize storage in a storage and distribution coal base. The distance from Datong to the Cangzhou coal chemical plant is relatively far, and using the Daqin line, the Beijing–Kowloon line, and other national railways, both coal and bulk goods can be transported. Therefore, the CHN ENERGY Investment Group’s occupation of the national railways for transport may be subjected to the limitation of capacity, limited train frequencies, and the number of trains running. As the number of trains that runs is limited, the coal storage and distribution base will play a role in transit storage and guarantee coal supply, reducing the pressure on the stockpiles in coal consumption areas.

In terms of transport cost, the saving of inventory cost in the coal storage and distribution base is only 2680 CNY because the research period of the small example in this section is only 2 days, the transport modes considered are only railway and road transport, and the coal in the coal storage and distribution base can only be transported to the place of coal consumption by road transport, which has a higher transport rate. The scale of the coal transport network is small, and if Huanghua Port, as a coal storage and distribution base, wants to give full play to its role in reducing transport and inventory costs and guaranteeing coal, it needs to be an important launching port for southward transport of coal from the north and make full use of multiple modes of transport for coal transport.

From the perspective of stockpiling, whether to consider the stockpiling of coal storage and distribution bases mainly affects the power plants and coal chemical plants which are closer to them. As shown in Table 7, the construction of coal storage and distribution bases reduces the inventory costs in the radiating coal consumption places by concentrating inventories in the coal consumption places in coal storage and distribution bases and then transporting them to the coal consumption places in small batches through small running trains according to the consumption rate in the coal consumption places so as to reduce the inventory costs in the coal consumption places. Due to the scale effect, although the transport distance and the cost of transport to the coal storage and distribution base increase, the inventory cost saved by storing at the coal storage and distribution base exceeds the increased transport cost, the total cost being reduced by 5.9% and the inventory cost by 5.2%.

As shown in Figure 7 and Figure 8, when coal storage and distribution bases are not considered, the coal-consuming places hold higher inventories of between 1000 tons and 6000 tons to prevent shortages which could affect production. When considering coal storage and distribution bases, when a coal storage and distribution base and a coal consumption place are relatively close, the time for transporting coal is more flexible using roads and a coal consumption place can hold a lower inventory of 1000 tons to 3000 tons and transfer the inventory to the coal storage and distribution base. For coal consumption places to hold smaller inventories, in real-life production, there needs to be a high degree of information transfer, production, transportation, and sales integration to overcome information barriers between various links within the enterprise. When the plan for coal production and consumption efficiency changes, it is necessary to communicate with the upstream and downstream actors in the coal production and consumption chain promptly.

(2): Comparison of whether or not to refine time comparisons

There are many problems in the existing coal transport system, such as when a coal source produces a sufficient amount of coal that is directly transported by rail without lean management, resulting in the accumulation of inventory in the coal consumption place, so this paper refines the study of the coal transfer program. The research period for the transport link is 15 min, and the rate of coal consumption by a power plant and a coal chemical plant within the enterprise is stable and continuous. The study period for the coal consumption link is 1 h, which can not only meet the coal demand of the coal consumption place on time but also achieve a balance between transport cost and inventory cost. At present, most of the studies on coal transfer schemes containing time factors are planned according to days and cycles; the consideration of storage, transport, and demand links with time factors is rougher, with an insufficient degree of refined management; and inventories of coal consumption places are expressed through demand intervals. This paper will compare these two optimization methods. If the coal transfer scheme is not refined, the demand for a coal consumption place is treated as a daily demand interval, and a two-day demand for coal consumption place is combined, as shown in Table 8.

The demand of each coal consumption place is expressed in intervals, and the coal arrival time is restricted to a desired time window, with no penalty for coal shipped within the time window, an early-arrival penalty for coal arriving earlier than the interval, and a late-arrival penalty for coal arriving later than the interval. The supply capacity of each coal source is combined with each coal consumer to obtain the alternative set of supply–demand matchings, the path with the minimum cost for each OD pair in a day is obtained, and whether or not k batches of coal are shipped at the minimum total cost is determined, as shown in Table 9.

Again, the problem is solved by invoking gurobi to obtain the demand information broken down to the daily minimized total cost of the mobilization scenario, as shown in Table 10.

The above transfer scheme only considers the transport cost, transit cost, train running cost, arrival penalty cost, and other factors, without considering the inventory cost. To meet the demand of a coal consumption place, a transfer scheme was employed, as shown in Table 10. In addition to the total inventory cost of CNY 3,004,605, a total of 41,000 tons of coal was issued. To compare the time for the refinement to the hourly transfer scheme, an inventory cost consideration was added in this calculation example, and the inventories for the coal consumption places of the Dingzhou power plant (node 11) and the Cangzhou coal chemical plant (node 14) were calculated. The rate of coal consumption is the rate of consumption of the day’s coal demand averaged to the hourly rate of consumption. The amount of change in the inventories was thus obtained, as shown in Figure 9. The inventory cost for the power plant was CNY 19,152 and the inventory cost for the coal chemical plant was CNY 18,045 for the study period.

Compared with the optimization scheme of transfer, which is refined to the hour, although the desired arrival time window is set when designing the demand of a coal consumption place, the inventory fluctuation volume of the derived coal transfer scheme is much larger, and the inventory stockpiled at the coal consumption place occupies a large amount of capital, which is not in line with the production and operation objectives. Moreover, if the coal transport is carried out according to the daily demand interval of the coal-consuming place, the value of the demand interval transmitted by the coal-consuming place is very important; however, this value is often the empirical value of the coal-consuming place, and it would be more scientific to calculate the relationship between the coal transport volume and the stockpile volume according to objectively available data, such as the consumption rate that is refined to the hour, so that the relationship between the coal transport volume and the stockpile volume can be better coordinated between the upstream and downstream coal transport in the integrated production, transportation, and sales mode. Therefore, hourly coal consumption needs to be considered in the optimization process of the transfer scheme.

(3): Impact of price volatility in the coal market

From the relevant data report of the CHN ENERGY Investment Group for the year 2021, it can be seen that the production of commodity coal was 307 million tons, the unit cost of production was CNY 155.5 per ton, the cost of purchased coal was CNY 48,742 million, the quantity of purchased coal was 126.3 million tons, and the unit cost of purchased coal was CNY 386 per ton. As the quality of coal required by the power generation segment and the coal chemical segment is different, and high-quality coal should be used for power generation, the selling price of the coal production department for the two segments is differentiated, these values being CNY 482 per ton and CNY 366 per ton, respectively, and the selling price to the outside world is CNY 599 per ton. The annual power generation of the Dingzhou power plant was 10.82 billion kWh, the standard coal consumption for power generation was 304 g/kWh, and the selling price of electricity was CNY 324/MWh, from which the revenue from coal generation of the internal power plant unit was calculated to be CNY 919.8/ton. The main products of the coal chemical division are polyethylene and polypropylene, with an operating income of CNY 4278 million and a consumption of 3.8 million tons of coal, which can be calculated as CNY 1126/ton of income per unit of coal reprocessing products in the coal chemical division. The revenue of the production and sales segments of the company was calculated, as shown in Table 11.

Among the coal sources, Datong and Daliuta are owned coal mines and Batuta is an externally purchased coal source. Among the places of coal consumption, the Dingzhou power plant is an internal power plant of the group, the China Resources coal chemical plant is an internal coal chemical product processing plant, and the demand for coal in Beijing is for external sales. When coal is sold externally, the purchase price of the sales segment is the same as the selling price, which is equal to the external selling price of the coal production segment, and the revenue from the coal is calculated for the production segment. In the context of the integration of production, transportation, and sales, the enterprise needs to consider the overall earnings of the coal supply chain after meeting certain special transportation needs, such as the need to protect the coal demand of power plants such as livelihood issues. The market needs to regulate the coal transfer program. For instance, when the market price of coal increases significantly, to maximize the earnings of a coal chemical plant, the supply of coal should be reduced and the sale of coal should be increased, which is reflected in the model as a combination of the lower limit of the demand interval of the coal consumption place and a reduction in non-essential satisfaction. The coal demand of a coal consumption place is shown in Table 8.

Based on the coal demand for a time period in a coal-consuming place, the time limit requirement for coal transportation to the coal-consuming place needs to be met, and different supply and demand relationships are obtained by considering the supply capacity of the coal-producing place and the supply capacity of external coal sources. A coal enterprise’s production cost is either self-produced or the result of external coal purchases. Comparatively speaking, the cost of self-produced coal is more stable, due to factors such as equipment depreciation and labor cost, and coal enterprises have a strong degree of control over their divisions, so the output and cost of self-produced coal is more stable and less affected by the market. For instance, Datong and Daliuta, having their own mines, have lower and more stable production costs. On the other hand, coal is generally purchased at the pit price, which has smaller supply elasticity and larger demand elasticity and is more affected by the external market. For instance, Batuta’s coal purchase cost fluctuates with the fluctuation in the pit price of coal in the market. Production segment revenue is the price of sales to different coal-consuming places, which is determined by the nature of coal-consuming places. There is a difference between the internal production price and the external sales price; the internal production price will also differ according to the quality of the coal used. An internal power plant uses coal to generate electricity, while a coal chemical plant uses anthracite coal for the manufacture of coal chemical products, the price of which is relatively low, and the external sales of a company selling coal are determined by the price at which coal is sold to outside companies, which is higher than the price of the latter and varies with the market. In addition, the cost of production for the sales segment is partly determined by operating costs and partly by the cost at which coal is purchased, i.e., the sale price for the production segment. The cost and selling price of each coal lot are shown in Table 12.

As the coal base price in China is set at CNY 710/ton, the reasonable range is CNY 610/ton to CNY 810/ton. The floating price is affected by the comprehensive price index of the coal trading center, and a reasonable range is set for the coal pit price, and the reasonable pit price range of Shanxi coal is CNY 410/ton to CNY 610/ton, while the pit price of Inner Mongolia coal fluctuates within the range of CNY 380/ton to CNY 580/ton. Three cases of coal revenue comparison were selected: when the coal price is reduced by 10% compared to the base price, when the coal price is the same as the base price, and when the coal price is increased by 10% compared to the base price. The price of coal when it is sold to external parties is the selling price of the production division to external parties, and under the integrated production, transportation, and marketing model, the selling price of this sales division is equal to the price of purchased coal, which will be fully converted to the revenue of the production division. Coal price fluctuation mainly refers to the change in coal market selling price, corresponding to the coal pit price, which is also market-oriented, and will also change, but the change is smaller than for the coal market selling price. For the calculation example in this section, the base price of the coal external selling price was set at CNY 680/ton and a sensitivity analysis was carried out on the coal price changes. The step length was taken to be 10%, and the coal external selling price was increased by 10%; for example, when the coal external selling price increased by 10%, the external selling price of coal was CNY 748/ton, and when the price of the coal market generally increased, the pithead price of the externally purchased coal also increased for the group, taking the percentage of change as 4%. Thus, revenues under different coal external selling prices were obtained, as shown in Figure 10 and Table 13.

When the coal price decreases by 10%, the total revenue is 97.78% of the revenue under the base price and does not decrease significantly with the coal price; when the coal price increases by 10%, the total revenue is 110.35% of the revenue under the base price, which indicates that the integrated mode of production, transportation, and marketing can effectively reduce the risk due to change in the price of coal and can bring greater revenue.

5. Conclusions

In this paper, we explore the critical decisions enterprises must make to enhance overall earnings in the context of the coal industry and other resource sectors continuously seeking new cooperation modes. Under the integrated model of production, transportation, and sales, it is essential for enterprises to fully utilize coal outsourcing resources, leverage storage and distribution bases to balance stockpiles and transportation, and judiciously set ratios for chemical product production and direct sales. The coal transfer program is not merely a matter of costs and earnings, but is influenced by various factors, such as supply and demand matching, flow allocation, arrival time, the necessity of transit through storage and distribution coal bases, and the chosen transportation routes. The main contributions of the thesis are as follows:

(1) As the state promotes the construction of coal storage and distribution bases in order to ensure energy security, it is very important to incorporate these bases into the coal supply chain. This paper focuses on optimizing the transfer scheme from multiple coal sources to multiple coal consumption sites by establishing coal storage and distribution bases. Coal can either be directly transported from a source to a coal consumption site or stored temporarily at a distribution base before being transported to a coal consumption place. In the transportation optimization model considering the inventory of multilevel nodes in the supply chain, we compare scenarios with and without the inclusion of coal storage and distribution bases. The analysis reveals that the cost savings achieved by using storage and distribution bases outweigh the increased costs of small-volume transportation. Specifically, the total cost is reduced by 5.9%, and inventory costs are reduced by 5.2%. Additionally, the construction of storage and distribution bases lowers the overall amount of inventory held, allowing coal consumption sites to maintain lower safety stock levels.

(2) To comply with the trend of refined supply chain management, this paper introduces a spatio-temporal state network, which describes the transportation process from a coal source to a coal-consuming place in fifteen-minute intervals using transportation arcs, storage arcs, and trans-shipment arcs, and describes the storage and trans-shipment operations in detail at the temporal level. Correspondingly, storage and trans-shipment operations are detailed at the temporal level. For power plants and coal chemical plants within coal enterprises, which consume coal at a specific rate for production, this paper details coal demand on an hourly basis to ensure a stable supply for uninterrupted production. In the transportation optimization model that considers the inventory of multilevel nodes in the supply chain, we compare scenarios with and without refining demand to the hour. Meeting demand within a specified time window can lead to significant inventory fluctuations, and the values of the demand interval and time windows are often dependent on empirical data. Thus, refining the rate of coal consumption to an hourly basis is more scientific and objective. This refined approach ensures that coal demand is met precisely, minimizing inventory costs and stabilizing the supply chain.

(3) This paper focuses on the collaborative optimization of coal resource enterprises within the framework of production, transportation, and sales integration. Building on the aforementioned inventory cost model, it incorporates the total return of the enterprise post-integration and aims to optimize for maximum total return. Compared to a transportation scheme that minimizes total cost, the transportation paths for minimizing total cost and maximizing total revenue are identical for the same batch of coal. However, the decision to dispatch each batch is based on the revenue from production, transportation, and sales. This paper examines transportation schemes under different coal prices, comparing the revenue of production divisions, transportation divisions, and sales divisions at different coal price points. When the coal price is reduced by 10%, the total revenue is 97.78% of the base price revenue, indicating a minimal decline. Conversely, when the coal price is increased by 10%, the total revenue is 110.35% of the revenue of the base price revenue. This demonstrates that the integrated model of production, transportation, and sales can effectively reduce the total costs and maximize revenue by balancing coal supply and demand. The findings suggest that this integrated approach can reduce risks associated with coal price fluctuations and yield greater overall benefits. Although this paper proposes a comprehensive optimization scheme, the integration of coal production, transportation, and sales is a complex process with numerous components and a broad scope. Thus, further in-depth research is necessary, particularly in the following areas:

(1): Further consideration of the impact of coal types is necessary, as supply and demand conditions and prices differ for various types of coal in actual transportation processes.
(2): In this paper, considering the time factor dramatically increased the problem’s complexity. To simplify, we introduced k batches of a coal preparation set, but in actual transportation problems it is necessary to determine actual transportation volumes, which requires further improvement.
(3): The transportation scheme studied in this paper did not consider the weather or other unforeseen circ*mstances. Future research should incorporate these variables to enhance the model’s robustness.
(4): The primary focus of this paper is deterministic warehousing planning based on optimization techniques. Due to the scope and length constraints, this study did not delve into related optimization algorithms. Future research will aim to design heuristic optimization algorithms to address large-scale problems.
(5): This paper did not address the predictions of the distribution model. In future research, appropriate machine learning models will be established based on relevant historical data to improve predictive accuracy.