Empty and heavy container joint optimization scheduling method considering foldable container and sea-land combined transportation

Abstract

The invention relates to an empty and heavy container joint optimization scheduling method considering foldable containers and sea-land combined transportation, which can solve the problems of high transportation cost, low container turnover efficiency and long cargo transportation period in the existing empty container transportation. Decision variables such as heavy box path selection, empty box dispatching quantity and path, folding equipment purchase and quantity of folding and unfolding foldable boxes are introduced into the mathematical planning model of the scheme for description, particularly, the states of the foldable boxes are subdivided into unfolding and folding states, the states are allowed to be flexibly converted according to the requirements of ports or stations in the empty box dispatching process, and therefore, the folding efficiency is improved. The cost reduction benefit of the foldable box can be better analyzed, and a new decision dimension is added for the empty box allocation and transportation problem. And meanwhile, by combining real factors such as time irreversibility and geographical location accessibility, the method is more suitable for the actual operation condition of a shipping company. In addition, a solution algorithm is provided, a satisfactory and feasible solution can be obtained within acceptable time for large-scale examples, and the method has excellent performance and applicability.

Description

Technical Field

[0001] The present disclosure relates to maritime transport, and in particular to a method for joint optimization scheduling of empty and loaded containers considering foldable containers and sea-land combined transport. Background Art

[0002] As the most important and economically efficient mode of transport in the global trade system, maritime transport plays a key role in connecting international trade. Container transport, as an efficient, safe, and standardized method of loading and unloading, has become a crucial means of global maritime cargo transportation. However, due to regional imbalances in economic and trade, the demand and supply of containers in different regions are significantly unbalanced. This has led to a large accumulation of empty containers at ports and terminals in many importing countries, while ports and terminals in exporting countries face a severe shortage of empty containers. This has led to a large number of empty container transfers, significantly increasing costs and wasting resources.

[0003] There are currently three main strategies to address the empty container transportation problem. The first is container leasing, but its high rental costs make widespread adoption unrealistic. The second is the use of collapsible containers, which are seen as a potential solution to reduce transportation costs by reducing their size. Collapsible containers can save 75% of space during transportation, reducing unit transportation and storage costs. However, the high manufacturing cost of collapsible containers, and the specialized equipment and operators required for folding and unfolding, have hindered their development. The third strategy is to redistribute empty containers from areas with an excess to areas with a shortage. The efficient and economical transfer of empty containers from areas with an oversupply to areas with a shortage is known as the empty container reallocation problem, or empty container redistribution. The core of this problem lies in optimizing resource allocation to reduce the costs associated with empty container redistribution. Excess empty containers often need to be transported around the globe, with empty container redistribution costs accounting for 30% of total costs by sea and 40% by land. Therefore, reducing empty container redistribution costs is of great operational value to shipping companies.

[0004] As a core component of the container logistics system, loaded container transport carries the crucial task of efficiently and safely transporting all kinds of goods from production sites to consumption locations. Fluctuations in global trade lead to dynamic fluctuations in the demand for loaded container transport. Loaded container transport is not only a process for transporting goods; it also triggers demand for empty containers, reshapes transportation routes, and restructures cost structures. Loaded container transport and empty container transfer are closely linked. Once a loaded container arrives at its destination and is unloaded, it becomes an empty container, preparing for the next round of transport. Empty container transfer is responsible for timely and appropriate redistribution of empty containers back to the source or to other locations in need to meet cargo loading needs. The conversion of empty and loaded containers is influenced by factors such as trade flows and transportation efficiency. These factors are interdependent and jointly drive the continuous operation of the logistics chain. Therefore, reducing costs across the entire container transport chain requires a comprehensive consideration of both loaded container transport and empty container transfer.

[0005] The importance of joint scheduling of empty and loaded containers lies in its ability to optimize resource allocation and maximize efficiency. By comprehensively considering factors such as the transportation demand, routing, and time of loaded and empty containers, joint scheduling can develop more reasonable and efficient transportation plans. This not only reduces transportation costs but also improves container turnover efficiency and shortens cargo transportation cycles. In today's complex and volatile trade environment and customer demands, joint scheduling of empty and loaded containers has become a key means of enhancing logistics competitiveness and supply chain flexibility. Therefore, strengthening the research and application of joint scheduling of empty and loaded containers is of great significance to the development of the container logistics industry. Summary of the Invention

[0006] To address the aforementioned issues in the existing technology, this paper proposes a method for optimizing the combined scheduling of empty and loaded containers, taking into account both collapsible containers and sea-land transport. By constructing an integer programming model and designing an acoustic search algorithm, this method solves the combined sea-land scheduling problem for empty and loaded containers. The specific technical solution is as follows.

[0007] On the one hand, this case proposes a joint optimization scheduling method for empty and heavy containers considering foldable containers and sea-land transport. The method includes: establishing a mathematical programming model for the joint scheduling of empty and heavy containers, whose objective function is to minimize the sum of the heavy container transportation cost, empty container transfer cost, container rental cost, folding equipment purchase cost and folding and unfolding operation cost. The decision variables include the empty and heavy container scheduling quantity and transportation path at each time node in the planning period, the empty container rental quantity, folding equipment purchase, and folding and unfolding empty container quantity at each time node in the planning period. The constraints include the heavy container transportation stage constraints, the empty container transfer stage constraints, the empty and heavy container relationship constraints, the sea-land combined transportation space-time network constraints, and the variable selection. Value range constraints; for each cargo order, based on time irreversibility and the reachability between geographical nodes, a transportation path is generated through a heuristic algorithm, and the transportation paths of all cargo orders are combined to form a heavy container transportation path plan, which is substituted into the empty and heavy container joint scheduling mathematical programming model for solution to obtain the empty and heavy container joint scheduling plan; the transportation path r of a cargo order is expressed as (b1|t)→(m|t′)→…→(b2|t"), where b1 is the shipping station and t is the departure time of the shipping station; m is the port or other station passed through along the way, and t′ is its corresponding time; b2 is the receiving station and t" is the arrival time of the receiving station.

[0008] In one embodiment of the above technical solution, the method also includes a search step: a number of initial heavy box transport path plans are used to form a heavy box transport path plan library, each heavy box transport path plan is substituted into the empty and heavy box joint scheduling mathematical programming model for solution, and the objective function value corresponding to each heavy box transport path plan is obtained; based on each cargo order, a new heavy box transport path plan is generated, and it is substituted into the empty and heavy box joint scheduling mathematical programming model for solution, and its corresponding objective function value and the empty and heavy box joint scheduling plan are obtained; based on the objective function value, when the new heavy box transport path plan is better than the worst heavy box transport path plan in the heavy box transport path plan library, the new heavy box transport path plan is used to replace the worst heavy box transport path plan in the heavy box transport path plan library to realize the update of the heavy box transport path plan library; if the termination condition is met, the empty and heavy box joint scheduling plan corresponding to the best heavy box transport path plan in the heavy box transport path plan library is used as the final empty and heavy box joint scheduling plan; if the termination condition is not met, the above steps are repeated.

[0009] In one embodiment of the above technical solution, the termination condition setting step includes: setting an accuracy threshold l and a comparison interval number n; if the absolute value of the difference between the kth iteration result μ and the knth iteration result σ is less than or equal to the preset accuracy threshold l, the algorithm is deemed to have reached the termination condition.

[0010] In one embodiment of the above technical solution, the step of generating a new heavy box transportation path plan based on each cargo order includes: for each cargo order cj, a new transportation path is generated according to the following formula:

[0011]

[0012] Where: Represents the set of transport routes for cargo order cj in the heavy-box transport route solution library. represents the transportation path of cargo order cj generated by a heuristic algorithm based on time irreversibility and reachability between geographical nodes, α1 represents a random number uniformly distributed between [0, 1], HMS represents the size of the heavy-box transportation path solution library, and HMCR represents the selection probability of the heavy-box transportation path solution library;

[0013] For each goods order cj from The departure time of the selected transport route is disturbed, and based on the new departure time after the disturbance, a new transport route is generated through a heuristic algorithm taking into account the irreversibility of time and the accessibility between geographical nodes;

[0014] The new transport routes for all cargo orders constitute a new heavy-box transport route plan.

[0015] In one implementation of the above technical solution, the disturbance strategy is:

[0016]

[0017] Where: α2 represents a random number uniformly distributed between [0, 1], bw represents the amplitude of the departure time disturbance, and PAR represents the disturbance variation probability of the cargo order transportation path.

[0018] Secondly, this case proposes a joint optimization scheduling system for empty and heavy containers, which includes a building module and a solving module; the building module is configured to: establish a mathematical programming model for the joint scheduling of empty and heavy containers, whose objective function is to minimize the sum of the heavy container transportation cost, empty container transfer cost, container rental cost, folding equipment purchase cost and folding and unfolding operation cost; the decision variables include the empty and heavy container scheduling quantity and transportation path at each time node during the planning period, the empty container rental quantity, folding equipment purchase, and folding and unfolding empty container quantity at each time node during the planning period; the constraints include the heavy container transportation stage constraints, the empty container transfer stage constraints, the empty and heavy container relationship constraints, the sea-land combined transportation space-time network constraints and the variable value range constraint; the solving module is configured to: for each cargo order, based on time irreversibility and the reachability between geographical nodes, generate a transportation path through a heuristic algorithm, and combine the transportation paths of all cargo orders to form a heavy container transportation path plan, substitute the plan into the empty and heavy container joint scheduling mathematical programming model for solution, and obtain the empty and heavy container joint scheduling plan; wherein the transportation path r of the cargo order is expressed as (b1|t)→(m|t′)→…→(b2|t″), b1 is the shipping station, t is the departure time of the shipping station; m is the port or other station passed through in the middle, t′ is its corresponding time; b2 is the receiving station, t″ is the arrival time at the receiving station.

[0019] On the third aspect, this case proposes a computer-readable storage medium storing a computer program that can be loaded by a processor and execute any of the above methods.

[0020] Beneficial technical effects of this case: This solution solves the complex problem of joint scheduling of empty and heavy containers and improves transportation efficiency. By adopting a mathematical model, it effectively integrates multiple decisions such as container heavy container transportation, empty container transfer, and foldable container application, and can provide one-stop decision support for shipping companies' related business operations. Through the model constructed based on the dynamic space-time network, it is possible to accurately characterize a series of dynamic relationships such as ship voyages, dynamic characteristics of ship schedules, empty and heavy container conversions, and foldable container state conversions, so that the optimization decision results of empty and heavy container transportation are more in line with actual needs. By developing a heuristic algorithm, the problem that common solvers cannot solve under large-scale examples is solved. First, a heavy container transportation path plan is randomly generated, and then it is substituted into the mathematical model to solve the empty container transfer plan, equipment purchase plan, folding and unfolding plan of foldable boxes, container rental plan, and comprehensive cost, which can obtain a satisfactory solution to the problem in a relatively short time. BRIEF DESCRIPTION OF THE DRAWINGS

[0021] In order to more clearly illustrate the technical solutions in the embodiments of the present application, the following briefly introduces the drawings required for use in the description of the embodiments. Obviously, the drawings described below are only some embodiments of the present application. For ordinary technicians in this field, other drawings can be obtained based on these drawings without any creative work.

[0022] Figure 1 , schematic diagram of the network structure for the joint sea and land dispatch of empty and heavy containers.

[0023] Figure 2 , Schematic diagram of the flow balance of containers in different states at port nodes.

[0024] Figure 3 , flow balance diagram of containers in different states at the terminal node.

[0025] Figure 4 , pseudocode diagram of harmony search algorithm.

[0026] Figure 5 , Schematic diagram of the flow conversion relationship of containers in different states at ports and terminals. DETAILED DESCRIPTION

[0027] The existing methods for solving the empty container transportation problem have problems such as the mathematical model is not realistic enough and the solver cannot solve the problem or is inefficient.

[0028] Existing mathematical models for optimizing empty container transportation rarely consider both the spatiotemporal network of sea-land intermodal transport and loaded container transport. These models often fail to fully incorporate the unique characteristics of sea-land intermodal transport, such as the connection efficiency and cost differences between different modes of transport, resulting in limitations in solving practical problems. Furthermore, considerations of loaded container transport are often simplistic, failing to accurately reflect its dynamic impact on empty container supply, empty container transport routes, and the overall cost structure, and ignoring the conversion relationship between loaded and empty containers.

[0029] Second, existing empty container dispatch optimization models fail to consider the dynamic properties of collapsible containers in various states within the transportation network. Because most studies focus solely on empty container dispatch, collapsible containers are often assumed to be in a folded state. However, in an intermodal sea-and-land transport network for both empty and loaded containers, collapsible containers dynamically transition between "expanded" and "folded." Specifically, the state of a collapsible container depends on decisions such as whether it is loaded or empty and whether it requires pre-folding or unfolding at a location with collapsible equipment.

[0030] Finally, existing empty container transportation optimization modeling is mainly based on spatial transportation networks. This type of model greatly simplifies the time-related characteristics of container transportation, such as multiple voyages and multiple ship schedules, resulting in limited decision-making effectiveness in dynamic environments.

[0031] As for solvers, the empty container dispatch optimization problem, which simultaneously considers collapsible containers, loaded container transport, and the spatiotemporal network of sea-land intermodal transport, is inherently an NP-hard problem. The core empty container dispatch problem has been proven to be NP-hard. This means that as the problem scale increases, the potential path selection combinations increase exponentially, greatly increasing the complexity of the solution. Conventional solvers often struggle to guarantee effective solutions for models with exponentially growing variables and constraints. This is especially true for large-scale and even medium-scale cases, where feasible solutions cannot be obtained within a reasonable timeframe.

[0032] To address the aforementioned technical issues, this case established a mathematical programming model for the joint scheduling of empty and loaded containers, taking into account foldable containers and sea-land intermodal transport. By developing a harmonic search algorithm, the problem was successfully solved efficiently. In particular, for large-scale problems, it was able to effectively find high-quality, optimal empty and loaded container scheduling solutions within a reasonable timeframe. The constructed model fully considers the temporal and spatial characteristics of transportation, constructing a space-time transportation network. On this basis, multiple decisions were introduced, including the application of foldable containers, the purchase of folding equipment, the leasing of empty containers, and the joint scheduling of empty and loaded containers. With the goal of minimizing comprehensive operating costs, the optimal empty container leasing plan, folding equipment purchase plan, and folding and unfolding plan for foldable containers were determined during the planning period, along with the optimal joint sea-land scheduling plan for empty and loaded containers.

[0033] The following provides a clear and complete description of how the technical solution of this case is implemented. Obviously, the described implementation methods are only part of the implementation methods of this case, not all of them. Based on the implementation methods of this case, all other implementation methods obtained by ordinary technicians in this field without making any creative efforts are within the scope of protection of this application.

[0034] (1) Problem description

[0035] Considering the empty and loaded container sea-land joint dispatching network of foldable containers Figure 1As shown, the network consists of two types of nodes: port nodes and inland terminal demand nodes. Port nodes can be located at nearby major international ports (such as Shanghai, Busan, and Singapore), while inland terminal demand nodes are inland container hubs. Within the entire spatiotemporal network framework for joint sea-and-sea scheduling of empty and loaded containers, the supply and demand for both loaded and empty containers originate from inland terminals. The problem can be divided into two interrelated parts: loaded container transportation and empty container dispatching. In the loaded container transportation part, due to the supply and demand relationships between different terminals, each batch of loaded containers has clear departure and arrival terminals. Therefore, a reasonable loaded container transportation plan must be developed to deliver the cargo to the inland demand terminal. The empty container dispatching part, on the other hand, requires a rational conversion relationship between loaded and empty containers. Specifically, after a loaded container arrives at the demand terminal, the cargo is unloaded and delivered to the customer, and the loaded container becomes an empty container. At this point, a reasonable empty container dispatching plan must be developed to meet the empty container demand at each terminal. In addition, the terminal nodes covered by each port node are connected to its corresponding port node, and the range covered by each port node is defined as a port area, which includes the port node and the inland terminal nodes covered by the port node. Direct transportation of loaded containers and transfer of empty containers are not possible between inland terminals in different port areas.

[0036] The entire planning period is divided into |T| time nodes. During this period, decisions must be made regarding the purchase of folding equipment (which incurs equipment purchase costs). Only after the port or terminal has purchased the folding equipment can the folding and unfolding of foldable containers be performed, which incurs operational costs. Furthermore, decisions must be made during the planning cycle regarding loaded container transport routes, empty container transfer volumes, empty container transfer routes, and empty container leasing volumes.

[0037] How to use appropriate methods, fully consider the application of foldable containers and the transportation of loaded containers within the specified time, and combine them with the sea-land transport network to arrange a joint sea-land dispatch plan for empty and loaded containers to reduce the overall cost (including the cost of loaded container transportation, the cost of empty container dispatch, the cost of equipment purchase, the cost of folding and unfolding, and the cost of renting empty containers) is of vital importance for sea-land container operators, shipping companies and ports.

[0038] The combined transport cost of empty and loaded containers refers to the sum of direct and indirect costs incurred from receiving information to arranging the transport of loaded and empty containers. The costs associated with these transports have a significant impact on shipping companies.

[0039] (1.1) Several factors are closely related to the cost of the heavy container transportation stage.

[0040] (1.1.1) Demand for full container loads

[0041] The impact of each terminal's heavy container demand on heavy container transport costs is obvious. The greater the heavy container demand determined by OD for cargo flow, the greater the volume of cargo that needs to be transported. All other things being equal, the higher the total heavy container transport cost, including both sea and land transport costs.

[0042] (1.1.2) Unit transportation cost of a heavy container and related costs

[0043] Heavy-load container transportation utilizes multimodal transport, resulting in different transportation costs depending on the mode of transport. The total heavy-load container transportation cost is the sum of the transportation costs for all batches of cargo orders. The transportation cost of each batch of cargo orders depends on the volume shipped and the transportation route. The transportation process for each batch of heavy-load container orders from the supply point to the demand point consists of three cost components: 1) the transportation cost from the supply terminal to the port in the port area; 2) the transportation cost between ports; and 3) the transportation cost from the port to the demand terminal.

[0044] After the above analysis, it can be concluded that the main cost in the heavy container transportation stage is the heavy container transportation cost.

[0045] (1.2) Several factors closely related to the cost of the empty container transportation stage.

[0046] (1.2.1) Empty container transport quantity and empty container unit transport cost

[0047] Empty container transport costs, similar to loaded container transport costs, are determined by the number of empty containers transported and their unit cost. They represent the total transportation cost of transporting a certain number of empty containers from a supply point to a demand point. The combined sea-land container transport process includes two major stages: sea and land. Therefore, the in-transit costs of empty containers are primarily composed of sea and land transport costs, encompassing four components: 1) Inter-terminal transport costs within the same port area; 2) Inter-port transport costs; 3) Inter-port to terminal transport costs within the same port area; and 4) Inter-terminal to port transport costs within the same port area.

[0048] (1.2.2) Empty container rental quantity and unit rental cost

[0049] When container supply is insufficient or due to cost considerations, shipping companies may choose to lease empty containers to meet demand. Empty container leasing costs are primarily determined by the number of empty containers leased and the unit cost of leasing. Therefore, shipping companies or logistics companies must consider the economic and reasonable nature of leasing costs when formulating their leasing strategies.

[0050] (1.2.3) Purchase of folding equipment at ports and terminals

[0051] Equipment purchase costs refer to the fixed costs of the equipment required to fold and unfold collapsible containers. This equipment primarily facilitates the folding and unfolding of collapsible containers, leveraging their volume to facilitate storage and transportation, thereby reducing costs. Folding and unfolding collapsible containers presupposes the availability of folding equipment at the port or terminal. Therefore, it's crucial to determine when ports or terminals should purchase this equipment.

[0052] The equipment purchase incurs fixed costs. The subsequent folding and unfolding of the collapsible container incurs a certain operational cost per unit, which is related to the number of collapsible containers folded and unfolded, and is a variable cost. Shipping companies need to consider the long-term cost advantages of collapsible containers and make appropriate decisions about when and where to purchase folding and unfolding equipment to meet the folding and unfolding needs of collapsible containers and save on transportation and storage costs during the empty container movement process.

[0053] Through the above analysis, we can summarize the cost structure of the empty container transportation stage: 1) the transportation cost of the empty container in transit 2) the purchase cost of the folding equipment 3) the folding and unfolding cost of the foldable box 4) the empty container rental cost.

[0054] (2) Mathematical programming model

[0055] The mathematical programming model constructed aims to minimize comprehensive operating costs (including the sum of loaded container transportation costs, empty container dispatching costs, container rental costs, folding equipment purchase costs, and folding and unfolding operation costs). The decision variables include the dispatch volume and transportation routes of empty loaded containers at each time point during the planning period, as well as the number of empty container rentals, folding equipment purchases, and folding and unfolding empty containers at each time point during the planning period. Based on the spatiotemporal network of combined sea and land transportation, and given the demand for loaded container transportation, an integer linear programming model is developed for this problem. The details are as follows.

[0056] (2.1) Basic assumptions

[0057] (2.1.1) Have sufficient number of ships and fleets of different specifications to meet cargo loading needs.

[0058] (2.1.2) Capacity limitations of ports or terminals are not considered.

[0059] (2.1.3) Rental containers at the terminal are available immediately on site, and there is no limit on the number of containers that can be rented.

[0060] (2.1.4) The cost of unloading empty loaded containers and the cost of converting loaded containers into empty containers are not included in the total comprehensive cost. The loss or damage of containers is not considered during the loaded container transportation stage or the empty container transfer stage.

[0061] (2.1.5) There is no supply and demand for empty containers at ports, but there is supply and demand for empty containers at inland terminals.

[0062] (2.1.6) The size of a standard container and a collapsible container in its unfolded state is 20 feet (1 TEU), and the size of a collapsible container in its folded state is 1 / 4 TEU.

[0063] (2.1.7) The empty containers required by the terminal are all 20 feet. Therefore, before the foldable containers are transported to the terminal, they need to be unfolded using folding equipment. Standard containers can be used directly to meet customer needs.

[0064] (2.1.8) The unit costs of a collapsible container in its unfolded state are the same as those of a standard container.

[0065] (2.2) Collection

[0066] P: The set of ports in the transportation network, p∈P.

[0067] B: The set of stations in the transportation network, b∈B.

[0068] M: The set of all geographical nodes in the transportation network, M = P∪B.

[0069] T: The set of time nodes in the transportation network, T = {t1, t2, t3, ...t n}.

[0070] L: The set of cargo batches in the transportation network, l∈L.

[0071] Ω: The set of OD pairs of cargo flows consisting of two different stations in the transportation network, h∈Ω={h|h=(b, b′), b∈B, b′∈B, b≠b′}.

[0072] C: A collection of different batches of cargo orders in the transportation network, including batch information, shipping location node information, and receiving location node information, c∈C={c|c=(l,h),l∈L,h∈Ω}.

[0073] O F : The set of virtual supply points for heavy containers determined by the OD pairing of cargo flows at two different terminals, including the OD pairing of cargo flows and the specified delivery location node information, P F ={o|o=(h, b), h=(b, b′)∈Ω, b∈B, b≠b′}.

[0074] D F : The set of virtual demand points for heavy containers determined by the OD pairing of cargo flows at two different stations, including the OD pairing of cargo flows and the specified receiving location node information, D F ={d|d=(h, b′), h=(b, b′)∈Ω, b′∈B, b≠b′}.

[0075] O E: The set of empty box virtual supply nodes in the network, O E ={i|i=(w, t′), w=(b, t)∈W, b∈B, t′>t}, that is, the number of empty containers arriving at station b at time t at time t′.

[0076] D E : The set of empty box virtual demand nodes in the network, D E ={j|j∈B}, that is, there is a demand for empty containers only at the terminal.

[0077] W: A two-dimensional set of nodes in the sea-land combined transport network composed of different times and geographical locations, W = {w|w = (m, t), m∈M, t∈T}.

[0078] V F : A collection of nodes in the heavy box supply and demand network, V F ={o, d, w|o, d, w∈O F ∪D F ∪W}.

[0079] V E : empty container supply and demand network node set, V E ={i, j, w|i, j, w∈O E ∪D E ∪W}.

[0080] V: The set of all nodes in the space-time network for joint sea-land dispatch of empty and heavy containers, V = {v|v∈V E ∪V F}.

[0081] A: The set of all arcs in the space-time network of the joint sea-land dispatch of empty and loaded containers, A = {a|a = (v, v′), v∈V, v′∈V, v≠v′}.

[0082] (2.3) Parameters

[0083] F v : Fixed cost of purchasing folding equipment at node v, v∈W.

[0084] The unit transportation cost of empty standard containers and unfolded foldable containers between nodes v and v′, including the unit transportation cost at sea and the unit transportation cost on land, v∈W, v′∈W, v≠v′.

[0085] The unit transportation cost of the folded empty foldable container between the v node and the v′ node includes the unit transportation cost at sea and the unit transportation cost on land, v∈W, v′∈W, v≠v′.

[0086] The unit empty container rental cost of leasing a standard empty container at node v, v∈W.

[0087] The unit empty container rental cost of the v node leasing the unfolded state collapsible container, v∈W.

[0088] The unit operation cost of collapsing a collapsible empty box at v nodes, v∈W.

[0089] The unit operation cost of unfolding a collapsible empty box at a v-node, v∈W.

[0090] θ vv′ : The unit transportation cost of a heavy box (cargo container) between the v node and the v′ node, including the unit transportation cost at sea and the unit transportation cost on land, v∈W, v′∈W, v≠v′.

[0091] The maximum transportation capacity limit between node v and node v′, v∈W, v′∈W, v≠v′.

[0092] β mm′ : The reachability between node m and node m′, 1 means that node m and node m′ are reachable; 0 means that node m and node m′ are unreachable, m∈M, m′∈M, m≠m′.

[0093] Each order batch uses the number of standard containers to load the goods, c∈C.

[0094] The number of loaded boxes of goods in each order batch using unfolded foldable containers, c∈C.

[0095] γ: The volume ratio coefficient between the unfolded and folded states of the foldable container, which is consistent with the relevant unit cost ratio coefficient of the two states.

[0096] qc: the total number of heavy boxes in each order batch, c∈C.

[0097] D b : The total demand for empty containers at station b within the planning period T, b∈B.

[0098] r: The number of full boxes converted into empty boxes per unit time.

[0099] G: A very large number.

[0100] (2.4) Decision variables

[0101] x cvv′ : 0-1 variables, c∈C, v∈VF ,v′∈V F , v≠v′, indicating whether the order batch c passes through the (v, v′) arc segment formed by the v node and the v′ node during the heavy container transportation process.

[0102] Integer variable, representing the number of empty standard containers transferred from node v to node v′, v∈V E ,v′∈V E , v≠v′.

[0103] Integer variable representing the number of empty foldable containers in the expanded state transferred from node v to node v′, v∈V E ,v′∈V E , v≠v′.

[0104] Integer variable representing the number of empty foldable containers transported from node v to node v′, v∈V E ,v′∈V E , v≠v′.

[0105] z v : A 0-1 variable indicating whether node v purchases the folding and unfolding equipment for the foldable container, v∈W.

[0106] An integer variable representing the number of empty standard containers leased by node v, v∈W.

[0107] An integer variable representing the number of empty foldable containers leased in the expanded state at node v, v∈W.

[0108] An integer variable representing the number of foldable containers folded by node v using the folding and unfolding device, v∈W.

[0109] An integer variable representing the number of foldable containers unfolded by node v using the folding and unfolding device, v∈W.

[0110] (2.5) Dependent variable

[0111] Integer variable, representing the number of empty standard containers supplied by terminal b at time t, i∈O E .

[0112] Integer variable, representing the number of empty foldable containers in the unfolded state supplied by terminal b at time t, i∈O E .

[0113] (2.6)Objective function:

[0114]

[0115] The objective function includes the transportation cost of full containers, the transportation cost of empty containers, the purchase cost of folding equipment, the operation cost of folding and unfolding, and the cost of renting empty containers.

[0116] (2.7) Constraints

[0117] The constraints of the joint sea-land dispatching model for empty and loaded containers considering foldable containers mainly include the following five aspects, namely, the constraints on the loaded container transportation stage, the constraints on the empty container dispatching stage, the constraints on the relationship between empty and loaded containers, the spatiotemporal network constraints, and the constraints on the variable value range.

[0118] 1. Constraints in the heavy container transportation stage

[0119]

[0120] Constraint (1) represents the connection constraint between the virtual heavy container supply node and the sea-land intermodal transport network. Constraint (2) represents the connection constraint between the virtual heavy container demand node and the sea-land intermodal transport network. Constraint (3) represents the flow balance constraint in the sea-land intermodal transport network.

[0121] 2. Constraints during the empty container transportation phase

[0122]

[0123] Constraint (4) represents the overall empty container flow balance constraint of each port node at each time node in the sea-land combined transport network. Constraint (5) represents the flow balance constraint of empty standard containers at the port node. Constraint (6) represents the flow balance constraint of empty foldable containers at the port node in the folded state. Constraint (7) represents the flow balance constraint of empty foldable containers at the port node in the unfolded state. The flow balance of containers in each state of the port node is as follows: Figure 2 shown.

[0124]

[0125] Constraints (8)-(11) indicate that the port node can only perform folding and unfolding operations on the foldable container if it has purchased the folding and unfolding equipment.

[0126]

[0127] Constraint (12) represents the overall empty container flow balance constraint of each terminal node at each time node in the sea-land combined transport network. Constraint (13) represents the flow balance constraint of the empty standard container at the terminal node. Constraint (14) represents the flow balance constraint of the empty foldable container at the folded state at the terminal node. Constraint (15) represents the flow balance constraint of the empty foldable container at the unfolded state at the terminal node. The flow balance of containers in each state at the terminal node is as follows: Figure 3 shown.

[0128]

[0129] Constraints (16)-(19) indicate that the terminal node can only perform folding and unfolding operations on the foldable container if it has purchased the folding and unfolding equipment.

[0130]

[0131] Constraint (20) represents the total empty container demand at each terminal during the planning period.

[0132]

[0133] Constraint (21) indicates that each port or terminal node can only purchase folding equipment once during the unit planning period.

[0134] 3. Empty and loaded container relationship constraints

[0135]

[0136] Constraint (22) indicates the number of empty containers converted from the total number of standard containers arriving at terminal b at time t′.

[0137]

[0138] Constraint (23) indicates the number of empty containers that are converted from the total number of loaded foldable containers in the unfolded state arriving at terminal b at time t′.

[0139]

[0140] Constraints (24) and (25) represent the flow constraints of the empty container supply at station b at time t, that is, the maximum empty container supply at the current time cannot be exceeded.

[0141]

[0142]

[0143] Constraints (26)-(29) indicate that a loaded container arriving at terminal b at time t′ can only be converted into an empty container at time t>t′.

[0144]

[0145] Constraint (30) represents the transport path capacity limit in the sea-land combined transport space-time network.

[0146] 4. Space-time network constraints

[0147]

[0148] Constraint (31) represents the time irreversibility constraint in the sea-land combined transport space-time network.

[0149]

[0150] Constraints (32)-(34) represent the accessibility constraints between ports, between terminals, and between ports and terminals.

[0151]

[0152]

[0153] Constraints (35)-(41) represent constraints on the characteristics of the heavy-box virtual node, that is, they stipulate the arc connection restrictions between the virtual heavy-box supply node and the virtual heavy-box demand node.

[0154]

[0155] Constraints (42)-(50) represent constraints on the empty container virtual node characteristics, that is, they stipulate the arc segment connection restrictions between the virtual empty container supply node and the virtual empty container demand node.

[0156] 5. Variable value range constraints

[0157]

[0158]

[0159] Constraints (51)-(61) define the domain of the variables in the model, including the variable value range constraints in the loaded container transportation stage and the empty container transfer stage.

[0160] In summary, the above integer linear programming model addresses existing research on the empty container dispatching problem by incorporating multiple real-world factors, including the use of collapsible containers, loaded container transportation, and the spatiotemporal network of sea-land intermodal transport. Existing empty container dispatching optimization models fail to comprehensively consider and effectively integrate these factors. However, the mathematical programming model described above addresses these issues by introducing decision variables such as the selection of loaded container transport routes, the purchase of folding equipment, and the number of collapsible containers that can be folded or unfolded. The collapsible containers are subdivided into two states, unfolded and unfolded, allowing for flexible state transitions during empty container dispatching based on port or terminal requirements. This allows for better analysis of the cost-saving benefits of collapsible containers and adds a new decision-making dimension to the empty container dispatching problem. Furthermore, the integer linear programming model comprehensively considers the multi-dimensional transportation network composed of time and space, fully simulating the complex process of combined sea-land dispatching of empty and loaded containers. Furthermore, by incorporating real-world factors such as the irreversibility of time and geographic accessibility, the overall modeling difficulty and complexity are increased, making it more relevant to the actual operations of shipping companies.

[0161] (3) Model solution method

[0162] Because existing solvers perform poorly in large-scale and even medium-scale cases, exceeding the computer's maximum running memory, it is impossible to obtain feasible solutions within an acceptable time.

[0163] To solve this problem, the present invention develops a heuristic algorithm to split the problem into two parts. First, a heavy box transportation path plan is randomly generated, and then it is substituted into the mathematical model and solved using the solver to obtain a satisfactory solution in a relatively short time.

[0164] Specifically, with the goal of minimizing the overall cost, decisions are made within the planning cycle regarding the volume and transportation route of each cargo order, the volume and transportation route of empty containers, when to rent empty containers and the number of empty containers to rent, when to purchase folding equipment, and the number of foldable containers to be folded and unfolded. If the transportation route of each heavy container cargo order is known, it is converted into the relevant decision variables and corresponding values in the heavy container transportation model, and substituted into the entire empty and heavy container joint scheduling mathematical model. The solver can be used to give the objective function value of the entire problem and the empty and heavy container decision plan in a short time. Therefore, the difficulty lies in how to randomly generate the transportation route for each heavy container cargo order. This patent is based on the framework of the harmony search algorithm and uses the idea of a search tree to generate the transportation route, which is then substituted into the mathematical model as a known parameter to solve the empty and heavy container joint scheduling problem. This case does not limit the specific type of solver.

[0165] The process of the above harmony search algorithm is as follows.

[0166] ① Initialize the optimization problem and algorithm parameters:

[0167] Firstly, the elements in the harmony search algorithm are compared with the relevant elements in the cost minimization problem and the relevant parameters of the harmony search algorithm are initialized, including the size of the initial heavy-box transport path solution library (HMS), the selection probability of the heavy-box transport path solution library (HMCR), the perturbation mutation probability (PAR) of the cargo order transport path, the perturbation amplitude (bw) of the cargo order transport path, the algorithm termination accuracy threshold, etc.

[0168] ② Initialize the heavy container transport path solution library:

[0169] For each cargo order in a heavy-load transport, a transport path r is generated using a heuristic algorithm. r is expressed as (b1|t)→(m|t′)→…→(b2|t"), where b1 is the shipping station and t is the departure time from the shipping station; m is the port or other station passed through along the way, and t′ is its corresponding time; b2 is the receiving station and t" is the arrival time at the receiving station. If there is reachability between the shipping station and the receiving station, then other geographical nodes may or may not be passed through. This shows that the transport path of a cargo order is composed of different two-dimensional nodes connected together. Each two-dimensional node is represented by (geographic node|time) and represents a port or station at a specific time.

[0170] The combination of all cargo order transportation routes constitutes a complete heavy box transportation route plan P, where P = (r1, r2, ..., r n ), n represents the number of cargo orders. If the size of the heavy-box transport path solution library is set to m, m heavy-box transport path solutions P1, P2, ..., P can be generated by the heuristic algorithm. m At the same time, the objective function value must be calculated for each heavy-box transport route solution in the library. This value reflects the quality of the solution in the library. In this problem, the objective function is to minimize the overall cost, so the smaller the objective function value, the better the solution with the lowest overall cost. The specific calculation process is shown in step ③.

[0171] ③Calculate the objective function value of each heavy box transportation path plan:

[0172] Specifically, the problem is how to calculate the comprehensive cost corresponding to the heavy container transport routing plan, that is, how to derive the relevant decision-making plans for the empty container transportation phase (including the empty container transportation plan, the empty container leasing plan, the folding equipment purchase plan, and the folding and unfolding plan) under the determined heavy container transport routing plan. By substituting the variable values related to the heavy container transport routing plan as known parameters into the mathematical model of the entire problem and solving it using the solver, the objective function value of the overall problem corresponding to the current heavy container transport routing plan and the empty and heavy container joint scheduling plan are obtained.

[0173] ④Generate a new heavy container transport route plan:

[0174] This paper expands the musical instruments in the traditional harmony search algorithm into cargo orders, and the tones into feasible transportation paths for cargo orders. Therefore, it is necessary to generate a new transportation path for each cargo order. When all cargo orders have generated new transportation paths, they are combined into a new heavy box transportation path solution P new The strategy for generating new transportation routes for cargo orders is as follows.

[0175] There are three ways to generate a new transport path for each cargo order: (1) randomly select a transport path from the heavy-box transport path solution library; (2) perturb and mutate the transport path randomly selected from the heavy-box transport path solution library; (3) generate a new transport path.

[0176] Method 1: Randomly select a transport route from the heavy container transport route solution library

[0177] According to the algorithm parameter settings, each cargo order has HMS transport routes in the heavy-box transport route solution library, where HMS is the number of heavy-box transport route solutions in the heavy-box transport route solution library. Equation (62) is used to determine whether cargo order cj needs to randomly select an existing transport route from the heavy-box transport route solution library.

[0178]

[0179] Among them, α1 represents a random number uniformly distributed between [0,1]. Represents the set of transport routes for cargo order cj in the heavy-box transport route solution library. represents the transportation route generated by a heuristic algorithm for cargo order cj based on time irreversibility and reachability between geographical nodes. HMCR represents the probability of selecting a route from the existing heavy-box transportation route library. When α1 < HMCR, cargo order cj randomly selects a route from the existing heavy-box transportation route library. When α1 ≥ HMCR, a new route is generated.

[0180] Method 2: Disturbance and variation in the transportation path

[0181] For the transport path selected from the heavy-box transport path solution library in the first method, further determine whether disturbance and mutation are needed. The present invention draws on the idea of search tree to construct the transport path, in which the interval range of the random selection of nodes in each layer will be affected by the selection results of the previous layer. Therefore, the disturbance strategy for the transport path tends to disturb the departure time of the heavy-box shipping station. Based on the new departure time after the disturbance, taking into account the irreversibility of time and the accessibility between geographical location nodes, a new transport path is generated through a heuristic algorithm. Finally, a new heavy-box transport path solution consisting of the new transport paths for all cargo orders is obtained.

[0182] Specifically, for the transportation route selected from the heavy container transportation route plan library Set the departure time of the shipping yard in this transportation route as t. The specific perturbation strategy is shown in formula (63).

[0183]

[0184] Among them, α2 represents a random number uniformly distributed between [0, 1], bw represents the amplitude of departure time perturbation, generally a positive integer, and PAR represents the perturbation mutation probability of the cargo order transportation route. When α2 < PAR, the perturbation amplitude of the departure time t is between [-bw, +bw]. After the perturbation, a new transportation route needs to be generated based on the new departure time; when α2 ≥ PAR, the transportation route is not perturbed.

[0185] Method 3: Generate a completely new transportation route

[0186] According to the given formula (62), when α1 ≥ HMCR, a new transportation route is regenerated.

[0187] To sum up, for each cargo order, three strategies are proposed to generate a new transportation route. By integrating the newly generated transportation routes of each cargo order, a completely new heavy container transportation route plan P new is formed, and then the solver is used to calculate the objective function value of the new heavy container transportation route plan P new .

[0188] ⑤ Update the heavy container transportation route plan library:

[0189] First, refer to step ③ to calculate the objective function value of the new plan P new and compare it with the objective function values of each heavy container transportation route plan in the existing heavy container transportation route plan library. If the objective function value of P new is better than the objective function value of the worst heavy container transportation route plan in the heavy container transportation route plan library, then P new will replace the worst heavy container transportation route plan in the heavy container transportation route plan library, thus realizing the update of the heavy container transportation route plan library. At this time, the objective function value corresponding to the optimal heavy container transportation route plan in the heavy container transportation route plan library is the current iteration result.

[0190] ⑥ Algorithm iteration and termination:

[0191] The update iteration process of the algorithm is realized through steps ④ and ⑤. In order to improve the rationality and accuracy of the iteration, the present invention introduces two key parameters: the accuracy threshold l and the number of comparison intervals n. In the algorithm iteration process, the result μ obtained by the kth iteration is compared with the result σ of the knth iteration. If the absolute value of the difference between μ and σ is less than or equal to the preset accuracy threshold l (i.e. |μ-σ|≤l), the algorithm is deemed to have reached the termination condition, and the current optimal objective function value (comprehensive cost) and its corresponding optimal solution are output, otherwise steps ④ and ⑤ are repeated. The optimal solution includes the optimal empty and heavy box joint scheduling plan. The current iteration result is the optimal objective function value in the current heavy box transportation path plan library, rather than the objective function value of the newly generated heavy box transportation path plan. By designing this iterative termination condition, the algorithm is prevented from converging to a local optimal solution too early.

[0192] The pseudo code diagram of the harmony search algorithm is as follows Figure 4 shown.

[0193] Example of shipping routes for goods orders in the harmony search algorithm above.

[0194] Assume that there are a set of port nodes A and a set of terminal nodes B in the transportation network, where A = {p1, p2} and B = {b1, b2, b3, b4}. At the same time, the connectivity between the points is specified, where the geographical locations accessible to port p1 are {p2, b1, b2}, the geographical locations accessible to port p2 are {p1, b3, b4}, the geographical locations accessible to terminal b1 are {p1, b2}, the geographical locations accessible to terminal b2 are {p1, b1}, the geographical locations accessible to terminal b3 are {p2, b4}, and the geographical locations accessible to terminal b4 are {p2, b3}. By (L, b m , b n ) represents a goods order, where L represents the batch, b m Indicates the shipping station, b n Represents the receiving station. Each two-dimensional node in the sea-land transport network can also be represented by (geographic location node | time node). The total planning period is 5 days, i.e., T = {1, 2, 3, 4, 5}.

[0195] Assuming the cargo order is (L1, b1, b2), the cargo departure nodes may be: (b1|1), (b1|2), (b1|3), (b1|4).

[0196] If the starting node selected is (b1|1), the next nodes may be: (b2|2), (b2|3), (b2|4), (b2|5), (p1|2), (p1|3), (p1|4).

[0197] If the starting node selected is (b1|2), the next nodes may be: (b2|3), (b2|4), (b2|5), (p1|3), (p1|4).

[0198] If the starting node selected is (b1|3), the next nodes may be: (b2|4), (b2|5), (p1|4).

[0199] If the starting node selected is (b1|4), the next node may be: (b2|5).

[0200] The selection of each two-dimensional node must adhere to the constraints of time irreversibility and geographic connectivity. The possible outcomes of each node selection depend on the previous node selection. This process continues until a feasible transportation path from shipping station b1 to receiving station b2 is randomly found. In this example, the feasible transportation paths for the cargo order (L1, b1, b2) are summarized below.

[0201] Depart at 1:00: (b1|1)→(b2|2), (b1|1)→(b2|3), (b1|1)→(b2|4), (b1|1)→(b2|5), (b1|1)→(p1|2)→(b2|3), (b1|1)→(p1|2)→(b2|4), (b1|1)→(p1|3)→(b2|4), (b1|1)→(p1|2)→(b2|5), (b1|1)→(p1|3)→(b2|5), (b1|1)→(p1|4)→(b2|5).

[0202] Departure time is 2:00: (b1|2)→(b2|3), (b1|2)→(b2|4), (b1|2)→(b2|5), (b1|2)→(p1|3)→(b2|4), (b1|2)→(p1|3)→(b2|5), (b1|2)→(p1|4)→(b2|5).

[0203] Departure time is 3:00: (b1|3)→(b2|4), (b1|3)→(b2|5), (b1|3)→(p1|4)→(b2|5).

[0204] Departure time is 4:00: (b1|4)→(b2|5).

[0205] The flow conversion relationship of containers in different states at ports and terminals during the entire empty container transportation phase is as follows: Figure 5 shown.

[0206] In summary, the Harmony Search algorithm proposed in this paper addresses the joint scheduling problem of empty and loaded containers, taking into account the use of collapsible containers and sea-land transport. This problem is extremely challenging due to the complex nature of logistics networks and models. Traditional optimization methods often struggle to escape local optima and find a global optimal solution. In contrast, the Harmony Search algorithm demonstrates the following advantages:

[0207] 1. Highly versatile algorithm: The harmony search algorithm does not rely on problem-specific information and has broad applicability. It can be applied to a variety of optimization problems, including continuous optimization, discrete optimization, and mixed integer optimization, demonstrating its strong versatility.

[0208] 2. Simple principle and flexible structure: The principle of the harmony search algorithm is relatively simple, the structure is flexible, the parameters are few, and it is easy to understand and implement, so that the algorithm can be quickly combined with the empty and loaded box scheduling problem in practical applications.

[0209] 3. Strong global search capability: By introducing the harmonic memory library, the algorithm can save and utilize existing good solutions during the search process. At the same time, combined with the random selection mechanism, the algorithm has the opportunity to jump out of the local optimal solution and explore new search space, thereby enhancing the global search capability.

[0210] 4. High local search accuracy: The pitch adjustment operation in the harmony search algorithm allows fine-tuning of the harmony vectors selected from the harmony memory library, which helps the heavy box transportation path explore better solutions in the local range and improve the accuracy of the solution.

[0211] 5. Ease of integration with other algorithms: The structure and principles of the Harmony Search algorithm make it easy to integrate with other heuristic algorithms, creating hybrid algorithms with enhanced performance. By combining commercial solvers, this invention can fully leverage the strengths of different algorithms, improve the efficiency of random solution generation, and further enhance its ability to solve complex problems.

[0212] 6. Good handling of integer constraints: Ensures that the solution obtained during the optimization process satisfies integer constraints, such as the number of empty and loaded containers to be transported. By properly setting algorithm parameters and fine-tuning mechanisms, the harmony search algorithm can effectively solve such discrete optimization problems and find reasonable integer solutions.

[0213] Therefore, the Harmony Search algorithm is a more effective approach to the complexity of the empty and loaded container joint scheduling problem. With its unique Harmony Memory mechanism and its excellent balance between global search and local exploitation, the Harmony Search algorithm demonstrates strong adaptability, flexibility, and search efficiency, significantly improving the optimization results for solving the empty and loaded container joint sea and land scheduling problem.

[0214] (IV) Summary

[0215] This case mainly solves two problems: (1) It solves the problem that the mathematical model used in the current empty container transportation optimization problem is not practical enough, and comprehensively considers the application of foldable containers, the joint decision-making of empty and heavy containers, and the sea-land transport network. (2) In view of the fact that the existing commercial linear programming solver cannot solve complex optimization models under large-scale examples, the empty and heavy container joint scheduling problem is divided into networks, and an improved harmony search algorithm is proposed. By analyzing the differences between the heavy container transportation stage and the empty container transportation stage, the heavy container transportation problem is expanded to conform to the process framework of the harmony search algorithm, and the optimization solver is embedded in the harmony search algorithm framework to obtain the comprehensive cost and specific decision-making plan of the entire empty and heavy container sea-land joint scheduling space-time network corresponding to this heavy container transportation path plan. Finally, according to the preset iteration termination conditions of the algorithm, a feasible solution that meets the solution accuracy requirements under large-scale examples can be given within a reasonable time, with excellent performance and applicability.

[0216] Through the description of the above implementation methods, those skilled in the art can clearly understand that a corresponding system can be realized according to the disclosed method. Exemplarily, a system for joint scheduling of empty and heavy containers, the system includes a construction module and a solution module; the construction module is configured to: establish a mathematical programming model for joint scheduling of empty and heavy containers, the objective function of which is to minimize the sum of the heavy container transportation cost, empty container transfer cost, container rental cost, folding equipment purchase cost, and folding and unfolding operation cost; the decision variables include the empty and heavy container scheduling quantity and transportation path at each time node during the planning period, the empty container rental quantity, folding equipment purchase, and folding and unfolding empty container quantity at each time node during the planning period; the constraints include heavy container transportation stage constraints, empty container transfer stage constraints, empty and heavy container relationship constraints, sea-land combined transportation space-time network constraints, and variable value range constraints. ; The solution module is configured as follows: for each cargo order, based on the irreversibility of time and the accessibility between geographical nodes, a transportation path is generated through a heuristic algorithm, and the transportation paths of all cargo orders are combined to form a heavy box transportation path plan, which is substituted into the empty and heavy box joint scheduling mathematical programming model for solution to obtain the empty and heavy box joint scheduling plan; wherein the transportation path r of the cargo order is expressed as (b1|t)→(m|t′)→…→(b2|t″), b1 is the shipping station, t is the departure time of the shipping station; m is the port or other station passed through in the middle, t′ is its corresponding time; b2 is the receiving station, t" is the arrival time at the receiving station.

[0217] In some embodiments, the system also includes a search module, which is configured to: form a heavy box transportation path plan library with several initial heavy box transportation path plans, substitute each heavy box transportation path plan into the empty and heavy box joint scheduling mathematical programming model for solution, and obtain the objective function value corresponding to each heavy box transportation path plan; based on each cargo order, generate a new heavy box transportation path plan, substitute it into the empty and heavy box joint scheduling mathematical programming model for solution, and obtain its corresponding objective function value and the empty and heavy box joint scheduling plan; based on the objective function value, when the new heavy box transportation path plan is better than the worst heavy box transportation path plan in the heavy box transportation path plan library, use the new heavy box transportation path plan to replace the worst heavy box transportation path plan in the heavy box transportation path plan library to update the heavy box transportation path plan library; if the termination condition is met, the empty and heavy box joint scheduling plan corresponding to the best heavy box transportation path plan in the heavy box transportation path plan library is used as the final empty and heavy box joint scheduling plan; if the termination condition is not met, repeat the above process.

[0218] Through the above description of the embodiments, those skilled in the art will clearly understand that the present disclosure can be implemented using software plus necessary general-purpose hardware. Of course, it can also be implemented using dedicated hardware, including application-specific integrated circuits, dedicated CPUs, dedicated memories, and dedicated components. Generally speaking, any function performed by a computer program can be easily implemented using corresponding hardware. Moreover, the specific hardware structures used to implement the same function can also be diverse, such as analog circuits, digital circuits, or dedicated circuits. However, for the present disclosure, software implementation is often the preferred embodiment.

[0219] Although the embodiments of the present disclosure have been described above with reference to the accompanying drawings, the present disclosure is not limited to the specific embodiments and application areas described above. The specific embodiments described above are merely illustrative and instructive, and not restrictive. A person of ordinary skill in the art, guided by this specification and without departing from the scope of protection of the claims of the present disclosure, may devise various other forms, all of which fall within the scope of protection of the present disclosure.

Claims

1. A joint optimization scheduling method for empty and loaded containers considering foldable containers and sea-land transport, characterized by: The method comprises: A mathematical programming model for the combined scheduling of empty and loaded containers was established. Its objective function was to minimize the sum of the costs of loaded container transportation, empty container dispatching, container rental, folding equipment purchase, and folding and unfolding operations. Decision variables included the empty and loaded container dispatch volume and transportation routes at each time point during the planning period, the empty container rental volume, folding equipment purchase, and empty container folding and unfolding volume at each time point during the planning period. Constraints included constraints on the loaded container transportation phase, the empty container dispatching phase, the empty and loaded container relationship, the spatiotemporal network constraints for combined sea and land transportation, and the variable value range constraints. For each cargo order, a transportation route is generated using a heuristic algorithm based on time irreversibility and the reachability between geographical nodes. The transportation routes of all cargo orders are combined to form a heavy container transportation route plan. This plan is then substituted into the mathematical programming model for the joint scheduling of empty and heavy containers and solved to obtain the empty and heavy container joint scheduling plan. The transportation path r of a cargo order is represented as (b1|t)→(m|t′)→…→(b2|t″), where b1 is the shipping station and t is the departure time of the shipping station; m is the port or other station passed through along the way and t′ is the corresponding time; b2 is the receiving station and t″ is the arrival time at the receiving station.

2. The method according to claim 1, characterized in that The method further comprises the step of searching: A number of initial heavy-box transport path plans are used to form a heavy-box transport path plan library. Each heavy-box transport path plan is substituted into the empty-and-heavy-box joint scheduling mathematical programming model to solve it and obtain the objective function value corresponding to each heavy-box transport path plan. Based on each cargo order, a new heavy container transport route plan is generated and substituted into the empty and heavy container joint scheduling mathematical programming model to obtain the corresponding objective function value and the empty and heavy container joint scheduling plan; Based on the objective function value, when the new heavy-box transportation path solution is better than the worst heavy-box transportation path solution in the heavy-box transportation path solution library, the new heavy-box transportation path solution is used to replace the worst heavy-box transportation path solution in the heavy-box transportation path solution library, thereby updating the heavy-box transportation path solution library; If the termination condition is met, the empty and heavy container joint scheduling plan corresponding to the optimal heavy container transport path plan in the heavy container transport path plan library will be used as the final empty and heavy container joint scheduling plan; if the termination condition is not met, repeat the above steps.

3. The method according to claim 2, characterized in that The termination condition setting step includes: Set the accuracy threshold l and the number of comparison intervals n; If the absolute value of the difference between the kth iteration result μ and the knth iteration result σ is less than or equal to the preset accuracy threshold l, the algorithm is considered to have reached the termination condition.

4. The method according to claim 2, characterized in that The steps of generating a new heavy-box transportation route plan based on each cargo order include: For each cargo order cj, a new transportation path is generated according to the following formula Where: Represents the set of transport routes for cargo order cj in the heavy-box transport route solution library. represents the transportation path of cargo order cj generated by a heuristic algorithm based on time irreversibility and reachability between geographical nodes, α1 represents a random number uniformly distributed between [0, 1], HMS represents the size of the heavy-box transportation path solution library, and HMCR represents the selection probability of the heavy-box transportation path solution library; For each goods order cj from The departure time of the selected transport route is disturbed, and based on the new departure time after the disturbance, a new transport route is generated through a heuristic algorithm taking into account the irreversibility of time and the accessibility between geographical nodes; The new transport routes for all cargo orders constitute a new heavy-box transport route plan.

5. The method according to claim 4, characterized in that The perturbation strategy is: Where: α2 represents a random number uniformly distributed between [0, 1], bw represents the amplitude of the departure time disturbance, and PAR represents the disturbance variation probability of the cargo order transportation path.

6. An empty and loaded container joint dispatching system, characterized in that: The system includes a building module and a solving module; The building module is configured to: establish a mathematical programming model for the joint scheduling of empty and heavy containers, wherein the objective function is to minimize the sum of heavy container transportation costs, empty container transfer costs, container rental costs, folding equipment purchase costs, and folding and unfolding operation costs; the decision variables include the empty and heavy container scheduling quantity and transportation routes at each time point during the planning period, the empty container rental quantity, folding equipment purchase quantity, and folding and unfolding empty container quantity at each time point during the planning period; and the constraints include heavy container transportation stage constraints, empty container transfer stage constraints, empty and heavy container relationship constraints, sea-land combined transportation spatiotemporal network constraints, and variable value range constraints; The solution module is configured to: generate a transportation path for each cargo order using a heuristic algorithm based on time irreversibility and reachability between geographical nodes, combine the transportation paths of all cargo orders to form a heavy-box transportation path plan, substitute the plan into the mathematical programming model for joint scheduling of empty and heavy boxes, and obtain an empty and heavy-box joint scheduling plan; The transportation path r of a cargo order is represented as (b1|t)→(m|t′)→…→(b2|t″), where b1 is the shipping station and t is the departure time of the shipping station; m is the port or other station passed through along the way and t′ is the corresponding time; b2 is the receiving station and t″ is the arrival time at the receiving station.

7. The system according to claim 6, characterized in that The system also includes a search module, which is configured to: form a heavy box transportation path solution library with several initial heavy box transportation path solutions, substitute each heavy box transportation path solution into the empty and heavy box joint scheduling mathematical programming model for solution, and obtain the objective function value corresponding to each heavy box transportation path solution; based on each cargo order, generate a new heavy box transportation path solution, substitute it into the empty and heavy box joint scheduling mathematical programming model for solution, and obtain its corresponding objective function value and the empty and heavy box joint scheduling solution; based on the objective function value, when the new heavy box transportation path solution is better than the worst heavy box transportation path solution in the heavy box transportation path solution library, use the new heavy box transportation path solution to replace the worst heavy box transportation path solution in the heavy box transportation path solution library to realize the update of the heavy box transportation path solution library; if the termination condition is met, the empty and heavy box joint scheduling solution corresponding to the best heavy box transportation path solution in the heavy box transportation path solution library is used as the final empty and heavy box joint scheduling solution; if the termination condition is not met, repeat the above process.

8. The system according to claim 7, characterized in that The steps of generating a new heavy-box transportation route plan based on each cargo order include: For each cargo order cj, a new transportation path is generated according to the following formula Where: Represents the set of transport routes for cargo order cj in the heavy-box transport route solution library. represents the transportation path of cargo order cj generated by a heuristic algorithm based on time irreversibility and reachability between geographical nodes, α1 represents a random number uniformly distributed between [0, 1], HMS represents the size of the heavy-box transportation path solution library, and HMCR represents the selection probability of the heavy-box transportation path solution library; For each goods order cj from The departure time of the selected transport route is disturbed, and based on the new departure time after the disturbance, a new transport route is generated through a heuristic algorithm taking into account the irreversibility of time and the accessibility between geographical nodes; The new transport routes for all cargo orders constitute a new heavy-box transport route plan.

9. The system according to claim 8, characterized in that The perturbation strategy is: Where: α2 represents a random number uniformly distributed between [0, 1], bw represents the amplitude of the departure time disturbance, and PAR represents the probability of disturbance variation of the cargo order transportation path.

10. A computer-readable storage medium, characterized in that: A computer program is stored which can be loaded by a processor and execute the method according to any one of claims 1 to 5.

Images