A supply chain system control method and device, a terminal device and a medium

Abstract

This invention provides a supply chain system control method, apparatus, terminal equipment, and storage medium, including: collecting state parameters of a three-layer supply chain network; generating inventory path vector samples based on historical lead time samples and constructing their empirical distribution for paths from manufacturer nodes to factory nodes, thereby establishing a Wasserstein spherical uncertainty set; constructing a box uncertainty set for paths from raw material supplier nodes to manufacturer nodes, and constructing maximum and minimum cumulative arrival trajectories; constructing the supply chain total cost function of the Wasserstein spherical uncertainty set and the box uncertainty set; employing a two-layer solution architecture, using dual transformation to reconstruct the supply chain total cost function optimization problem containing nonlinear terms into a mixed-integer linear programming model, and solving it with the goal of minimizing the supply chain total cost function to obtain the execution instruction set for controlling physical equipment. This invention can improve the stability and efficiency of the three-layer supply chain network operation.

Description

Technical Field

[0001] This invention belongs to the field of supply chain management, inventory control and robust optimization technology, specifically involving a supply chain system control method, device, terminal equipment and medium. Background Technology

[0002] Against the backdrop of increasing globalization and uncertainty, large enterprises often allocate production and supply resources globally, serving diverse customer needs through multiple factories, manufacturers, and regions. At the same time, increased volatility in key raw material prices, frequent supply disruptions, geopolitical conflicts, natural disasters, and public health events can all lead to a short- or medium-term decline in upstream raw material supply capacity, making traditional inventory and production planning methods based on the assumption of stable supply inapplicable.

[0003] For a three-tiered supply chain consisting of a single raw material supplier, multiple manufacturers, and multiple factories (or regional distribution centers), a key challenge in addressing widespread shortages of critical raw materials is coordinating production and distribution among manufacturers and factories within the constraints of limited raw material supply capacity. A lack of overall coordination can easily lead to improper allocation of upstream raw materials, resulting in severe material shortages and shutdowns for some manufacturers, while others face excessive inventory or idle capacity. Each tier focusing solely on its own cost optimization leads to high overall supply chain costs and makes it difficult to assess the risks of stockouts and service level declines caused by low inventory levels.

[0004] Traditional inventory control methods, such as replenishment strategies based on Economic Order Quantity (EOQ), and (s, Q) or (s, S) strategies, are primarily designed for single- or two-tier supply chains, and assume relatively stable demand and supply, and controllable replenishment cycles when designing decision rules. These methods struggle to simultaneously cover the following characteristics: (1) Uncertain lead time: The geographical distance and transportation capacity between regions are unstable, and the lead time fluctuates due to various factors. (2) Three-layer network structure: There are complex material and information flows between raw material suppliers, manufacturers, factories or customer nodes; (3) Raw material shortage constraint: The total supply of key upstream raw materials is limited and needs to be optimally allocated among multiple manufacturers; (4) Trade-offs among multiple modes of transportation: How to make dynamic choices among multiple modes of transportation, requiring both timely and sufficient fulfillment of production and customer needs, and minimizing total costs.

[0005] In existing literature, research related to this invention can be mainly divided into several categories: (1) Two-layer supply chain joint economic batch model, with a simple network structure.

[0006] (2) Multi-layer serial supply chain model, with limited network structure, mostly serial rather than mesh.

[0007] (3) The decision-making process of multiple modes of transportation and joint economic batches is not integrated.

[0008] (4) Most methods for dealing with uncertainty are stochastic programming, which is computationally complex and depends on precise distribution, while traditional robust optimization is too conservative.

[0009] Therefore, a systematic joint decision-making method is needed that can simultaneously consider raw material supply shortages, adjustable production capacity, multiple transportation modes, multiple batches en route, and uncertain lead times. Through appropriate uncertainty set modeling and theoretical reconstruction, the originally difficult-to-solve model can be transformed into a form that can be efficiently solved by a general mixed integer programming solver, providing precise control instructions for actual physical equipment (such as production lines, transportation vehicles, and warehousing equipment). Summary of the Invention

[0010] The purpose of this invention is to provide a supply chain system control method, device, terminal equipment, and storage medium, aiming to solve the problems in existing supply chain management methods that cannot effectively handle three-layer network structures, supply shortages, and multiple uncertainties, resulting in inaccurate decision-making, unstable system operation, and low resource utilization.

[0011] In a first aspect, the present invention provides a supply chain system control method, the method comprising the following steps: The system collects state parameters of a three-tiered supply chain network consisting of raw material suppliers, multiple manufacturers, and multiple factories. These state parameters include the unit-time demand rate of factory nodes, the unit-time productivity and equipment capacity limit of manufacturer nodes, the planned productivity and adjustable overtime load range of raw material supplier nodes, and historical samples or fluctuation boundaries of lead time under different transportation modes between nodes. For the first material path from the manufacturer node to the factory node, an inventory path vector sample is generated based on the historical lead time sample and its empirical distribution is constructed. Then, a Wasserstein spherical uncertainty set centered on this empirical distribution is established to optimize inventory costs by dividing the Bruker bar, thereby reflecting the impact of lead time distribution shift on inventory costs. For the second material path from the raw material supplier node to the manufacturer node, a box-type uncertainty set is constructed based on the shortest and longest lead time boundaries, and a maximum cumulative arrival trajectory and a minimum cumulative arrival trajectory are constructed based on the box-type uncertainty set to describe the upper and lower bound fluctuations of inventory levels. Based on the law of conservation of materials, a supply chain total cost function is constructed that couples the Wasserstein spherical uncertainty set and the box uncertainty set. The supply chain total cost function includes the expected inventory holding cost and stockout risk cost determined by the inventory status of each node, production setup cost, ordering cost, transportation cost, and overtime capacity adjustment cost of raw material suppliers. A two-layer solution architecture is adopted, consisting of an outer layer that discretely enumerates candidate values ​​for the control cycle and an inner layer that optimizes parameters for a given control cycle. The dual transformation is used to reconstruct the supply chain total cost function optimization problem, which includes nonlinear terms, into a mixed-integer linear programming model. The solution is obtained by a solver with the objective of minimizing the supply chain total cost function, resulting in an execution instruction set for controlling physical equipment. The execution instruction set consists of the basic cycle period, the order production batch and shipment start time of each node, the transportation mode selection, and the overtime capacity adjustment of raw material suppliers.

[0012] Optionally, inventory path vector samples are generated based on historical lead time samples, and their empirical distribution is constructed. Then, a Wasserstein spherical uncertainty set centered on this empirical distribution is established, including: Construct based on experience distribution Centered on, with A Wasserstein sphere with radius ; where, Indicated in the first material path Real inventory path random vector distribution Compared to the empirical distribution constructed from historical samples The permissible deviation is used to quantify the distribution shift caused by non-stationarity of lead time distribution, extreme delays, and sample finiteness; the expression for the Wasserstein spherical uncertainty set is: , Represents the 1-Wasserstein distance, used to measure the transportation cost between an arbitrary distribution and an empirical distribution. Indicates in the support set The space of all probability distributions on the [space].

[0013] Optional, inventory recursion formulas include: Factory node at the Inventory at the end of each time segment The following formula can be used for recursion:

[0014] in, Indicates the first The actual delivery volume within a given time period is obtained by mapping historical lead times. Indicates the length of the control cycle. This represents the rate of demand per unit time for each type of component at the factory node; Manufacturer node at Inventory at the end of each time segment The following formula can be used for recursion:

[0015] in, Indicates as of the date The cumulative arrivals at the end of each time segment. This indicates the cumulative consumption, reflecting the actual consumption of raw materials according to the production plan. This indicates the manufacturer's initial inventory.

[0016] Optionally, a box-shaped uncertainty set is constructed based on the shortest and longest lead times, and a maximum cumulative arrival trajectory and a minimum cumulative arrival trajectory are constructed based on the box-shaped uncertainty set, including: For raw material supplier nodes To the manufacturer node Second material path A box-shaped uncertainty set is constructed to describe the range of lead time fluctuations; the expression for the box-shaped uncertainty set is:

[0017] in, Indicates the mode of transport, which can be sea transport, land transport, or air transport. This indicates the lead time corresponding to different modes of transportation. , These represent the modes of transportation. The shortest lead time and the longest lead time; Through calculation formula

[0018]

[0019]

[0020] Achieve a large cumulative delivery trajectory ;in, These correspond to sea freight, land freight, and air freight modes, respectively. Used to indicate the order batch Select transportation mode According to the shortest lead time Calculate whether the material can be used in the first... Arriving at the end or before of a time segment , A value of 1 indicates that the destination is reachable. A value of 0 indicates that the destination cannot be reached. Indicates the batch of orders placed. , , Indicates the manufacturer's initial inventory. Indicates an integer multiple of the factory cycle period. This indicates the quantity of raw materials shipped by the raw material supplier. This represents the effective contribution coefficient of the lead time within its respective time segment. The effective contribution coefficient indicates the proportion of time that the batch contributes to the average inventory of the segment after its arrival. This indicates the relative proportion of the lead time within its time segment. The relative proportion represents the percentage from the start of the time segment to the arrival time. Used to indicate the order batch Select transportation mode According to the shortest lead time Calculate whether the material is exactly in the [number]th [period]. A time segment arrives, Indicates as of the date Manufacturer node at the end of each time segment Total cumulative raw material consumption; maximum cumulative arrival trajectory is used to assess maximum inventory holding cost; Through calculation formula

[0021] Obtain a minimal cumulative delivery trajectory Minimal cumulative delivery trajectory is used to assess the cost of maximum stockout risk.

[0022] Optionally, the expression for the total supply chain cost function is:

[0023]

[0024]

[0025]

[0026] in, Represents the total cost of the supply chain. This represents the total cost of the factory. This represents the manufacturer's total cost. This represents the total cost to raw material suppliers. This indicates the cost per order for the factory. This represents the unit holding cost of factory parts per unit of time. Indicates average inventory. , This represents the cost per unit of stockout at the factory per unit of time. Indicates from the manufacturer node to factory node The unit transportation cost Represents factory node For manufacturer nodes The rate of demand per unit time This represents the unit holding cost of a manufacturer's components per unit of time. and These represent the positive and negative parts of the function, used to distinguish between inventory holding and stockout states. This indicates the manufacturer's productivity per unit time. Indicates from raw material supplier node To the manufacturer node In transportation mode Lower transportation costs Used to indicate the Batch materials from raw material supplier nodes To the manufacturer node Select transportation mode And whether it is connectable, , Indicates the first Batch materials from raw material supplier nodes To the manufacturer node Select transportation mode And they can be connected. Represents the raw material supplier node per unit time. Assigned to manufacturer node The quantity of raw materials, This represents the manufacturer's ordering cost. This indicates the manufacturer's production setup cost. This represents the unit holding cost of finished products from raw material suppliers and raw materials from manufacturers per unit of time. This represents the manufacturer's unit stockout cost per unit of time. This indicates the cost per production run set up by the raw material supplier. This indicates the cost per order from the raw material supplier. Indicates an integer multiple of the manufacturer's cycle time. This represents the unit holding cost of raw materials from the raw material supplier per unit of time. This indicates the normal total production capacity of the raw material suppliers. This indicates the amount of additional production capacity required by raw material suppliers. This represents the hourly labor cost per unit of overtime for raw material suppliers. This indicates the number of overtime hours worked by raw material suppliers.

[0027] Optional, the two-layer solution architecture includes: Outer enumeration control cycle discrete candidate values ; , Indicates the number of discrete candidate values; Inner layer in a given control cycle The following optimization problem is constructed:

[0028] in, Represents the total cost. This represents the sum of ordering costs, production setup costs, and transportation costs identified in a three-tier supply chain network. This refers to the first material path at the manufacturer-to-factory level. The worst-case scenario for W-DRO is expected to include inventory and stockout costs. This represents robust inventory holding and stockout costs at the raw material supplier to manufacturer level, under lead time and box-type uncertainty. Indicates the candidate instruction set to be executed; Through calculation formula

[0029]

[0030] Obtain the final control cycle and the final execution instruction set , It represents the set of all decision variables.

[0031] Optionally, the instruction set to be executed includes Production frequency and batch size of each manufacturer; Order cycles and order quantities for each factory; The choice of transportation mode and the frequency of shipments for each transportation route; Overtime start instructions and overtime hours from raw material suppliers.

[0032] In a second aspect, the present invention provides a supply chain system control device, comprising: The data acquisition module is used to collect the status parameters of a three-tier supply chain network consisting of raw material suppliers, multiple manufacturers, and multiple factories. The status parameters include the unit time demand rate of factory nodes, the unit time productivity and equipment capacity limit of manufacturer nodes, the planned productivity and adjustable overtime load range of raw material supplier nodes, and historical samples or fluctuation boundaries of lead time under different transportation modes between nodes. The first data processing module is used to generate inventory path vector samples based on historical lead time samples for the first material path from the manufacturer node to the factory node and construct its empirical distribution. Then, it establishes a Wasserstein spherical uncertainty set centered on the empirical distribution, which is used to optimize inventory costs by dividing the data into Bruker bars, thereby reflecting the impact of lead time distribution shift on inventory costs. The second data processing module is used to construct a box-shaped uncertainty set based on the shortest and longest boundaries of the lead time for the second material path from the raw material supplier node to the manufacturer node, and to construct the maximum cumulative arrival trajectory and the minimum cumulative arrival trajectory based on the box-shaped uncertainty set to describe the upper and lower bound fluctuations of the inventory level. The third data processing module is used to construct a supply chain total cost function that couples the Wasserstein spherical uncertainty set and the box uncertainty set based on the law of conservation of materials. The supply chain total cost function includes the expected inventory holding cost and stockout risk cost determined by the inventory status of each node, production setup cost, ordering cost, transportation cost, and overtime capacity adjustment cost of raw material suppliers. The instruction acquisition module employs a two-layer solution architecture: an outer layer that discretely enumerates candidate values ​​for the control cycle, and an inner layer that optimizes parameters for a given control cycle. It utilizes dual transformation to reconstruct the supply chain total cost function optimization problem, which includes nonlinear terms, into a mixed-integer linear programming model. The solver then solves this model with the objective of minimizing the supply chain total cost function, yielding an execution instruction set for controlling physical equipment. This execution instruction set consists of the basic cycle period, order production batch size and shipping start time for each node, transportation mode selection, and overtime capacity adjustment for raw material suppliers.

[0033] Thirdly, the present invention provides a terminal device, including a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor executes the computer program to implement the above-described method.

[0034] Fourthly, the present invention provides a computer-readable storage medium storing a computer program that, when executed by a processor, implements the above-described method.

[0035] The present invention has at least the following beneficial effects: By constructing a unified total cost function, the decision variables of raw material suppliers, manufacturers, and factories are coupled and optimized. This coordinates material allocation, production, and inventory from a global perspective, solving the material flow imbalance problem caused by decision decoupling in traditional methods and significantly improving the operational stability of the supply chain system. For the uncertainty characteristics of different paths, Wasserstein robust optimization and box-type robust optimization are used for modeling, respectively. The composite robust model effectively suppresses the impact of lead time fluctuations on inventory status, ensuring the reliability of control instructions in uncertain environments. The model integrates transportation mode selection with order quantity and production batch size, accurately describing the dynamic coupling relationship between transportation time and inventory levels, optimizing the allocation of multi-mode transportation resources, and avoiding the incoordination problem caused by the disconnect between transportation and inventory decisions in traditional methods. Attached Figure Description

[0036] The accompanying drawings are provided to further understand the technical solutions of the present invention and constitute a part of the specification. They are used together with the embodiments of the present invention to explain the technical solutions of the present invention, and do not constitute a limitation on the technical solutions of the present invention.

[0037] Figure 1 This is a flowchart of a supply chain system control method in one embodiment of this application; Figure 2 This is a structural diagram of a supply chain system control device according to one embodiment of this application; Figure 3 This is a structural diagram of a terminal device in one embodiment of this application. Detailed Implementation

[0038] The technical solution of the present invention will now be described in detail and completely with reference to the accompanying drawings. Obviously, the described embodiments are only some, not all, of the embodiments of the present invention. All other embodiments obtained by those skilled in the art based on the embodiments of the present invention without creative effort are within the scope of protection of the present invention.

[0039] In the description of this invention, it should be noted that the terms "upper", "lower", "inner", "outer", etc., indicate the orientation or positional relationship based on the orientation or positional relationship shown in the accompanying drawings. They are only for the convenience of describing this invention and simplifying the description, and do not indicate or imply that the device or element referred to must have a specific orientation, or be constructed and operated in a specific orientation. Therefore, they should not be construed as limitations on this invention.

[0040] Example 1 This embodiment provides a supply chain system control method. This method can be applied to servers, industrial control computers, or cloud control platforms. By executing the control commands generated by this method, it can directly act on physical equipment in the supply chain, such as starting production lines, dispatching transport vehicles, and operating warehouse stacker cranes. Figure 1 As shown, the method includes the following steps: Step 11: Collect the status parameters of the three-tier supply chain network consisting of raw material suppliers, multiple manufacturers, and multiple factories.

[0041] In this embodiment of the invention, the state parameters include the unit time demand rate of the factory node, the unit time production rate and equipment capacity limit of the manufacturer node, the planned production rate and adjustable overtime load range of the raw material supplier node, and historical samples of lead time or fluctuation boundaries under different transportation modes between nodes.

[0042] In one feasible implementation, the following real-time and historical status parameters are extracted from the ERP and warehousing systems of each factory: Demand rate Collection Factory For from the manufacturer The average demand per unit time for components. For example: Factory 1 needs 100 bearings from Manufacturer 2 per day.

[0043] Unit holding cost : The unit time storage cost of parts in the factory warehouse.

[0044] Unit out-of-stock cost Losses due to production line shutdowns or order default penalties in the event of stockouts.

[0045] Cost per order Fixed administrative and processing costs incurred by a factory for each order placed with a manufacturer.

[0046] In one feasible implementation, the following status parameters are extracted from the manufacturer's MES and production control system: Productivity per unit time The capacity is determined by the production line's design capacity.

[0047] Single production setup cost This includes costs for equipment adjustment, cleaning, and first-piece inspection.

[0048] Unit time finished goods holding cost The unit time storage cost of finished products at the manufacturer.

[0049] Cost of ordering raw materials from suppliers per order .

[0050] Cost of raw material shortage per unit time This refers to the losses caused by production stoppages due to raw material shortages.

[0051] From raw material supplier nodes To the manufacturer node Different modes of transportation ( Sea freight, Land transport, Unit transportation cost (air freight) .

[0052] In one feasible implementation, the following status parameters are extracted from the capacity agreement and logistics contract provided by the supplier: Planned productivity Normal production speed.

[0053] Normal total capacity Maximum output without working overtime.

[0054] Maximum total capacity The maximum output that can be achieved through overtime work.

[0055] Cost of finished goods and raw materials per unit time and .

[0056] Single production setup cost Cost per order .

[0057] Overtime unit hourly labor cost .

[0058] Furthermore, for the three transportation modes, this invention also collects the fluctuation range of their lead times. For example, from supplier to manufacturer, sea freight takes a maximum of 20 days and a maximum of 35 days; air freight takes a maximum of 3 days and a maximum of 5 days. These samples can be extracted from the company's logistics information system to record the actual transit time for each shipment.

[0059] It also collected unit transportation costs under different transportation modes. This data can be obtained from the terms of the transport contract, historical transport records, or carrier commitments.

[0060] This step provides a data foundation for building an accurate mathematical model by comprehensively collecting structured state parameters of the three-layer network. These parameters include not only deterministic physical quantities (such as productivity and cost) but also uncertain statistical quantities (such as lead time samples and ranges), enabling the model to accurately reflect the actual situation of the physical supply chain and thus ensuring the practical feasibility of the generated decision instructions.

[0061] Step 12: For the first material path from the manufacturer node to the factory node, generate inventory path vector samples based on historical lead time samples and construct its empirical distribution. Then, establish a Wasserstein spherical uncertainty set centered on this empirical distribution to optimize inventory costs using a multi-bar algorithm, thereby reflecting the impact of lead time distribution shift on inventory costs.

[0062] Specifically, for each node from the manufacturer to factory node First material path ,collection A historical early-stage sample, denoted as These samples reflect actual logistics fluctuations over a past period. Meanwhile, based on the established basic cycle... (Control cycle, in units such as days) and factory demand rate Determine the order quantity for each batch. The number of cycles per unit time is defined based on the factory's basic cycle time. , No. The intervals corresponding to each time segment are ,in, ,in, It is the length of the time window (in days, for example, 90 days). Define the order batch set , The factory places orders at the end of each cycle, the first... The delivery time for this batch is , No. Delivery volume in a specific time period By all in the The result is obtained by summing up the batches that arrived at each time segment. , Rules for determining the delivery cycle of bulk shipments.

[0063] This batch of goods will arrive at some point in the future. Due to the uncertainty of the manufacturer's lead time to the factory, it may arrive earlier or later, resulting in certain inventory holding costs or stockout costs. This embodiment uses an inventory recursion formula to calculate the lead time for each sample. Mapped to a containing Average inventory path sample for each time segment , Specifically, through the inventory recursion formula Calculate the sample in the historical lead time period Next, the factory node is at the 1st Inventory at the end of each time segment Then through the calculation formula Calculate the average inventory level for each segment. This yields a sample inventory trajectory vector. .

[0064] Will Each inventory trajectory sample is considered as Construct a discrete empirical distribution for each equally probable scenario. , , Indicates the Dirac measure, .

[0065] To describe the deviation between the true distribution and the empirical distribution, a model is constructed based on the empirical distribution. Centered on, with Let be the radius of the Wasserstein sphere. The expression for the uncertainty set of the Wasserstein sphere is: , Represents the 1-Wasserstein distance, used to measure the transportation cost between an arbitrary distribution and an empirical distribution. Indicated in the first material path Real inventory path random vector distribution Compared to the empirical distribution constructed from historical samples The allowable deviation is used to quantify the distribution shift caused by non-stationarity of lead time distribution, extreme delays, and sample finiteness. The larger the value, the wider the distribution set covered by the Wasserstein sphere, and the more robust but conservative the resulting strategy is to distribution shifts. The smaller the value, the closer the strategy is to historical samples, but the more sensitive it is to distribution shifts. Indicates in the support set The space of all probability distributions on the [space].

[0066] In practical implementation, to measure the impact of material arrival time probability distribution shifts on costs, this embodiment constructs a sub-model of the plant layer using the Wasserstein sphere. Its objective is to find the expected inventory loss in the worst-case scenario within the Wasserstein sphere.

[0067]

[0068]

[0069] In this model, the cost impact is explicitly characterized by the following constraint: the impact of holding costs: Impact of stockout costs: ; The global robust dual coefficients are defined by the following constraints: .

[0070] Step 13: For the second material path from the raw material supplier node to the manufacturer node, construct a box-type uncertainty set based on the shortest and longest lead time boundaries, and construct the maximum cumulative arrival trajectory and the minimum cumulative arrival trajectory based on the box-type uncertainty set to describe the upper and lower bound fluctuations of the inventory level.

[0071] It should be noted that the manufacturer node is at the... Inventory at the end of each time segment The following formula can be used for recursion:

[0072] in, Indicates as of the date The cumulative arrivals at the end of each time segment. This indicates the cumulative consumption, reflecting the actual consumption of raw materials according to the production plan. This indicates the manufacturer's initial inventory.

[0073] For the "raw material supplier-manufacturer" route, sufficient historical data is often lacking, but the fluctuation range of lead times for each mode of transportation can be known based on transportation contracts or experience. Therefore, a box-type uncertainty set is used to describe it: .in, Indicates the mode of transport, which can be sea transport, land transport, or air transport. This indicates the lead time corresponding to different modes of transportation. , These represent the modes of transportation. The shortest and longest lead times are given. This means that the lead time can take any value within its range without assuming any distribution information.

[0074] To make robust decisions under such strong uncertainty, this invention constructs two extreme scenarios: maximum cumulative arrival trajectory and minimum cumulative arrival trajectory.

[0075] For a large cumulative arrival trajectory, assuming all batches are handled with the shortest lead time Arrival times are the earliest for materials to be received, resulting in the highest inventory levels and thus the greatest inventory holding costs. Calculating this trajectory requires considering the precise contribution of each order batch's arrival time to inventory. For the manufacturer node... The cumulative amount of its production consumption is defined as (As determined by the production plan). (Note) The shipment volume of raw materials for each batch. . No. The order time for the batch of goods is Under the shortest lead time, the first The batch of goods will be in time segments Arrival within the region. To accurately calculate the impact of arrival time on average inventory per segment, two coefficients are introduced: location coefficient. and effective contribution coefficient .

[0076] Position coefficient This indicates the relative position of the lead time within the delivery segment, and its expression is: .

[0077] Effective contribution coefficient This indicates the proportion of the goods' contribution to the average inventory during the remaining time of the arrival segment. Its expression is: .

[0078] So, in the shortest lead time scenario, the manufacturer In time segment The average inventory is:

[0079] in, This refers to the extremely large cumulative delivery trajectory. These correspond to sea freight, land freight, and air freight modes, respectively. Used to indicate the order batch Select transportation mode According to the shortest lead time Calculate whether the material can be used in the first... Arriving at the end or before of a time segment , A value of 1 indicates that the destination is reachable. A value of 0 indicates that the destination cannot be reached. Indicates the batch of orders placed. , , Indicates the manufacturer's initial inventory. Indicates an integer multiple of the factory cycle period. This indicates the quantity of raw materials shipped by the raw material supplier. This represents the effective contribution coefficient of the lead time within its respective time segment. The effective contribution coefficient indicates the proportion of time that the batch contributes to the average inventory of the segment after its arrival. This indicates the relative proportion of the lead time within its time segment. The relative proportion represents the percentage from the start of the time segment to the arrival time. Used to indicate the order batch Select transportation mode According to the shortest lead time Calculate whether the material is exactly in the [number]th [period]. A time segment arrives, Indicates as of the date Manufacturer node at the end of each time segment Total cumulative raw material consumption; maximum cumulative arrival trajectory is used to assess maximum inventory holding cost.

[0080] For extremely small cumulative arrival trajectories, assuming all batches are based on the longest lead time. Arrival. This will result in materials being received last, inventory levels being lowest, and potentially even stockouts. Similarly, through calculation formulas...

[0081] Obtain a minimal cumulative delivery trajectory Minimal cumulative delivery trajectory is used to assess the cost of maximum stockout risk.

[0082] It is worth noting that, in the absence of probability distribution information, this step transforms the complex inventory dynamics problem into two easily computable boundary problems by constructing a box-shaped uncertainty set and extreme trajectories. This guarantees that the final decision, under any lead time fluctuations (within a given range), will not exceed the worst-case scenario calculated from these two boundaries in terms of inventory holding costs and stockout costs, thus achieving system robustness to uncertainty. This "boundary trajectory" method accurately describes the physical evolution of inventory, avoiding the coarseness of using only intervals to represent inventory in traditional robust optimization.

[0083] Step 14: Based on the law of conservation of material, construct a supply chain total cost function that couples the Wasserstein spherical uncertainty set and the box uncertainty set.

[0084] The total supply chain cost function includes expected inventory holding costs and stockout risk costs determined by the inventory status of each node, production setup costs, ordering costs, transportation costs, and overtime capacity adjustment costs of raw material suppliers.

[0085] Specifically, the expression for the total supply chain cost function is:

[0086]

[0087]

[0088]

[0089] in, Represents the total cost of the supply chain. This represents the total cost of the factory. This represents the manufacturer's total cost. This represents the total cost to raw material suppliers. This indicates the cost per order for the factory. This represents the unit holding cost of factory parts per unit of time. Indicates average inventory. , This represents the cost per unit of stockout at the factory per unit of time. Indicates from the manufacturer node to factory node The unit transportation cost Represents factory node For manufacturer nodes The rate of demand per unit time This represents the unit holding cost of a manufacturer's components per unit of time. and These represent the positive and negative parts of the function, used to distinguish between inventory holding and stockout states. This indicates the manufacturer's productivity per unit time. Indicates from raw material supplier node To the manufacturer node In transportation mode Lower transportation costs Used to indicate the Batch materials from raw material supplier nodes To the manufacturer node Select transportation mode And whether it is connectable, , Indicates the first Batch materials from raw material supplier nodes To the manufacturer node Select transportation mode And they can be connected. Represents the raw material supplier node per unit time. Assigned to manufacturer node The quantity of raw materials, This represents the manufacturer's ordering cost. This indicates the manufacturer's production setup cost. This represents the unit holding cost of finished products from raw material suppliers and raw materials from manufacturers per unit of time. This represents the manufacturer's unit stockout cost per unit of time. This indicates the cost per production run set up by the raw material supplier. This indicates the cost per order from the raw material supplier. Indicates an integer multiple of the manufacturer's cycle time. This represents the unit holding cost of raw materials from the raw material supplier per unit of time. This indicates the normal total production capacity of the raw material suppliers. This indicates the amount of additional production capacity required by raw material suppliers. This represents the hourly labor cost per unit of overtime for raw material suppliers. This indicates the number of overtime hours worked by raw material suppliers.

[0090] In addition, the constraints of the total supply chain cost function include: Capacity constraints: ,and .

[0091] Transportation method selection: (If there is a need for transportation); (If the allocation quantity is non-zero, at least one shipment is required, and only one shipping mode can be selected for each shipment.) For manufacturers, the total amount is conserved, indicating that within a time window... Within the specified time window, the manufacturer's finished goods shipment rate should be less than or equal to the sum of the contribution rate of beginning inventory allocated to the unit time and the raw material allocation rate. This constraint ensures that within the time window... Within this period, the total shipment volume will not exceed the total available resources.

[0092] Step 15: A two-layer solution architecture is adopted, consisting of an outer layer that discretely enumerates candidate values ​​for the control cycle and an inner layer that optimizes parameters for a given control cycle. The dual transformation is used to reconstruct the supply chain total cost function optimization problem containing nonlinear terms into a mixed-integer linear programming model. The solution is then obtained by minimizing the supply chain total cost function through a solver, resulting in the set of execution instructions for controlling the physical equipment.

[0093] The original model contains , The stochastic expectation and the product of binary and continuous variables constitute a complex mixed-integer nonlinear programming problem. This step transforms it into a solvable MILP through a sophisticated two-layer framework and mathematical transformations.

[0094] Specifically, the outer enumeration control cycle discrete candidate values ; , This indicates the number of discrete candidate values, such as 1 day, 2 days, 1 week, etc.

[0095] For the inner layer, within a given control cycle The following is an example of the plant-level distribution bar problem: ,in, Indicates the first The inventory loss function of the segment, Represents the radius of the Wasserstein sphere. The Lipschitz constant represents the inventory loss function and is used to represent the sensitivity of the cost function to lead time fluctuations.

[0096] Using the strong duality theory of Wasserstein's partial Bruker bar optimization, this problem is equivalent to:

[0097] Furthermore, due to It is a piecewise linear and Lipschitz continuous function, whose Lipschitz constant is... It can be proven that for the global robustness coefficient... ,because To minimize the objective function, its optimal value should be the maximum value among all slope constraints. , representing the maximum rate of change of the cost function (Lipschitz constant), denoted as Furthermore, the supremum problem of the inner layer can be solved explicitly, ultimately yielding a simplified form:

[0098] The first term can be pre-calculated using historical samples, while the second term is a constant. This transforms the originally complex expected cost of the split bar into a deterministic linear term. This achieves the dual reconstruction of the Wasserstein DRO model.

[0099] The robust cost of the box at the manufacturer level is expressed as ,in, The values ​​are taken under the box uncertainty set. To minimize the total cost in the worst case, this invention introduces an auxiliary variable. The worst-case cost is defined using the following constraints:

[0100] The calculations have been performed in the previous text. and ,then, .

[0101] After the above transformation, for a given T, the inner problem To become a MILP, you can directly call solvers such as Gurobi and CPLEX. Compare all candidate T. Take the minimum value corresponding to and decision variables As the final solution. This is the final set of execution instructions.

[0102] In one feasible implementation, the above-mentioned execution instruction set consists of a basic cycle period, order production batch and shipping frequency at each node, transportation mode selection, and overtime capacity adjustment of raw material suppliers.

[0103] This step, through theoretical reconstruction, transforms a complex, non-convex, and nonlinear optimization problem into a standard MILP problem, enabling the solver to solve it directly. The outer enumeration addresses the discrete nature of the core decision variable T, while the inner transformation makes each subproblem solvable. This solvability is crucial for the method's engineering feasibility. The final output execution instruction set is clear and specific, encompassing comprehensive control parameters from production and inventory to transportation. It can be directly executed by physical equipment, achieving a closed loop from "optimization algorithm" to "physical control," significantly improving the real-time performance and feasibility of the supply chain control system.

[0104] Example 2 To verify the effectiveness of the supply chain system control method provided by this invention, a simulation comparison will be conducted with existing mature algorithms in the embodiments of this invention: Set up a three-tier supply chain network, providing demand data for each factory, lead time samples for each route, cost parameters for each node, etc.

[0105] In the constructed three-layer supply chain example, discrete candidate basic cycles are enumerated one by one. For each candidate cycle, a corresponding inner-layer mixed-integer linear programming problem is constructed and solved using the Gurobi solver. The optimal total cost, solution time, and MIPGap for each candidate cycle are recorded. By comparing the optimal objective values ​​corresponding to all candidate basic cycles, the globally optimal basic cycle and its corresponding decision variables such as raw material allocation, production batch size, transportation mode, and batch number are selected.

[0106] To evaluate the computational performance of this invention under network scaling conditions, a baseline three-layer network was used. As a prototype, a replication factor is introduced. The factory and manufacturer set is copied block by block and concatenated on the index to obtain The upstream supplier set remains unchanged. Raw material supplier capacity according to By scaling up proportionally, various demands, initial inventory, cost parameters, lead time samples, and optional transportation methods are replicated at the baseline value within each replication block, thus ensuring that the expanded case has a consistent statistical structure with the baseline case. The model is built in a Python environment and solved using Gurobi on a computer with 2.60 GHz and 32 GB of memory.

[0107] Table 1 shows the replication factor. and The solution results include the number of entities, total runtime, average / maximum solution time for a single inner MIP, and the optimal candidate ( , , The model size (number of variables / number of binary variables / number of linear constraints / number of non-zero elements) and the maximum MIPGap under the candidate with the longest solution time.

[0108] Table 1

[0109] As shown in Table 1, with the network scale increasing from... Expand to The number of variables, binary variables, linear constraints, and non-zero elements in the inner MIP all roughly doubled, and the total running time and single solution time increased significantly, indicating that the solution difficulty increased after scaling up. However, the maximum MIPGap of the inner problem did not exceed 0.01% under both scales, indicating that the inner solution quality is stable and reliable under a given solution accuracy setting, thus the outer layer has high credibility in comparing different candidate target values.

[0110] Compared with the prior art, the main advantages and positive effects of this invention can be summarized as follows: 1. Achieve overall collaborative optimization of multi-phase, three-tier network supply chains By placing the three-tier structure of "raw material supplier-manufacturer-factory" in a unified model, the system simultaneously optimizes raw material capacity and allocation, manufacturer production and shipping, and factory ordering and inventory strategies within a unit of time. This avoids the problem of high global costs caused by fragmented optimization at each level and local optima in traditional methods, and effectively reduces the overall cost of the supply chain.

[0111] 2. Explicitly depicting the shortage of key raw materials and the mechanism for adjusting production capacity, it is closer to reality. By explicitly incorporating the normal capacity, maximum capacity, overtime capacity increase, and overtime costs of raw material suppliers into the model, it better meets the actual decision-making needs of enterprises in raw material shortage scenarios than setting fixed capacity or manual adjustment.

[0112] 3. Integrated decision-making on combined economic ordering quantities and transportation strategies comprehensively reflects inventory dynamics. By jointly considering order quantity, production quantity, number of shipments, and transportation mode (sea / land / air) selection within the same framework, and using a time-segment-based inventory recursion method to characterize in-transit inventory, inventory trajectories under different lead times, and their impact on holding costs and stockout risks, the resulting inventory and transportation strategies are closer to the actual logistics and production rhythm, which helps to reduce excessive reliance on high-cost air freight.

[0113] 4. Data-driven modeling of uncertain lead times and solveable robust optimization refactoring For the manufacturer-factory level, historical lead time samples are mapped to inventory trajectory samples. A distribution ambiguity set centered on the empirical distribution is constructed using Wasserstein distance, and a closed upper bound for factory-level inventory costs under the worst-case distribution is obtained using duality theory. For the raw material supplier-manufacturer level, a box-shaped uncertainty set is constructed under the condition that only the upper and lower bounds of lead time are known. The worst-case scenarios of holding costs and stockout costs are characterized by the earliest and latest arrival inventory trajectories, respectively. Through these two types of robust modeling and equivalent reconstruction, this invention transforms the robust joint economic batch problem, which originally involved stochastic expectations and nonlinear inventory functions, into a well-structured mixed-integer linear programming model.

[0114] 5. The model can be directly solved by commercial MILP solvers, facilitating engineering implementation and expansion. Since the reconstructed model is in the form of mixed-integer linear programming, it can be directly solved using commercial solvers such as Gurobi. Numerical results show that, under typical three-layer network examples and their extended scales, the model can converge in an acceptable time with a very small MIPGap (<0.1%), and the ordering of objective values ​​among the outer discrete candidate basic periods is insensitive to solution errors, thus ensuring the reliability of the selected basic periods and corresponding batch configuration schemes. This facilitates embedding into existing enterprise ERP systems and allows for flexible adjustment as business expands and parameters are updated.

[0115] Example 3 like Figure 2 As shown, an embodiment of the present invention provides a supply chain system control device, the device 200 comprising: The data acquisition module 201 is used to collect the status parameters of a three-layer supply chain network consisting of raw material suppliers, multiple manufacturers, and multiple factories. The status parameters include the unit time demand rate of factory nodes, the unit time productivity and equipment capacity limit of manufacturer nodes, the planned productivity and adjustable overtime load range of raw material supplier nodes, and historical samples or fluctuation boundaries of lead time under different transportation modes between nodes. The first data processing module 202 is used to generate inventory path vector samples based on historical lead time samples and construct their empirical distribution for the first material path from the manufacturer node to the factory node, and then establish a Wasserstein spherical uncertainty set centered on the empirical distribution, which is used to optimize inventory costs by dividing the data into Brussels bars, thereby reflecting the impact of lead time distribution shift on inventory costs. The second data processing module 203 is used to construct a box-shaped uncertainty set based on the shortest and longest boundaries of the lead time for the second material path from the raw material supplier node to the manufacturer node, and to construct the maximum cumulative arrival trajectory and the minimum cumulative arrival trajectory based on the box-shaped uncertainty set to describe the upper and lower bound fluctuations of the inventory level. The third data processing module 204 is used to construct a supply chain total cost function that couples the Wasserstein spherical uncertainty set and the box uncertainty set based on the law of conservation of materials. The supply chain total cost function includes the expected inventory holding cost and stockout risk cost determined by the inventory status of each node, production setup cost, ordering cost, transportation cost, and overtime capacity adjustment cost of raw material suppliers. The instruction acquisition module 205 employs a two-layer solution architecture: an outer layer that discretely enumerates candidate values ​​for the control cycle and an inner layer that optimizes parameters for a given control cycle. It utilizes dual transformation to reconstruct the supply chain total cost function optimization problem, which includes nonlinear terms, into a mixed-integer linear programming model. The model is then solved by a solver with the objective of minimizing the supply chain total cost function, resulting in an execution instruction set for controlling physical equipment. The execution instruction set consists of the basic cycle period, the order production batch and shipment start time for each node, the transportation mode selection, and the overtime capacity adjustment amount of raw material suppliers.

[0116] It should be noted that the information interaction and execution process between the above-mentioned devices / units are based on the same concept as the method embodiments of this application. Their specific functions and technical effects can be found in the method embodiments section, and will not be repeated here. Those skilled in the art will understand that, for the sake of convenience and brevity, the division of the above-mentioned functional units and modules is only used as an example. In practical applications, the above functions can be assigned to different functional units and modules as needed, that is, the internal structure of the device can be divided into different functional units or modules to complete all or part of the functions described above. The functional units and modules in the embodiments can be integrated into one processing unit, or each unit can exist physically separately, or two or more units can be integrated into one unit. The integrated unit can be implemented in hardware or as a software functional unit. Furthermore, the specific names of the functional units and modules are only for easy differentiation and are not intended to limit the scope of protection of this application. The specific working process of the units and modules in the above system can be referred to the corresponding process in the foregoing method embodiments, and will not be repeated here.

[0117] like Figure 3 As shown, embodiments of the present invention provide a terminal device, such as... Figure 3 As shown, the terminal device D10 of this embodiment includes: at least one processor D100 ( Figure 3The diagram shows only one processor, a memory D101, and a computer program D102 stored in the memory D101 and executable on the at least one processor D100, wherein the processor D100 executes the computer program D102 to implement the steps in any of the above method embodiments.

[0118] Specifically, when the processor D100 executes the computer program D102, it collects the state parameters of a three-layer supply chain network consisting of raw material suppliers, multiple manufacturers, and multiple factories. For the first material path from the manufacturer node to the factory node, it generates inventory path vector samples based on historical lead time samples and constructs their empirical distribution, thereby establishing a Wasserstein spherical uncertainty set centered on this empirical distribution. For the second material path from the raw material supplier node to the manufacturer node, it constructs a box uncertainty set based on the shortest and longest lead time boundaries, and constructs a maximum cumulative arrival trajectory and a minimum cumulative arrival trajectory based on the box uncertainty set to describe the upper and lower bound fluctuations of inventory levels. Based on the law of conservation of materials, it constructs a supply chain total cost function that couples the Wasserstein spherical uncertainty set and the box uncertainty set. It adopts a two-layer solution architecture: an outer layer that discretely enumerates candidate values ​​for the control cycle and an inner layer that optimizes parameters for a given control cycle. Using dual transformation, it reconstructs the supply chain total cost function optimization problem containing nonlinear terms into a mixed-integer linear programming model, and solves it with the goal of minimizing the supply chain total cost function, obtaining the execution instruction set for controlling physical equipment. Specifically, by constructing a unified total cost function, the decision variables of raw material suppliers, manufacturers, and factories are coupled and optimized, coordinating material allocation, production, and inventory from a global perspective. This solves the material flow imbalance problem caused by decision decoupling in traditional methods and significantly improves the operational stability of the supply chain system. For the uncertainty characteristics of different paths, Wasserstein partial robust optimization and box-type robust optimization are used for modeling, respectively. The composite robust model effectively suppresses the impact of lead time fluctuations on inventory status, ensuring the reliability of control instructions in uncertain environments. The model integrates transportation mode selection with order quantity and production batch size, accurately describing the dynamic coupling relationship between transportation time and inventory level, optimizing the allocation of multi-mode transportation resources, and avoiding the incoordination problem caused by the disconnect between transportation and inventory decisions in traditional methods.

[0119] The processor D100 can be a central processing unit (CPU), or it can be other general-purpose processors, digital signal processors (DSPs), application-specific integrated circuits (ASICs), field-programmable gate arrays (FPGAs), or other programmable logic devices, discrete gate or transistor logic devices, discrete hardware components, etc. A general-purpose processor can be a microprocessor or any conventional processor.

[0120] In some embodiments, the memory D101 may be an internal storage unit of the terminal device D10, such as a hard disk or memory of the terminal device D10. In other embodiments, the memory D101 may be an external storage device of the terminal device D10, such as a plug-in hard disk, smart media card (SMC), secure digital card (SD), flash card, etc., equipped on the terminal device D10. Furthermore, the memory D101 may include both internal and external storage units of the terminal device D10. The memory D101 is used to store the operating system, applications, bootloader, data, and other programs, such as the program code of the computer program. The memory D101 can also be used to temporarily store data that has been output or will be output.

[0121] This application also provides a computer-readable storage medium storing a computer program that, when executed by a processor, implements the steps described in the various method embodiments above.

[0122] This application provides a computer program product that, when run on a terminal device, enables the terminal device to implement the steps described in the various method embodiments above.

[0123] Those skilled in the art should understand that the discussion of any of the above embodiments is merely exemplary and is not intended to imply that the scope of protection of this application is limited to these examples; within the framework of this application, the technical features of the above embodiments or different embodiments can also be combined, the steps can be implemented in any order, and there are many other variations of different aspects of one or more embodiments of this application as described above, which are not provided in detail for the sake of brevity.

[0124] One or more embodiments in this application are intended to cover all such substitutions, modifications, and variations that fall within the broad scope of this application. Therefore, any omissions, modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of one or more embodiments in this application should be included within the protection scope of this application.

Claims

1. A supply chain system control method, characterized in that, include: Collect status parameters of a three-tiered supply chain network consisting of raw material suppliers, multiple manufacturers, and multiple factories; The state parameters include the unit time demand rate of the factory node, the unit time productivity and equipment capacity limit of the manufacturer node, the planned productivity and adjustable overtime load range of the raw material supplier node, and historical samples or fluctuation boundaries of lead time under different transportation modes between nodes. For the first material path from the manufacturer node to the factory node, an inventory path vector sample is generated based on the historical lead time sample and its empirical distribution is constructed. Then, a Wasserstein spherical uncertainty set centered on the empirical distribution is established to optimize inventory costs using a multi-bar method, thereby reflecting the impact of lead time distribution shift on inventory costs. For the second material path from the raw material supplier node to the manufacturer node, a box-shaped uncertainty set is constructed based on the shortest and longest lead time boundaries, and a maximum cumulative arrival trajectory and a minimum cumulative arrival trajectory are constructed based on the box-shaped uncertainty set to describe the upper and lower bound fluctuations of the inventory level. Based on the law of conservation of mass, a supply chain total cost function is constructed that couples the Wasserstein spherical uncertainty set and the box uncertainty set. The supply chain total cost function includes the expected inventory holding cost and stockout risk cost determined by the inventory status of each node, production setup cost, ordering cost, transportation cost, and overtime capacity adjustment cost of raw material suppliers. A two-layer solution architecture is adopted, consisting of an outer layer that discretely enumerates candidate values ​​for the control cycle and an inner layer that optimizes parameters for a given control cycle. The supply chain total cost function optimization problem, which includes nonlinear terms, is reconstructed into a mixed-integer linear programming model using dual transformation. The solution is then performed by a solver with the objective of minimizing the supply chain total cost function, resulting in an execution instruction set for controlling physical equipment. The execution instruction set consists of the basic cycle period, the order production batch and shipment start time for each node, the transportation mode selection, and the overtime capacity adjustment of raw material suppliers.

2. The supply chain system control method according to claim 1, characterized in that, Based on the historical samples of lead time, inventory path vector samples are generated and their empirical distribution is constructed. Then, a Wasserstein spherical uncertainty set centered on this empirical distribution is established, including: For manufacturer nodes To factory node First material path The historical lead time sample is obtained through the inventory recursion formula. Mapping to include Average inventory path sample set for each time segment And construct the experience distribution ;in, , , Indicates the Dirac measure, , Indicates the length of the control cycle; Construct based on experience distribution Centered on, with A Wasserstein sphere with radius ; where, Indicated in the first material path Real inventory path random vector distribution Compared to the empirical distribution constructed from historical samples The permissible deviation is used to quantify the distribution shift caused by non-stationarity of lead time distribution, extreme delays, and sample finiteness; the expression for the Wasserstein spherical uncertainty set is: , Represents the 1-Wasserstein distance, used to measure the transportation cost between an arbitrary distribution and an empirical distribution. Indicates in the support set The space of all probability distributions on the [space].

3. The supply chain system control method according to claim 2, characterized in that, The inventory recursion formula includes: Factory node at the Inventory at the end of each time segment The following formula can be used for recursion: in, Indicates the first The actual delivery volume within a given time period is obtained by mapping historical lead times. Indicates the length of the control cycle. This represents the rate of demand per unit time for each type of component at the factory node; Manufacturer node at Inventory at the end of each time segment The following formula can be used for recursion: in, Indicates as of the date The cumulative arrivals at the end of each time segment. This indicates the cumulative consumption, reflecting the actual consumption of raw materials according to the production plan. This indicates the manufacturer's initial inventory.

4. The supply chain system control method according to claim 3, characterized in that, The construction of a box-shaped uncertainty set based on the shortest and longest boundaries of lead time, and the construction of a maximum cumulative arrival trajectory and a minimum cumulative arrival trajectory based on the box-shaped uncertainty set, includes: For raw material supplier nodes To the manufacturer node Second material path A box-shaped uncertainty set is constructed to describe the range of lead time fluctuations; the expression for the box-shaped uncertainty set is: in, This indicates the mode of transport, which may be sea transport, land transport, or air transport. This indicates the lead time corresponding to different modes of transportation. , These represent the modes of transportation. The shortest lead time and the longest lead time; Through calculation formula Achieve a large cumulative delivery trajectory ;in, These correspond to sea freight, land freight, and air freight modes, respectively. Used to indicate the order batch Select transportation mode According to the shortest lead time Calculate whether the material can be used in the first... Arriving at the end or before of a time segment , A value of 1 indicates that the destination is reachable. A value of 0 indicates that the destination cannot be reached. Indicates the batch of orders placed. , , Indicates the manufacturer's initial inventory. Indicates an integer multiple of the factory cycle period. This indicates the quantity of raw materials shipped by the raw material supplier. This represents the effective contribution coefficient of the lead time within its respective time segment. The effective contribution coefficient indicates the proportion of time that the batch contributes to the average inventory of the segment after its arrival. This indicates the relative proportion of the lead time within its respective time segment, where the relative proportion represents the period from the start of the time segment to the arrival time. Used to indicate the order batch Select transportation mode According to the shortest lead time Calculate whether the material is exactly in the [number]th [period]. A time segment arrives, Indicates as of the date Manufacturer node at the end of each time segment The total amount of raw materials consumed cumulatively; the maximum cumulative arrival trajectory is used to assess the maximum inventory holding cost; Through calculation formula Obtain a minimal cumulative delivery trajectory The minimum cumulative arrival trajectory is used to assess the maximum cost of stockout risk.

5. The supply chain system control method according to claim 4, characterized in that, The expression for the total supply chain cost function is: in, Represents the total cost of the supply chain. This represents the total cost of the factory. This represents the manufacturer's total cost. This represents the total cost to raw material suppliers. This indicates the cost per order for the factory. This represents the unit holding cost of factory parts per unit of time. Indicates average inventory. , This represents the cost per unit of stockout at the factory per unit of time. Indicates from the manufacturer node to factory node The unit transportation cost Represents factory node For manufacturer nodes The rate of demand per unit time This represents the unit holding cost of a manufacturer's components per unit of time. and These represent the positive and negative parts of the function, used to distinguish between inventory holding and stockout states. This indicates the manufacturer's productivity per unit time. Indicates from raw material supplier node To the manufacturer node In transportation mode Lower transportation costs Used to indicate the Batch materials from raw material supplier nodes To the manufacturer node Select transportation mode And whether it is connectable, , Indicates the first Batch materials from raw material supplier nodes To the manufacturer node Select transportation mode And they can be connected. Represents the raw material supplier node per unit time. Assigned to manufacturer node The quantity of raw materials, This represents the manufacturer's ordering cost. This indicates the manufacturer's production setup cost. This represents the unit holding cost of finished products from raw material suppliers and raw materials from manufacturers per unit of time. This represents the manufacturer's unit stockout cost per unit of time. This indicates the cost per production run set up by the raw material supplier. This indicates the cost per order from the raw material supplier. Indicates an integer multiple of the manufacturer's cycle time. This represents the unit holding cost of raw materials from the raw material supplier per unit of time. This indicates the normal total production capacity of the raw material suppliers. This indicates the amount of additional production capacity required by raw material suppliers. This represents the hourly labor cost per unit of overtime for raw material suppliers. This indicates the number of overtime hours worked by raw material suppliers.

6. The supply chain system control method according to claim 5, characterized in that, The two-layer solution architecture includes: Outer enumeration control cycle discrete candidate values ; , Indicates the number of discrete candidate values; Inner layer in a given control cycle The following optimization problem is constructed: in, Represents the total cost. This represents the sum of ordering costs, production setup costs, and transportation costs identified in a three-tier supply chain network. This refers to the first material path at the manufacturer-to-factory level. The worst-case scenario for W-DRO is expected to include inventory and stockout costs. This represents robust inventory holding and stockout costs at the raw material supplier to manufacturer level, under lead time and box-type uncertainty. Indicates the candidate instruction set to be executed; Through calculation formula Obtain the final control cycle and the final execution instruction set , It represents the set of all decision variables.

7. The supply chain system control method according to claim 6, characterized in that, The execution instruction set includes Production frequency and batch size of each manufacturer; Order cycles and order quantities for each factory; The choice of transportation mode and the frequency of shipments for each transportation route; Overtime start instructions and overtime hours from raw material suppliers.

8. A supply chain system control device, characterized in that, include: The data acquisition module is used to collect status parameters of a three-tiered supply chain network consisting of raw material suppliers, multiple manufacturers, and multiple factories. The state parameters include the unit time demand rate of the factory node, the unit time productivity and equipment capacity limit of the manufacturer node, the planned productivity and adjustable overtime load range of the raw material supplier node, and historical samples or fluctuation boundaries of lead time under different transportation modes between nodes. The first data processing module is used to generate inventory path vector samples based on the historical lead time samples for the first material path from the manufacturer node to the factory node and construct its empirical distribution, and then establish a Wasserstein spherical uncertainty set centered on the empirical distribution, which is used to optimize inventory costs by dividing the data into Brussels bars, thereby reflecting the impact of lead time distribution shift on inventory costs. The second data processing module is used to construct a box-shaped uncertainty set based on the shortest and longest boundaries of the lead time for the second material path from the raw material supplier node to the manufacturer node, and to construct the maximum cumulative arrival trajectory and the minimum cumulative arrival trajectory based on the box-shaped uncertainty set to describe the upper and lower bound fluctuations of the inventory level. The third data processing module is used to construct a supply chain total cost function that couples the Wasserstein spherical uncertainty set and the box uncertainty set based on the law of conservation of materials. The supply chain total cost function includes the expected inventory holding cost and stockout risk cost determined by the inventory status of each node, production setup cost, ordering cost, transportation cost, and overtime capacity adjustment cost of raw material suppliers. The instruction acquisition module employs a two-layer solution architecture: an outer layer that discretely enumerates candidate values ​​for the control cycle, and an inner layer that optimizes parameters for a given control cycle. It utilizes dual transformation to reconstruct the supply chain total cost function optimization problem, which includes nonlinear terms, into a mixed-integer linear programming model. The solver then solves this model with the objective of minimizing the supply chain total cost function, yielding an execution instruction set for controlling physical equipment. This execution instruction set consists of the basic cycle period, the order production batch size and shipment start time for each node, the transportation mode selection, and the overtime capacity adjustment amount for raw material suppliers.

9. A terminal device, comprising a memory, a processor, and a computer program stored in the memory and executable on the processor, characterized in that, When the processor executes the computer program, it implements the method as described in any one of claims 1 to 7.

10. A computer-readable storage medium storing a computer program, characterized in that, When the computer program is executed by a processor, it implements the method as described in any one of claims 1 to 7.

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