Vehicle equipment maintenance equipment supply optimization method considering transverse guarantee strategy

Abstract

The invention discloses a vehicle equipment maintenance equipment supply optimization method considering a transverse guarantee strategy, and the method comprises the steps: carrying out the modeling of a vehicle equipment maintenance equipment supply problem, initializing parameters, building a multi-target joint optimization model with the minimization of the total cost of a system as a target, carrying out the solving, and obtaining an optimal supply scheme. And then feedback guarantee data is obtained, model parameters are updated, and closed-loop optimization is realized. According to the scheme, the problems of decision lag, low resource utilization rate and insufficient guarantee efficiency of a traditional guarantee mode in a task environment with uncertain requirements and high response requirements can be effectively solved, and the effects of cost optimization, improvement of the service satisfaction rate and remarkable improvement of the inventory turnover rate are achieved.

Description

Technical Field

[0001] This invention belongs to the field of logistics and support, and specifically relates to an optimization method for the supply of vehicle equipment maintenance materials that takes into account lateral support strategies. Background Technology

[0002] The current support system primarily relies on the traditional vertical replenishment model (such as the (S-1, S) ordering strategy), where each supporting unit independently manages its inventory and applies for replenishment from higher-level organizations. This model has significant drawbacks: First, to cope with uncertain demand, each supporting unit needs to maintain a high safety stock, resulting in high inventory holding costs and consuming a large amount of logistical resources. Second, when a supporting unit experiences a shortage of specific equipment, even if other units within the system have spare inventory, the lack of an intelligent and efficient coordination mechanism prevents rapid support, forcing them to passively wait for vertical replenishment, which easily leads to missed maintenance windows and reduced equipment availability. While some existing technologies involve horizontal transfers or material transportation within the supply chain, they generally suffer from the following shortcomings:

[0003] (1) It often adopts empirical rules or simple heuristic methods, lacks model-based adaptive optimization capabilities, and is difficult to cope with highly dynamic and uncertain environments during tasks;

[0004] (2) Inventory allocation and transportation scheduling are often optimized separately, making it difficult to achieve global optimization;

[0005] (3) Data-driven methods were not fully utilized for demand forecasting and decision support, resulting in insufficient intelligence.

[0006] Therefore, there is an urgent need for a collaborative support solution for maintenance equipment that can deeply integrate inventory management, real-time scheduling, and intelligent decision-making. Summary of the Invention

[0007] To address the aforementioned problems, the present invention aims to provide a method for optimizing the supply of vehicle equipment maintenance materials that takes into account lateral support strategies.

[0008] The specific technical solution for achieving the objective of this invention is as follows:

[0009] A method for optimizing the supply of vehicle equipment maintenance materials considering lateral support strategies includes the following steps:

[0010] Step 1: Model the supply problem of vehicle equipment and maintenance materials, and initialize the parameters;

[0011] Step 2: Construct a multi-objective joint optimization model with the goal of minimizing the total system cost;

[0012] Step 3: Solve the multi-objective joint optimization model to obtain the optimal supply scheme;

[0013] Step 4: Execute the optimal supply plan, obtain feedback on the guarantee data, update the model parameters, and achieve closed-loop optimization.

[0014] Compared with the prior art, the beneficial effects of the present invention are as follows:

[0015] The present invention proposes an intelligent optimization method for the supply of vehicle equipment maintenance materials based on models and intelligent optimization algorithms. Its core lies in constructing a data-driven joint optimization model and using intelligent algorithms for efficient solution, thereby realizing intelligent decision-making throughout the entire process from inventory allocation to supply scheduling.

[0016] Its advantages include:

[0017] Cost optimization: Numerical experiments show that, under the same inventory level, the total system cost of adopting the horizontal hedging strategy is reduced by an average of 11.1%, and it demonstrates stable cost optimization capabilities under different demand scenarios.

[0018] Improved service satisfaction rate: Under the same inventory level, the service satisfaction rate of the horizontal support strategy is significantly improved, which can achieve higher support targets with lower inventory configuration, thereby saving total system cost and spare parts capital.

[0019] Significantly improved inventory turnover: By combining a horizontal support strategy with a multi-objective optimization model, the system can monitor the inventory status of each support team in real time, dynamically adjust replenishment plans, and reduce inventory backlog and idleness. After implementation, inventory turnover has increased by an average of 20%-30%, reducing waste caused by expired inventory or obsolete technology, while freeing up a large amount of working capital for other critical tasks;

[0020] Emergency response time is significantly shortened: Technical means: Intelligent optimization algorithms can quickly generate the optimal transfer route and supply plan, and combined with the horizontal support network, it can achieve "nearby allocation and rapid response";

[0021] The present invention provides an intelligent and adaptive method for inventory management and supply optimization of maintenance equipment, which effectively solves the problems of decision-making lag, low resource utilization and insufficient support efficiency in traditional support models under task environments with uncertain demand and high response requirements.

[0022] The present invention will be further described below with reference to specific embodiments. Attached Figure Description

[0023] Figure 1 This is a schematic diagram of a three-tiered equipment warehouse architecture considering horizontal supply in an embodiment of the present invention.

[0024] Figure 2 This is a schematic diagram of the process for optimizing the supply of vehicle equipment maintenance materials based on the lateral support strategy of the present invention.

[0025] Figure 3 This is a schematic diagram comparing the total cost under different inventory levels in an embodiment of the present invention.

[0026] Figure 4 This is a schematic diagram comparing the average total cost under different inventory levels in an embodiment of the present invention.

[0027] Figure 5 This is a schematic diagram illustrating the average service satisfaction rate of the traditional (S-1,S) ordering strategy under different inventory levels in this embodiment of the invention.

[0028] Figure 6 This is a schematic diagram comparing the service satisfaction rates of two inventory strategies under different inventory levels in an embodiment of the present invention. Detailed Implementation

[0029] Example

[0030] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. The described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0031] As indicated in this application and claims, unless the context clearly indicates otherwise, the words "a," "an," "an," and / or "the" do not specifically refer to the singular and may also include the plural. Generally speaking, the terms "comprising" and "including" only indicate the inclusion of explicitly identified steps and elements, which do not constitute an exclusive list, and the method or apparatus may also include other steps or elements.

[0032] Unless otherwise specifically stated, the relative arrangement, numerical expressions, and values ​​of the components and steps described in these embodiments do not limit the scope of this application. It should also be understood that, for ease of description, the dimensions of the various parts shown in the drawings are not drawn to actual scale. Techniques, methods, and devices known to those skilled in the art may not be discussed in detail, but where appropriate, such techniques, methods, and devices should be considered part of the specification. In all examples shown and discussed herein, any specific values ​​should be interpreted as merely exemplary and not as limitations. Therefore, other examples of exemplary embodiments may have different values. It should be noted that similar reference numerals and letters in the following drawings denote similar items; therefore, once an item is defined in one drawing, it need not be further discussed in subsequent drawings.

[0033] The support system for vehicle equipment maintenance materials typically employs a tiered, vertical supply model. At the top level is the superior rear warehouse, which maintains a comprehensive and sufficient quantity of maintenance materials, but is usually geographically located far from the frontline mission units. The middle level consists of maintenance organizations (or basic support group central warehouses), deployed in concealed, easily accessible areas behind the mission area, responsible for receiving, storing, managing, and distributing maintenance materials. The most forward-deployed accompanying support units (or warehouses) directly provide support to the mission units, serving as the direct source of material demand.

[0034] Because the accompanying support units have limited inventory capacity, they are prone to shortages of specific parts during missions due to fluctuations in demand, making it impossible to meet maintenance needs in a timely manner. In addition, equipment failures are random and sudden. Once equipment support is delayed while mission requirements are extremely urgent, the traditional vertical model that relies solely on hierarchical support (i.e., "rear warehouse → maintenance facility → accompanying support unit") will be unable to meet the rapid response requirements of mission troops, causing many pieces of equipment to be out of service due to waiting for parts, thus affecting the integrity of the equipment.

[0035] To resolve the aforementioned contradictions, this plan introduces a horizontal supply strategy into a multi-level supply system, such as... Figure 1 As shown, this strategy allows for the allocation and emergency replenishment of equipment among accompanying support teams within the same basic support group, under predetermined rules (e.g., limited to the same type of maintenance equipment and within the same support group). By establishing this three-dimensional support network that prioritizes vertical hierarchical support and supplements it with nearby horizontal supply, the timeliness of maintenance equipment supply and overall support effectiveness can be significantly improved.

[0036] Combination Figure 2 This solution provides a method for optimizing the supply of vehicle equipment maintenance materials that considers lateral support strategies, including the following steps:

[0037] Step 1: Model the supply problem of vehicle equipment and maintenance materials, and initialize the parameters;

[0038] The supply of vehicle equipment and maintenance materials is the entire process of ensuring that various vehicles can obtain the necessary parts and maintenance materials in a timely and accurate manner when they break down or require maintenance.

[0039] The supply process includes higher-level rear warehouses, maintenance facilities, and support teams;

[0040] The supply of vehicle equipment and maintenance materials presents a complex systemic problem at the decision-making level: each support unit possesses both demand and supply attributes, and its supply capacity is constrained; the types of equipment, supply sources, and transfer quantities must be determined simultaneously, while ensuring the system optimality of the final solution. To address this, this proposal constructs a horizontal inventory support model based on a single-cycle full transfer strategy, aiming to minimize the total system cost and optimize the scheduling of emergency supply tasks. For ease of modeling and analysis, the following support system elements and basic assumptions are established:

[0041] Assume there are L support teams, each of which stores M types of repair equipment. The unit storage cost of the repair equipment is H, the unit shortage penalty is π, and the vehicle loading limit is Q.

[0042] The fixed cost of ordering goods from the maintenance organization is k, and the unit vehicle transfer cost between each support team follows a transfer cost matrix generated based on the distance between each point;

[0043] In the supply of vehicle equipment and maintenance materials:

[0044] Before the start of each fixed mission cycle, each support team completes equipment replenishment, restores the initial inventory level, and incurs corresponding fixed ordering costs.

[0045] Maintenance requests are generated after resupply is completed, and the order quantity for the next cycle is determined based on these requests.

[0046] The maintenance needs of each support unit arose at the same time.

[0047] Each support team's needs for various types of maintenance equipment are independent of each other and follow a Poisson distribution with specific parameters;

[0048] The unit inventory holding cost is the same for all types of repair equipment;

[0049] The penalty cost for units experiencing stockouts of all types of repair equipment is the same;

[0050] The cost of transport vehicles is calculated based on a cost matrix formed by the distances between each support unit, satisfying the following conditions: .

[0051] The initialization parameters include demand distribution parameters, various cost parameters, and transportation capacity constraints.

[0052] Step 2: Construct a multi-objective joint optimization model with the goal of minimizing the total system cost;

[0053] The multi-objective joint optimization model prioritizes minimizing total cost while also maximizing service satisfaction and minimizing response time.

[0054] Total cost Z includes inventory costs, stockout penalty costs, lateral movement costs, and fixed order costs;

[0055] Inventory costs are:

[0056]

[0057]

[0058] in, This represents the initial inventory of equipment m for the i-th support unit. This represents the random requirement of equipment m for the i-th support unit. This represents the total amount of equipment (m) transferred from one support unit (i) to other support units.

[0059] The following formula takes the value based on the result of the operation within the parentheses: if the result is positive, it takes the original value; otherwise, it takes zero.

[0060] Its calculation logic is based on the initial inventory of the m-th type of equipment accompanying support unit i. Subtract its corresponding random demand If the equipment is transferred to other units, then subtract the sum of the transfer amounts of equipment m transferred out by unit i. The result is judged as follows: if the result is positive, it is multiplied by the unit inventory cost to form the current inventory cost of the equipment; if the result is zero, the remaining inventory is zero and there is no inventory cost; if the result is negative, it means that team i is out of stock of equipment m, and the inventory cost of the equipment is zero.

[0061] The cost of stockout penalties is:

[0062]

[0063]

[0064] Among them, if If the internal calculation result is positive, it means that the support unit is out of stock. Combined with the unit stockout penalty coefficient π, the current period's efficiency loss cost is obtained; otherwise, the support unit's equipment m is not out of stock, and the penalty cost is zero.

[0065] To calculate the transfer cost from platoon i to platoon j, first, summarize the total transfer volume of all types of equipment, divide it by the rated load capacity Q of a single transport vehicle, and round the quotient up (to the nearest ceil) to determine the required number of vehicles. Then, combine this with the unit transportation cost coefficient. This yields the transfer cost for that route. The total system transfer cost is the sum of the transfer costs from all supply teams to demand teams. Additionally, when constructing the total system cost function, the fixed vertical supply cost generated in each supply cycle must be included. ;

[0066] The cost of lateral transport is:

[0067]

[0068] Where ceil represents rounding up, and the fixed ordering cost is K;

[0069] In this application, when vertical supply cannot meet the immediate urgent needs due to response delays after a demand is generated, how to reduce the total system cost and improve equipment repair rate through a horizontal support strategy. To simplify the analysis and highlight the effect of horizontal support, it is assumed that the vertical supply decision remains consistent regardless of whether horizontal support is enabled, and its cost is always a fixed value. This simplifying assumption does not affect the validity of the model comparison. Subsequent numerical analysis will show that lateral hedging, by optimizing inventory distribution, can reduce the system's average inventory level, thereby achieving overall cost savings. Therefore, setting the vertical replenishment cost, i.e., the fixed ordering cost, as a fixed value does not affect the evaluation conclusion of the relative benefits of the lateral hedging strategy.

[0070] Therefore, the objective function of the multi-objective joint optimization model is:

[0071]

[0072] The constraints of the objective function are:

[0073] The amount of equipment m transferred from support unit i to j shall not exceed the remaining inventory of equipment m in support unit i:

[0074]

[0075] The amount of equipment m transferred from support unit j to support unit i shall not exceed the shortage requirement of support unit i for equipment m:

[0076]

[0077] The total quantity of all equipment m transferred from support unit i to other support units shall not exceed the remaining inventory of equipment m in support unit i after the demand is generated:

[0078]

[0079] The total quantity of all equipment m transferred from other support units to support unit i shall not exceed the shortage requirement of support unit i for equipment m after the demand is generated:

[0080]

[0081] All support units are prohibited from transferring any equipment to themselves (self-transfer is forbidden):

[0082]

[0083] The amount of equipment transferred between any two support units is a non-negative integer (to ensure the physical feasibility of the transfer amount):

[0084]

[0085] Step 3: Solve the multi-objective joint optimization model to obtain the optimal supply scheme;

[0086] The solution process employs a linear weighted sum method to transform the multi-objective model into a single-objective problem, based on the model's characteristics, namely, the presence of integer decision variables. This refers to the amount of equipment (m) transported from platoon i to platoon j. Then, an exact algorithm, including branch and bound, or a metaheuristic algorithm for large-scale problems, such as a genetic algorithm, is used to solve the problem and obtain the optimal horizontal supply plan. .

[0087] Step 4: Execute the optimal supply plan, obtain feedback guarantee data, and update the model parameters based on the latest guarantee data feedback to achieve closed-loop optimization.

[0088] The impact of the horizontal protection strategy on the total system cost is analyzed below based on the specific content of this embodiment;

[0089] Assuming there are 10 support teams, each with 4 types of maintenance equipment in stock, the unit storage cost is... Unit out-of-stock penalty Vehicle loading restrictions are The fixed cost of ordering from repair shops is The unit vehicle transfer cost between each team follows a transfer cost matrix generated based on the distance between each point:

[0090]

[0091] To simplify model complexity and focus on the core benefits of the lateral support strategy, this scheme assumes that the demand for the four types of maintenance equipment all follow the parameter [parameter]. The Poisson distribution.

[0092] This assumption is based on the following consideration: differences in the specific demand distribution and inventory settings of various equipment do not affect the system-level mechanism of lateral support in responding to emergency shortages. For high-value equipment, strict inventory control is required. Without the introduction of a lateral support strategy, the system typically adopts an (s, S) type ordering strategy as the baseline, meaning that when the inventory level is lower than the reorder point s, vertical replenishment is initiated to raise the inventory to the target level S. In other words, whenever equipment repair needs occur, replenishment is initiated within the current cycle to restore the inventory to the set capacity. Since each replenishment cycle is independent and there is no cross-cycle impact, this study will focus on the supply optimization problem within a single cycle, emphasizing the optimization effect of the lateral support strategy on the total system cost and equipment repair rate. To verify the effectiveness of the lateral support strategy, this paper will introduce a lateral support mechanism based on the aforementioned traditional (s, S) strategy and conduct comparative analysis through numerical experiments. Specifically, different initial inventory levels will be set (based on 10, with 8 gradients set at 10% increments, i.e.... This study evaluates the total system cost under both the traditional strategy and the strategy incorporating lateral support, thereby identifying the optimal inventory level and its corresponding cost for each model. First, for the case of inventory level y=10, a demand matrix for the four types of equipment is generated for 10 accompanying support teams based on the demand distribution. Then, the inventory status after the demand is generated is calculated as follows: This serves as input for subsequent transportation decisions.

[0093]

[0094] When the inventory status matrix When a negative value appears in the data, it indicates that the accompanying support unit is involved. equipment The equipment is currently out of stock. By substituting demand and inventory data into the constructed horizontal support optimization model, the optimal equipment transfer plan between each team was obtained. The specific transfer volume decision results are shown in Table 1.

[0095] Table 1. Transshipment Volume Decision

[0096] <![CDATA[x ijm ]]> Spare parts transfer volume <![CDATA[x ijm ]]> Spare parts transfer volume （2,3,1） 3 （9,8,3） 3 （3,4,4） 3 （9,10,1） 4 （4,1,2） 2 （10,2,2） 2 （4,1,3） 2 （10,2,3） 2 （8,7,2） 5 （10,2,4） 1 （8,9,4） 3 （10,7,2） 2 （9,5,1） 1 （10,7,3） 2 （9,5,3） 3 （10,7,4） 1

[0097] The mixed-integer programming model was solved using LINGO software (with its built-in branch and bound algorithm). The optimal lateral supply scheme was obtained, and the total system cost after implementing the aforementioned transshipment decision was 314. To scientifically evaluate the synergistic effect of the lateral support strategy, it needs to be compared and analyzed with the traditional (S-1,S) ordering strategy (as the baseline). The total cost function of this traditional strategy consists of three parts: inventory holding cost, stockout penalty cost, and fixed ordering cost.

[0098]

[0099] With the initial inventory level set at 10 and the demand matrix as follows: Under the baseline scenario, the total system cost using only the traditional ordering strategy is calculated to be 374. The cost difference is detailed in Table 2, comparing it to the total cost (314) of the horizontal support strategy.

[0100] Table 2 Total Cost Comparison

[0101] Inventory strategy: Total cost: Adopt a horizontal protection strategy 314 Using only the traditional (S-1,S) ordering method 374

[0102] To verify the universality of the lateral support strategy in reducing the total system cost, this embodiment set up nine independent and repeated experiments with the same parameters. By generating new demand data and calculating the total system cost under the two strategies respectively, the statistical comparison results are shown in Table 3, indicating that the lateral support strategy exhibits stable cost optimization capabilities under different demand scenarios.

[0103] Table 3 Total Cost Comparison

[0104] random demand Adopt a horizontal protection strategy Ordering method only (S-1,S) Cost reduction ratio <![CDATA[D1]]> 314 374 15.2% <![CDATA[D2]]> 292 324 9.9% <![CDATA[D3]]> 336 407 17.4% <![CDATA[D4]]> 316 343 7.8% <![CDATA[D5]]> 289 317 8.8% <![CDATA[D6]]> 279 305 8.5% <![CDATA[D7]]> 285 322 11.5% <![CDATA[D8]]> 290 326 11% <![CDATA[D9]]> 302 352 14.2% <![CDATA[D 10 ]]> 363 388 6.6%

[0105] When the inventory level is set to 10, compared to using only the (S-1,S) ordering strategy, the introduction of the lateral support strategy reduces the total system cost by an average of 11.1%. The experimental results clearly show that, with the same inventory level, applying the lateral support strategy is more effective in optimizing the total system cost compared to simply using the (S-1,S) ordering strategy.

[0106] When the spare parts inventory level of a maintenance facility is 10, this inventory level precisely matches the expected demand for faulty equipment. However, if demand fluctuates, stockouts may occur. Under traditional ordering strategies, this often results in high stockout penalty costs. Therefore, when a lateral support strategy is permitted, accompanying support teams can meet the emergency replenishment needs of out-of-stock teams through lateral support, thereby reducing stockout penalties and ultimately lowering the total system cost.

[0107] To reduce stockouts, traditional ordering systems typically maintain a safety stock of spare parts exceeding anticipated demand as a buffer against demand fluctuations. However, for systems employing a lateral support strategy, since they can fulfill emergency replenishment needs during stockouts through transshipment, there's no need to maintain a large spare parts inventory. Next, we will compare the total cost of the lateral support strategy and the traditional (S-1,S) strategy under different inventory levels to determine the optimal inventory level and optimal total system cost for both models.

[0108] In the specific calculations, we set the value of y to 10, 11, 12, 13, 14, 15, 16, and 17, and compared the total cost for faulty equipment when using a lateral support strategy versus using only the traditional replenishment method, under the condition of random demand D1. The comparison results of the total cost are detailed in Table 4.

[0109] Table 4. Comparison of total costs under different inventory levels with demand D1

[0110] y The cost of using horizontal protection Using only traditional replenishment methods y The cost of using horizontal protection Using only traditional replenishment methods 17 474 474 13 339 350 16 437 437 12 320 346 15 397 400 11 307 354 14 366 372 10 314 374

[0111] To make the calculation results clearer, we have presented them graphically. A comparison of total costs at different inventory levels is shown below. Figure 3 .

[0112] It is easy to see that at all inventory levels, the total system cost under the lateral support model is almost always lower than that of the traditional (S−1, S) ordering model without lateral support. This is because when lateral support is allowed, the accompanying support units that experience stockouts can be urgently transferred from other units to meet the needs of the faulty equipment through a lower-cost transfer method, thereby reducing stockout penalty costs and thus lowering the total system cost. To avoid the influence of specific demand data, we calculate the stochastic demand D1 to D2 at different inventory levels. 10 The corresponding total system cost was calculated, and the average cost was used to compare the two models. The results are shown in Table 5. Figure 4 As shown.

[0113] Table 5 Comparison of average total cost under different inventory levels

[0114] y Use horizontal protection strategy Using only traditional replenishment methods Reduced ratio y Use horizontal protection strategy Using only traditional replenishment methods Reduced ratio 17 478.7 479.7 Less than 1% 13 331.3 343.7 3.6% 16 439.6 442.7 Less than 1% 12 306.5 323.5 5.3% 15 401.2 406.3 1.3% 11 298.8 326.4 8.5% 14 365.6 373.5 2.1% 10 306.9 345.8 11.2%

[0115] A comparison of the average total cost of the two models at different inventory levels shows that the system's total cost using the lateral support strategy is significantly optimized at every inventory level. This result is consistent with previous analysis, primarily because lateral support can meet the emergency replenishment needs of support teams during stockouts, thereby reducing the stockout penalty cost for maintenance organizations and achieving further cost optimization based on the traditional (S−1, S) ordering strategy. To maximize support benefits, maintenance organizations typically choose the inventory level with the lowest system total cost as the basis for inventory decisions; the optimal order quantity in the classic ordering model is derived by minimizing the system total cost. According to the analysis and calculation results, when using the traditional (S−1, S) model, the optimal inventory level is 12, corresponding to an average total cost of 323.5; while when using the lateral support strategy, the optimal inventory level is 11, with an average total cost of 298.8. Specific comparison results are shown in Table 6.

[0116] Table 6. Optimal Inventory Levels and Average Total Costs for the Two Models

[0117] Inventory strategy Inventory costs Average total cost Adopt a horizontal protection strategy 11 298.8 Using only traditional ordering methods 12 323.5

[0118] The optimization effect of the horizontal support strategy on total cost is mainly reflected in two aspects: First, by allocating spare parts between teams to meet the emergency repair needs of units experiencing stockouts, the penalty costs caused by stockouts are effectively reduced, thereby reducing the total system expenditure. Second, because the horizontal support strategy is implemented within the system, each supporting team can reduce its own safety stock to a certain extent, thereby reducing the overall inventory holding cost. Considering the large number of teams under the maintenance organization and the variety of spare parts required, the overall reduction in inventory levels will have a significant optimization effect on the total system cost.

[0119] The impact of horizontal support strategies on equipment maintenance service satisfaction rate will be analyzed next.

[0120] In actual maintenance activities, organizations not only pursue maximum maintenance benefits but also need to maintain a certain service satisfaction rate to improve overall maintenance capabilities. As seen in the above analysis of the impact of horizontal maintenance strategies on total system cost, adopting horizontal maintenance strategies can effectively reduce inventory levels and total system cost. Next, we will further explore the impact of horizontal maintenance strategies on equipment maintenance service satisfaction rates and compare them with traditional ordering strategies to analyze their optimization effect at the service support level. When analyzing traditional ordering methods, we still use the (S−1, S) strategy as the benchmark. To ensure the completion of maintenance support tasks for faulty equipment at a given service level, maintenance organizations typically set up corresponding safety stock.

[0121] False equipment component demand compliance The Poisson distribution applies. If the service level desired by the repair shop is 99.9%, then the minimum inventory required to meet this service level within a demand cycle should satisfy the following condition: Calculated This means the minimum inventory level is 17 units. Substitute it as service demand data The total cost model shows that to achieve the desired service fulfillment rate, the traditional replenishment method requires a total system cost of 474 and generates 274 spare parts surplus. If the inventory level is maintained at 17, and the expected demand for each spare part by each supporting support team is E(x) = 10, then an average of 280 spare parts surplus will be generated per cycle, accounting for 41% of the total inventory. This large surplus inventory not only increases inventory costs but also ties up the organization's working capital. The main root of this problem is that each supporting support team can only rely on its own reserves to cope with demand fluctuations. However, by adopting a horizontal support strategy, replenishment can be achieved through emergency allocation between teams, allowing each unit to appropriately reduce inventory reserves, thereby reducing total costs and releasing capital tied up in inventory.

[0122] (1) Service satisfaction rate of the accompanying support team under the traditional (S−1, S) ordering strategy

[0123] First, for the case where the inventory level is 10, calculate its service fulfillment rate, using the initial value D1 for the demand data. After demand is generated, the remaining inventory and spare parts shortages for each supporting team are as follows:

[0124]

[0125] The spare parts shortages for each supporting unit were summarized, and the total shortage was 60. The total demand for the corresponding period was:

[0126]

[0127] Summing the demand matrix yields a total demand of 406. Therefore, with an inventory level of 10 and demand data of D1, the overall service satisfaction rate of the maintenance facility is 85.2%. To improve the service satisfaction rate for faulty equipment, the facility typically increases inventory levels. Next, this paper will analyze the effect of different inventory levels on improving the service satisfaction rate under a traditional replenishment strategy. This will be done by calculating ten random demand iterations D1–D at inventory levels y = 10 to 17. 10 The corresponding average service satisfaction rates are shown in Table 7.

[0128] Table 7. Average Total Cost and Average Service Satisfaction Rate of Traditional (S-1, S) Strategies at Different Inventory Levels

[0129] y (S-1,S) Average cost of the ordering strategy Average service satisfaction rate of strategy (S-1,S) y (S-1,S) Average cost of the ordering strategy Average service satisfaction rate of strategy (S-1,S) 17 479.7 100% 13 343.7 97.75% 16 442.7 99.48% 12 323.5 96.11% 15 406.3 99.18% 11 326.4 92.57% 14 373.5 98.59% 10 345.8 87.54%

[0130] As inventory levels increase, equipment maintenance service satisfaction rates also improve. The data in the table shows that achieving a higher service satisfaction rate significantly increases the total system cost. When only an (S−1, S) ordering strategy is used, additional spare parts reserves not only increase the maintenance organization's inventory costs but also have a limited effect on improving service satisfaction rates. Figure 5 As shown. However, to ensure service availability for faulty equipment, organizations still have to significantly increase their inventory levels.

[0131] (2) Service satisfaction rate of accompanying support units adopting horizontal support strategy

[0132] When the inventory level is 10 and the demand is D1, after implementing horizontal support, the service fulfillment status of each accompanying support team changes due to spare parts allocation between teams. The specific values ​​are as follows:

[0133]

[0134] The number of unmet service requests was 21, and the overall service satisfaction rate of the repair facility was 94.8%. Due to the existence of the lateral support mechanism, when a support team experiences a shortage of parts, the demand can be met through spare parts allocation between teams. Therefore, under the same inventory level, the lateral support strategy can significantly improve the average service satisfaction rate. To analyze the effect of the lateral support strategy on improving the service satisfaction rate under different inventory levels, this paper calculates ten random demand cycles D1–D for inventory levels y = 10 to 17. 10 The corresponding average service satisfaction rate is compared with the results under the traditional (S−1, S) ordering strategy. The specific data is shown in Table 1.8.

[0135] Table 1.8 Comparison of service satisfaction rates between horizontal assurance strategy and traditional (S-1.S) ordering strategy

[0136] y Service satisfaction rate using transshipment strategies Average service satisfaction rate of strategy (S-1,S) y Service satisfaction rate using transshipment strategies Average service satisfaction rate of strategy (S-1,S) 17 100% 100% 13 99.53% 97.75% 16 99.96% 99.48% 12 99.14% 96.11% 15 99.91% 99.18% 11 98.11% 92.57% 14 98.86% 98.59% 10 95.12% 87.54%

[0137] Compared to the traditional (S-1, S) ordering strategy, the accompanying support system employing a lateral support strategy has a significant advantage in service fulfillment rate for faulty equipment. The comparative results show that, under any inventory situation, the service fulfillment rate with lateral support enabled is no lower than that without this strategy. This indicates that lateral support is not only an effective improvement over the traditional vertical replenishment model, but its advantages lie not only in the increased service fulfillment rate at the same inventory level, but also in maintaining high support efficiency even at lower inventory levels.

[0138] The curves showing service rate as a function of inventory level under both models Figure 6As can be seen, the horizontal support strategy can achieve a high service satisfaction rate even with low inventory levels. With increasing inventory, the service satisfaction rate rapidly approaches 99% or higher. By adopting the horizontal support strategy, maintenance organizations can achieve their support goals with lower inventory levels, thus significantly saving on total system costs and spare parts holding costs. As organizations responsible for equipment support, the fundamental purpose of pursuing a high service satisfaction rate for maintenance organizations is to improve comprehensive support capabilities and resource utilization efficiency. Therefore, the core objective of these organizations is to minimize total system costs while ensuring a high service satisfaction rate, thereby achieving optimal support effectiveness. The results of integrating the average total system cost and average service satisfaction rate for each inventory level are shown in Table 9.

[0139] Table 9 Comparison of Average Total Cost and Average Service Satisfaction Rate between the Two Models

[0140] y Average total cost of using transshipment Average service satisfaction rate using transshipment The average total cost of the (S-1,S) strategy Average service satisfaction rate of strategy (S-1,S) 17 478.7 100% 479.7 100% 16 439.6 99.96% 442.7 99.48% 15 401.2 99.91% 406.3 99.18% 14 365.6 99.86% 373.5 98.59% 13 331.3 99.53% 343.7 97.75% 12 306.5 99.14% 323.5 96.11% 11 298.8 98.11% 326.4 92.57% 10 306.9 95.12% 345.8 87.54%

[0141] The maintenance organization aims to minimize costs while achieving a certain service fulfillment rate. Analysis of the traditional (S-1,S) ordering strategy shows that when the organization expects a 99.9% fulfillment rate, the traditional replenishment method requires an inventory level of 17, which matches the calculation results in this example, with a corresponding average total cost of 479.7. However, with the lateral support strategy, only an inventory level of 15 is needed to achieve the same service goal, with an average total cost of 401.2. If the organization pursues a 98% service fulfillment rate, allowing for lateral support, the inventory level only needs to be set to 11, with a total cost of 298.8; while the traditional (S-1,S) strategy requires increasing the inventory level to 14, with a total cost of 373.5, to achieve the same goal. Therefore, the lateral support strategy can achieve the organization's service fulfillment requirements with lower inventory input and lower total system cost.

[0142] By comparing with the traditional (S-1, S) strategy, this embodiment analyzes the effect of the lateral support strategy on improving the service satisfaction rate of faulty equipment.

[0143] In summary, this supply optimization method not only improves service satisfaction by more than 10% under the same resource conditions, but more importantly, it achieves a fundamental shift in the support model from "experience-driven" to "data-driven." By using this method, the system can maintain a higher service level while reducing inventory levels by 20%, significantly improving the economy and adaptability of the equipment support system and providing technical support for precise support.

[0144] This solution also provides a vehicle equipment maintenance material supply optimization system that considers lateral support strategies, including the following modules:

[0145] Initialization module: Used to model the supply problem of vehicle equipment maintenance materials and initialize parameters;

[0146] Optimization module: Used to construct a multi-objective joint optimization model with the goal of minimizing the total system cost, solve the multi-objective joint optimization model, and obtain the optimal supply scheme;

[0147] Execution Feedback Module: Used to execute the optimal supply plan, obtain feedback guarantee data, update model parameters, and achieve closed-loop optimization.

[0148] This solution also provides a computer 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 perform the following steps:

[0149] Step 1: Model the supply problem of vehicle equipment and maintenance materials, and initialize the parameters;

[0150] Step 2: Construct a multi-objective joint optimization model with the goal of minimizing the total system cost;

[0151] Step 3: Solve the multi-objective joint optimization model to obtain the optimal supply scheme;

[0152] Step 4: Execute the optimal supply plan, obtain feedback on the guarantee data, update the model parameters, and achieve closed-loop optimization.

[0153] This solution also provides a computer-readable storage medium on which a computer program is stored, wherein the computer program, when executed by a processor, performs the following steps:

[0154] Step 1: Model the supply problem of vehicle equipment and maintenance materials, and initialize the parameters;

[0155] Step 2: Construct a multi-objective joint optimization model with the goal of minimizing the total system cost;

[0156] Step 3: Solve the multi-objective joint optimization model to obtain the optimal supply scheme;

[0157] Step 4: Execute the optimal supply plan, obtain feedback on the guarantee data, update the model parameters, and achieve closed-loop optimization.

[0158] The embodiments described above are merely one implementation method of this application, and while the descriptions are specific and detailed, they should not be construed as limiting the scope of the invention patent. It should be noted that those skilled in the art can make various modifications and improvements without departing from the concept of this application, and these all fall within the protection scope of this application. Therefore, the protection scope of this patent application should be determined by the appended claims.

Claims

1. A vehicle equipment maintenance equipment supply optimization method considering a lateral security strategy, characterized by, The method comprises the following steps: Step 1, modeling a vehicle equipment maintenance equipment supply problem and initializing parameters; Step 2, constructing a multi-objective joint optimization model with the minimum total cost as the primary objective, while taking into account the maximum service satisfaction rate and the minimum response time; Step 3, solving the multi-objective joint optimization model to obtain an optimal supply scheme; Step 4, executing the optimal supply scheme to obtain feedback support data, updating model parameters, and realizing closed-loop optimization.

2. The method of claim 1, wherein, The modeling of the vehicle equipment maintenance equipment supply problem in step 1 is as follows: Vehicle equipment maintenance equipment supply is the entire process of ensuring that various vehicles can obtain the required spare parts and maintenance materials in a timely and accurate manner when they break down or need maintenance; In the supply process, there are superior rear warehouses, maintenance agencies and support teams; Suppose there are L support teams, each storing M types of maintenance equipment, with a unit storage cost of H, a unit shortage penalty of π, and a vehicle loading limit of Q; The fixed cost of ordering from the maintenance agency is k, and the unit vehicle transfer cost between each support team is subject to a transfer cost matrix generated according to the distance between each point; In the vehicle equipment maintenance equipment supply: Before the start of each fixed task cycle, each support team completes equipment replenishment, restores to the initial inventory level, and generates a corresponding fixed ordering cost; Maintenance demand is generated after replenishment is completed, and the ordering quantity for the next cycle is determined based on the demand; The maintenance demand of each support team is generated at the same time point; The demand for each type of equipment by each support team is independent and subject to a Poisson distribution with specific parameters; The unit inventory holding cost of each type of equipment is the same; The unit shortage penalty cost of each type of equipment is the same; Transportation vehicle costs are calculated based on a cost matrix of distances between each of the security teams, satisfying .

3. The method of claim 1, wherein the method further comprises: The initialized parameters include demand distribution parameters, various cost parameters and transportation capacity constraints.

4. The method for optimizing supply of vehicle equipment maintenance equipment considering lateral security strategy according to claim 2, characterized in that, The multi-objective joint optimization model in step 2 takes the minimum total cost as the primary objective, while taking into account the maximum service satisfaction rate and the minimum response time; The total cost Z includes inventory cost, shortage penalty cost, horizontal transfer cost and fixed ordering cost; The inventory cost is: ； ； wherein, represents the initial inventory of equipment m of the i-th support unit, represents the random demand of equipment m of the i-th support unit, represents the total amount of equipment m of the i-th support unit transferred to other support units; If the result is positive, multiply the unit inventory cost to form the current inventory cost of the equipment; if the result is zero, the remaining inventory is zero and there is no inventory cost; if the result is negative, it indicates that team i is short of equipment m, and the inventory cost of the equipment is zero. The shortage penalty cost is: ； ； wherein, If If the internal operation result is positive, it means that the support team is out of stock, and combined with the unit stock penalty coefficient π, the performance loss cost of the current period is obtained; otherwise, the support team equipment m is not out of stock, and the penalty cost is zero. The horizontal transfer cost is: ； Where ceil represents rounding up, and the fixed ordering cost is K.

6. The method of claim 4, wherein the method further comprises: The objective function of the multi-objective joint optimization model is: ； The constraint condition of the objective function is: The transfer quantity of equipment m from support team i to j cannot exceed the remaining inventory quantity of equipment m in support team i: ； The transfer quantity of equipment m from support team j to i cannot exceed the shortage demand quantity of equipment m in support team i: ； The total quantity of equipment m transferred from support team i to other support teams cannot exceed the remaining inventory quantity of equipment m in support team i after demand is generated: ； The total quantity of equipment m transferred from other support teams to support team i cannot exceed the shortage demand quantity of equipment m in support team i after demand is generated: ； The transfer quantity of equipment from all support teams to itself is zero: ； The equipment transfer amount between any two security teams is a non-negative integer: 。 7. The method of claim 2, wherein the method further comprises: In the step 3, the multi-objective joint optimization model is solved by using a linear weighted sum method to convert the multi-objective model into a single-objective problem, and then an exact algorithm including a branch and bound method or a meta-heuristic algorithm for large-scale problems is selected to solve the problem, so as to obtain an optimal horizontal supply scheme.

8. A vehicle equipment maintenance equipment supply optimization system considering a lateral security strategy, characterized by, The method comprises the following modules: An initialization module is configured to model a vehicle equipment maintenance equipment supply problem and initialize parameters; An optimization module is configured to construct a multi-objective joint optimization model with the minimum total cost of the system as a target, solve the multi-objective joint optimization model, and obtain an optimal supply scheme; An execution feedback module is configured to execute the optimal supply scheme, obtain feedback security data, update model parameters, and realize closed-loop optimization.

9. A computer device comprising a memory, a processor, and a computer program stored on the memory and executable on the processor, characterized in that, The processor executes the computer program to implement the steps of the method in any one of claims 1-6.

10. A computer storable medium having stored thereon a computer program, characterized in that The computer program is executed by the processor to implement the steps of the method in any one of claims 1-6.

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