Decomposition-based multi-stage demand-supply pairing inventory optimization method and system

Abstract

The application relates to a kind of based on the multi-stage demand supply pairing inventory optimization method and system of decomposition, its method includes: step S1: obtaining inventory system initial state, the demand of customer and the inventory in inventory pipeline are decomposed into independent unit, they are paired and combined into supply-demand pair, and a single product-single demand dynamic system model is established accordingly;Step S2: the expected total cost of supply-demand pair is constructed, and it is minimized;Step S3: the optimal purchase time of supply-demand pair is solved according to the expected total cost;Step S4: the optimal purchase quantity is calculated according to the optimal purchase time, so that the optimal inventory control strategy is obtained.The method provided by the application can more efficiently solve the procurement decision problem, and has certain reference value for promoting the efficiency improvement and cost control in actual production and circulation.

Description

Technical Field

[0001] This invention relates to the field of inventory management, and specifically to a decomposed, multi-stage demand-supply matching inventory optimization method and system. Background Technology

[0002] When demand information is complete, dynamic programming is a widely used method in the field of inventory management. It obtains the optimal solution by recursively traversing all decision and state spaces. In recent years, many scholars have continued to use dynamic programming to solve procurement problems. For example, Shenet et al. (2022) studied optimal inventory ordering, expediting, and allocation decisions in a multi-level supply chain within a finite scope and used dynamic programming to describe the optimal strategy form; Li et al. (2022a) proposed a dynamic programming model for jointly optimizing the preparation and inventory management of blood components to better meet demand. Although dynamic programming is very common in solving inventory problems, it also has some drawbacks: First, the state space is often very large because it requires enumerating all possible states, which is infeasible in both time and space. Second, since dynamic programming is recursive, it usually requires a lot of computation to obtain a solution, which may lead to very long running times or even make the algorithm unusable. Finally, dynamic programming usually needs to satisfy certain constraints, such as optimal substructure and no aftereffects. If the problem does not meet these constraints, dynamic programming may not be usable or may not produce an optimal solution. Therefore, it is clear that, to date, there is still no highly effective optimal algorithm that can replace dynamic programming in solving optimization problems in inventory management. Summary of the Invention

[0003] To address the aforementioned technical problems, this invention provides a decomposition-based multi-stage demand-supply matching inventory optimization method and system.

[0004] The technical solution of this invention is: a multi-stage demand-supply matching inventory optimization method based on decomposition, comprising:

[0005] Step S1: Obtain the initial state of the inventory system, decompose customer demand and inventory in the inventory pipeline into independent units, pair them into supply and demand pairs, and establish a single product-single demand dynamic system model accordingly.

[0006] Step S2: Construct the expected total cost of the supply-demand pair and minimize it;

[0007] Step S3: Based on the expected total cost, determine the optimal procurement time for the supply-demand pair;

[0008] Step S4: Calculate the optimal purchase quantity based on the optimal purchase time to obtain the optimal inventory control strategy.

[0009] Compared with the prior art, the present invention has the following advantages:

[0010] This invention discloses a decomposition-based multi-stage demand-supply pairing inventory optimization method. It decomposes customer demand and inventory in the pipeline into independent entities, then pairs them to form "single demand - single product" supply-demand pairs. The expected cost of each supply-demand pair on the inventory system is evaluated, and the timing of satisfying each pair is determined to minimize the total expected cost. Compared to dynamic programming algorithms, this invention does not need to enumerate all possible states, thus minimizing the state space. Simultaneously, its computational complexity is relatively low, as it only requires evaluating each supply-demand pair and determining when to satisfy it. Therefore, this invention can solve procurement decision-making problems more efficiently. Furthermore, the inventory optimization method provided by this invention has a front-to-back solution property, making it easy to understand and allowing decision-makers to easily use it to assist in deciding the quantity of products to purchase and rationally optimize inventory levels. Attached Figure Description

[0011] Figure 1 This is a flowchart of a multi-stage demand-supply matching inventory optimization method based on decomposition, as described in an embodiment of the present invention.

[0012] Figure 2A This is a schematic diagram of the initial state of the single-product-single-demand dynamic system model in an embodiment of the present invention;

[0013] Figure 2B This is a schematic diagram of the status of a single-product-single-demand dynamic system model in an embodiment of the present invention, which has two units of products in stock and one unit of products in transit.

[0014] Figure 2C This is a schematic diagram illustrating the status of a single-product-single-demand dynamic system model after receiving a product in transit, as described in an embodiment of the present invention.

[0015] Figure 2D This is a schematic diagram of the state after the next two purchase orders in the single-product-single-demand dynamic system model in this embodiment of the invention;

[0016] Figure 2E This is a schematic diagram of the state after observing customer demand in the single-product-single-demand dynamic system model in an embodiment of the present invention;

[0017] Figure 2F This is a schematic diagram illustrating the arrival of demand and its fulfillment by in-stock products in the single-product-single-demand dynamic system model of this invention.

[0018] Figure 3 This is a flowchart of the algorithm for solving the optimal purchase quantity in an embodiment of the present invention;

[0019] Figure 4 This is a structural block diagram of a multi-stage demand-supply matching inventory optimization system based on decomposition, as described in an embodiment of the present invention. Detailed Implementation

[0020] This invention provides a decomposition-based multi-stage demand-supply matching inventory optimization method that can solve procurement decision-making problems more efficiently.

[0021] To make the objectives, technical solutions, and advantages of this invention clearer, the invention will be further described in detail below through specific implementations and in conjunction with the accompanying drawings.

[0022] Example 1

[0023] like Figure 1 As shown in the figure, an embodiment of the present invention provides a multi-stage demand-supply matching inventory optimization method based on decomposition, which includes the following steps:

[0024] Step S1: Obtain the initial state of the inventory system, decompose customer demand and inventory in the inventory pipeline into independent units, pair them into supply and demand pairs, and establish a single product-single demand dynamic system model accordingly.

[0025] Step S2: Construct the expected total cost of the supply and demand pair and minimize it;

[0026] Step S3: Based on the expected total cost, solve for the optimal procurement time for the supply and demand pair;

[0027] Step S4: Calculate the optimal purchase quantity based on the optimal purchase time to obtain the optimal inventory control strategy.

[0028] In one embodiment, step S1 above: obtaining the initial state of the inventory system, decomposing customer demand and inventory in the inventory pipeline into independent units, pairing them into supply-demand pairs, and establishing a single-product-single-demand dynamic system model accordingly, specifically including:

[0029] Step S11: Obtain the initial state of the inventory system: m, n, and n′, where m represents the customer demand waiting in the initial state of the inventory system, and m>0 indicates a stockout; n represents the inventory level in the initial state of the inventory system, and when n>0, m=0; n′ represents the quantity of inventory in transit in the initial state of the inventory system.

[0030] Step S12: Construct a single-product-single-demand dynamic system model to represent the logic of inventory status changes over time within a decision-making cycle. The single-product-single-demand dynamic system model includes:

[0031] In the single-product, single-demand dynamic system model, cylinders represent one unit of customer demand. Black cylinders represent demand that has arrived and needs to be met as soon as possible, while dashed cylinders represent demand that may arrive in the future. Cubes represent one unit of inventory. Black cubes represent products that have arrived at the warehouse and are ready for immediate use, white cubes represent inventory in transit (products for which purchase costs have been paid but have not yet arrived at the warehouse), and dashed cubes represent products that may be purchased in the future. The left side of the center line represents the demand queue, which is satisfied sequentially from right to left. The right side of the center line represents the inventory pipeline, which is used sequentially from left to right. The sequence number within the cylinder indicates the order in which the inventory is released into the queue, with values ​​ranging from 1 to n. Figure 2A The figure shows the dynamic system model in the initial state, where m = 0, n = 0, n' = 0, meaning there is no shortage of goods and no excessive inventory.

[0032] At the start of a decision period t, the inventory system has m unmet demands, n usable inventory products in the warehouse, and n' in-transit inventory that has not yet been delivered.

[0033] The order of changes in the inventory system state during decision period t is as follows:

[0034] (1) Treat the demand in the demand queue and the products in the inventory pipeline as a single unit, including products that have not yet arrived in the inventory system, and assign them numbers. The range of the numbers is 1, 2, ..., p, ..., N, where N is a very large constant. Demands and products with the same number form a supply-demand pair, that is, the product corresponding to the supply-demand pair p is product p, and the corresponding demand is demand p.

[0035] like Figure 2B As shown, this is the system state at the end of the previous decision period t-1. There is no shortage in the demand queue, which consists entirely of dashed cylinders; there are 2 units in the inventory pipeline that have arrived at the warehouse, and 1 unit in transit.

[0036] (2) The retailer receives n' previously ordered products, so there are n+n' in stock in the inventory pipeline;

[0037] like Figure 2C As shown, after the start of period t, the system state is 1. The warehouse has received 1 unit of the previously ordered product, so there are 3 units in the inventory pipeline that have arrived at the warehouse.

[0038] (3) The retailer decides whether to purchase product p based on the expected cost that each supply and demand pair p (p = 1, 2, ..., N) may generate, until a certain product is no longer purchased. Based on this, the retailer places a replenishment order for a quantity of q, and the corresponding product is released from the upstream into the inventory pipeline. At this time, there are q units of in-transit inventory in the inventory pipeline.

[0039] like Figure 2D As shown, in system state 2 after the start of period t, the decision-maker places a replenishment order of 2 units with the supplier, that is, 2 units of inventory are released from upstream into the pipeline. At this time, there are 3 units of inventory in the pipeline and 2 units of inventory in transit.

[0040] (4) Retailers observed that d demand items arrived;

[0041] like Figure 2E As shown, in system state 3 after the start of period t, 4 units of customer demand have been observed to arrive, therefore there are 4 units of black cylinders in the demand queue that need to be satisfied.

[0042] (5) Retailers use units of products that are already in the warehouse to meet the demand of units with the same number that have arrived. The met supply and demand pair is removed from the inventory system, and the remaining products and demands in the inventory system are renumbered.

[0043] like Figure 2F As shown, at the end of period t, the system state is such that the 3 units of customer demand in step (4) are satisfied by the 3 units of products in the warehouse. The remaining products and demands in the system are renumbered. At this time, there is still 1 unit of unmet demand and 2 units of in-transit inventory that are about to be delivered. The system is in a state of stockout.

[0044] (6) Update the system state. When n+n'>d, update n=n+n'-d, m=0; when n+n'≤d, update m=dn-n', n=0; in addition, update n'=q.

[0045] In one embodiment, S2 above: minimizing the expected total cost of constructing the supply-demand pair, specifically includes:

[0046] Step S21: Define decision variables In each period t, t = 1, ..., T, where T is the length of the entire decision-making cycle, the decision-maker needs to decide whether to order each product not in the inventory pipeline, i.e., whether the upstream supplier should release one unit of product, until a product is no longer ordered; decision variables For variables of 0-1, it is expressed as the following formula (1):

[0047]

[0048] in, This represents the purchasing decision for product p at time t, where p>n+n' indicates that initially, product p's number is after the total number of existing inventory products.

[0049] In this embodiment, the total decision period is set to T = 10. Therefore, in each period t (t = 1, ..., 10), the decision-maker needs to decide whether to order each product that is not in the inventory pipeline (i.e., the dashed cube in the single-product-single-demand dynamic system model), that is, whether the upstream supplier should release one unit of product, until a certain product is not ordered.

[0050] Step S22: Define the decision objective to minimize the expected costs incurred by the inventory system, including procurement costs, holding costs, and stockout costs; let the expected total cost incurred from purchasing product p be... The expected total cost is related to when product p is purchased;

[0051] When t'+L>Tt, proceed to step S23, where L is the lead time of the supplier; otherwise, calculate according to the following formulas (2) to (6).

[0052]

[0053]

[0054]

[0055]

[0056] Assuming the random demand distribution follows a Poisson distribution with an arrival rate of λ, we can obtain the probability that demand p will arrive in the kth period using the formula for the Poisson distribution. The expression:

[0057]

[0058] Where c: the procurement cost incurred for purchasing one unit of product, including the purchase price and logistics costs;

[0059] h: Holding costs for each unit of unsold product, including warehousing and management expenses;

[0060] b: The stockout cost per unit of unmet customer demand increases over time;

[0061] β (0≤β≤1): Time discount factor;

[0062] t' represents the number of periods for delayed procurement. When t' = 0, it means that product p is procured in the current period. When 1≤t'≤11-t, it indicates that the purchase of product p is postponed. When t' = T - t + 1, it means that product p will be purchased in period T + 1, that is, p will not be purchased during the entire decision-making period T.

[0063] Denotes the probability that demand p arrives in the k-th period starting from the current decision period;

[0064] B(t') represents the unit cumulative backorder cost;

[0065] H1(t') represents the unit cumulative holding cost;

[0066] H2(t') represents the total holding cost incurred when product p is held from period t+L+1 to period T when demand p does not arrive throughout the decision period L;

[0067] When t'+L<k, it means that product p in supply-demand pair p arrives at the warehouse earlier than the corresponding demand p, thus incurring a holding cost; when t'+L>k, it means that demand p arrives at the warehouse earlier than product p, thus incurring a backorder cost. The second term in formula (2) represents the holding cost incurred when demand p does not arrive throughout the entire total decision period T;

[0068] In this embodiment, the procurement cost c of the product is set to 0.2, the backorder cost b is 1, the holding cost h is 0.5, the time discount factor β is 0.8, the procurement lead time L is 3, and the arrival rate λ of the demand is 1;

[0069] Therefore, when t'+3≤10-t, formulas (2) to (5) can be written as:

[0070]

[0071]

[0072]

[0073]

[0074] When t' = 0, it means purchasing product p in the current period, When 1≤t'≤11-t, it means delaying the purchase of product p, When t' = 11-t, it means purchasing product p in the 11th period, that is, not purchasing p throughout the decision period.

[0075] Since it is assumed that the random demand distribution follows a Poisson distribution with an arrival rate of λ = 0.8, according to the formula of the Poisson distribution, the probability that demand p arrives in the k-th period Can be written as:

[0076]

[0077] Step S23: Define the termination condition: Due to the existence of supplier lead time, when t'+L>Tt, it means that no matter when the goods are purchased, they cannot be delivered to the warehouse before the end of the decision cycle. Therefore, only stockout costs will be incurred, and no holding costs will be incurred. Moreover, the stockout costs are independent of t'. At this time, the decision objective is expressed as the following formula (7):

[0078]

[0079] In this embodiment, the following processing method saves computational costs: if the demand p corresponding to the product p to be purchased has already reached the system in the initial state (i.e., p≤m), then purchasing at any time will only incur holding costs, not stockout costs. Furthermore, since the holding cost of delayed purchases monotonically increases with the delay period t', under this condition, it is only necessary to compare the cost of purchasing in the current period with the cost of not purchasing throughout the entire decision-making cycle, and select the option with the minimum cost.

[0080]

[0081] In one embodiment, step S3 above, which involves determining the optimal procurement time for the supply-demand pair based on the expected total cost, specifically includes:

[0082] According to formula (2), the optimal procurement time t' for supply and demand pair p can be solved. * , expressed as the following formula (8):

[0083]

[0084] If t' * =0, that is If product p is purchased in the current period, then assign the value p = p + 1, repeat step S3, and solve for the purchase time of the next supply-demand pair p;

[0085] If t' * ≥1, that is If product p is not purchased in the current period, proceed to step S4.

[0086] In this embodiment, the input parameters of the solution algorithm include the total number of decision periods T, the product's procurement cost c, the stockout cost b, the holding cost h, the time discount factor β, the procurement lead time L, the initial customer demand m, the existing inventory n and pipeline inventory n', and the demand arrival rate λ. The output is the optimal procurement quantity list q. * The solution algorithm consists of two main steps: calculating the optimal purchasing decision for each supply-demand pair within each decision period. And based on the optimal procurement decision for each product, calculate the optimal procurement quantity for each decision period within the entire decision-making cycle. Finally, update the system status.

[0087] like Figure 3 As shown, the algorithm first iterates through each decision period and each unpurchased product using a double loop, and then calculates the optimal purchase quantity for the current product by iterating through the number of delayed purchase periods t'. If the demand for the product has already reached the system in the initial state (i.e., p≤m), then we only need to compare the expected total cost of purchasing in the current period and not purchasing, and select the minimum value. Otherwise, we need to consider all possible purchasing opportunities from the current decision period to the demand arrival period, and select the purchasing opportunity with the minimum expected total cost as the optimal decision. It is important to note that for purchasing opportunities that have already passed the demand arrival period, only the holding cost needs to be calculated, and the stockout cost does not need to be calculated.

[0088] Then, based on the optimal purchase quantity for each product, calculate the optimal purchase quantity for the current decision-making period. The system status (including existing demand m, existing inventory n, and inventory in transit n') is updated according to the update rules. This process is repeated until the last decision period T = 10 is reached, at which point the algorithm terminates and outputs the optimal purchase quantity list q. * .

[0089] In this embodiment, the system state is updated according to the following rules:

[0090] m t =(m t-1 +d t -q t-3 ) +

[0091] n t =(n t-1 -d t +q t-3 ) +

[0092]

[0093] In addition, during the process of iterating through the number of delayed procurement periods t', the cost at t'=0 can be used as the baseline cost. Once a baseline cost is reached... If it's smaller, return. This is because as long as any but In other words, the purchase should not be made in the current period, but should be postponed to a later period.

[0094] In one embodiment, step S4 above, which calculates the optimal purchase quantity based on the optimal purchase time to obtain the optimal inventory control strategy, specifically includes:

[0095] Based on the optimal procurement time t' * Calculate the total replenishment quantity in period t. The sum of decision variables for all individual products is expressed as the following formula (9):

[0096]

[0097] in, This represents the optimal purchase quantity for period t, thus yielding the optimal inventory control strategy.

[0098] For example, when the input parameters are T=10, c=0.2, b=1, h=0.5, L=3, β=0.8, λ=1, m=0, n=0, n'=0, Table 1 shows the solution results of the optimal inventory strategy under this parameter combination, including the changes of the optimal purchase quantity over time, the changes of the optimal inventory level over time, the changes of the optimal inventory level in transit over time, and the changes of the stockout quantity over time.

[0099] Table 1 shows the solution results obtained using a decomposition-based multi-stage demand-supply matching inventory optimization algorithm in the embodiments.

[0100]

[0101] As can be seen from the results in Table 1, the inventory levels in the system and the inventory in transit change over time, while the cumulative stockout gradually decreases, eventually reaching zero in the sixth period. This indicates that the procurement strategy proposed in this invention, based on a decomposed multi-stage demand-supply matching inventory optimization algorithm, addresses the demand gap problem in the system to some extent, leading to a gradual reduction and eventual disappearance of the cumulative stockout.

[0102] This invention discloses a decomposition-based multi-stage demand-supply pairing inventory optimization method. It decomposes customer demand and inventory in the pipeline into independent entities, then pairs them to form "single demand - single product" supply-demand pairs. The expected cost of each supply-demand pair to the inventory system is evaluated, and a decision is made on when to satisfy the pair to minimize the total expected cost. Compared to dynamic programming algorithms, this invention does not need to enumerate all possible states, thus minimizing the state space. Simultaneously, its computational complexity is relatively low, as it only requires evaluating each supply-demand pair and determining when to satisfy it. Therefore, this invention can solve procurement decision-making problems more efficiently.

[0103] This invention provides an efficient and accurate solution to the single-product multi-stage inventory optimization problem in actual supply chain management, which has certain reference value for promoting efficiency improvement and cost control in actual production and circulation.

[0104] Example 2

[0105] like Figure 4 As shown, this embodiment of the invention provides a multi-stage demand-supply matching inventory optimization system based on decomposition, comprising the following modules:

[0106] Module 51 for constructing a single-product-single-demand dynamic system model is used to obtain the initial state of the inventory system, decompose customer demand and inventory in the inventory pipeline into independent units, pair them together into supply and demand pairs, and establish a single-product-single-demand dynamic system model accordingly.

[0107] The expected total cost calculation module 52 is used to construct the expected total cost of the supply and demand pair and minimize it;

[0108] The optimal procurement time calculation module 53 is used to solve for the optimal procurement time of the supply and demand pair based on the expected total cost.

[0109] The module 54 for obtaining the optimal inventory control strategy is used to calculate the optimal purchase quantity based on the optimal purchase time, thereby obtaining the optimal inventory control strategy.

[0110] The above embodiments are provided merely for the purpose of describing the present invention and are not intended to limit the scope of the invention. The scope of the invention is defined by the appended claims. Various equivalent substitutions and modifications made without departing from the spirit and principles of the invention should be covered within the scope of the invention.

Claims

1. A multi-stage demand-supply matching inventory optimization method based on decomposition, characterized in that, include: Step S1: Obtain the initial state of the inventory system, decompose customer demand and inventory in the inventory pipeline into independent units, pair them into supply and demand pairs, and establish a single-product-single-demand dynamic system model based on this, specifically including: Step S11: Obtain the initial state of the inventory system: m, n, and n′, where m represents the customer demand waiting in the initial state of the inventory system. This indicates a stockout has occurred; n represents the initial inventory level of the inventory system. hour, n′ represents the quantity of inventory in transit in the initial state of the inventory system; Step S12: Construct a single-product-single-demand dynamic system model to represent the dynamic evolution of the inventory system state during demand arrival, inventory replenishment, demand fulfillment, and state update within a decision-making cycle. Step S2: Construct the expected total cost of the supply-demand pair and minimize it, specifically including: Step S21: Define decision variables : (1) in, Indicates in Period of time for products The procurement decision, among which This indicates the product in its initial state. The product number is listed after the total number of products already in stock; Step S22: Define the decision objective to minimize the expected costs incurred by the inventory system, including procurement costs, holding costs, and stockout costs; let the procured products... The expected total cost generated is The expected total cost is related to when the product is purchased. related; when At that time, among them, For the lead time of supplying the supplier, where T is the total decision-making cycle length, proceed to step S23; otherwise, based on the number of delayed procurement periods... ,need In the The probability of reaching a certain period Procurement costs Unit cumulative holding cost Cumulative unit stockout cost and demand Throughout the decision-making period Total holding cost incurred when the destination is not reached Calculate the products to be purchased Expected total cost generated ; Step S23: Define termination conditions: Due to the existence of supplier lead time, when This means that regardless of when the purchase is made, the goods cannot be delivered to the warehouse before the end of the decision-making cycle. Therefore, only stockout costs are incurred, not holding costs. Furthermore, stockout costs are related to... Irrelevant, at this point, the expected total cost Includes only procurement costs and cumulative unit stockout costs; Step S3: Based on the expected total cost, solve for the optimal procurement time of the supply-demand pair, i.e., solve for the supply-demand pair. Make the expected total cost Minimum optimal procurement time ; Step S4: Calculate the optimal purchase quantity based on the optimal purchase time to obtain the optimal inventory control strategy, specifically including: Based on the optimal procurement time Calculate Total replenishment volume during the period , for all individual products, the decision variables And, that is, total replenishment quantity For the period The optimal purchase quantity.

2. A multi-stage demand-supply matching inventory optimization system based on decomposition, characterized in that, Includes the following modules: A module for constructing a single-product-single-demand dynamic system model is used to obtain the initial state of the inventory system, decompose customer demand and inventory in the inventory pipeline into independent units, pair them together into supply-demand pairs, and establish a single-product-single-demand dynamic system model based on this. Specifically, this includes: Step S11: Obtain the initial state of the inventory system: m, n, and n′, where m represents the customer demand waiting in the initial state of the inventory system. This indicates a stockout has occurred; n represents the initial inventory level of the inventory system. hour, n′ represents the quantity of inventory in transit in the initial state of the inventory system; Step S12: Construct a single-product-single-demand dynamic system model to represent the dynamic evolution of the inventory system state during demand arrival, inventory replenishment, demand fulfillment, and state update within a decision-making cycle. The module for calculating the expected total cost, used to construct and minimize the expected total cost of the supply-demand pair, specifically includes: Step S21: Define decision variables : (1) in, Indicates in Period of time for products The procurement decision, among which This indicates the product in its initial state. The product number is listed after the total number of products already in stock; Step S22: Define the decision objective to minimize the expected costs incurred by the inventory system, including procurement costs, holding costs, and stockout costs; let the procured products... The expected total cost generated is The expected total cost is related to when the product is purchased. related; when At that time, among them, For the lead time of supplying the supplier, where T is the total decision-making cycle length, proceed to step S23; otherwise, based on the number of delayed procurement periods... ,need In the The probability of reaching a certain period Procurement costs Unit cumulative holding cost Cumulative unit stockout cost and demand Throughout the decision-making period Total holding cost incurred when the destination is not reached Calculate the products to be purchased Expected total cost generated ; Step S23: Define termination conditions: Due to the existence of supplier lead time, when This means that regardless of when the purchase is made, the goods cannot be delivered to the warehouse before the end of the decision-making cycle. Therefore, only stockout costs are incurred, not holding costs. Furthermore, stockout costs are related to... Irrelevant, at this point, the expected total cost Includes only procurement costs and cumulative unit stockout costs; The optimal procurement time calculation module is used to solve for the optimal procurement time of the supply-demand pair based on the expected total cost, i.e., to solve for the optimal procurement time of the supply-demand pair. Make the expected total cost Minimum optimal procurement time ; The module for obtaining the optimal inventory control strategy is used to calculate the optimal purchase quantity based on the optimal purchase time, thereby obtaining the optimal inventory control strategy, specifically including: Based on the optimal procurement time Calculate Total replenishment volume during the period , for all individual products, the decision variables And, that is, total replenishment quantity For the period The optimal purchase quantity.

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