Method and apparatus for determining target inventory levels for items
By establishing a simulation environment based on historical sales data in the catering industry, the Monte Carlo method is used to simulate the sales process of goods, calculate expiration and order losses, determine the optimal inventory level, solve the problem of insufficient inventory in the catering industry, achieve accurate prediction of target inventory levels, and improve the balance between customer experience and product delivery efficiency.
Patent Information
- Application Number
- CN202111286359.6
- Authority / Receiving Office
- CN · China
- Patent Type
- Patents(China)
- Current Assignee / Owner
- Filing Date
- 2021-11-02
- Publication Date
- 2025-11-18
- Estimated Expiration
- 2041-11-02
AI Technical Summary
Existing technologies make it difficult to accurately predict the inventory levels of goods in the catering industry, leading to insufficient inventory or overstocking and waste during peak consumption periods, which negatively impacts customer experience and results in product waste.
By establishing a simulation environment based on historical sales data, the Monte Carlo method is used to simulate the product sales process, calculate the target inventory level for expiration losses and order losses, calculate the loss function for expiration losses and order losses, and determine the optimal inventory level to balance cost and delivery efficiency.
It enables accurate prediction of inventory levels in the catering industry, reduces waste, improves customer satisfaction, and finds a balance between cost savings and delivery efficiency.
Smart Images

Figure CN116090943B_ABST
Abstract
Description
Technical Field
[0001] This application relates to data statistics, and in particular, to methods, equipment, and computer storage media for determining and estimating target inventory levels of goods, such as those in restaurant establishments. Background Technology
[0002] In service industries such as catering and retail, it's crucial to prepare a certain amount of inventory in advance for different products to cope with the surge in customer demand during peak consumption periods. However, controlling the quantity of goods prepared in advance is often challenging. Insufficient inventory won't meet peak demand, while excessive inventory leads to unsold stockpiles. Many service industry products have strict requirements regarding shelf life. This is especially true for fast-food restaurants, where prepared food often has a short shelf life, and stockpiling can result in food exceeding its expiration date and going to waste. Therefore, meeting customer demand as much as possible while avoiding waste is one of the challenges of inventory management in the service industry. Furthermore, waiting for the restaurant to prepare goods on-site (e.g., food preparation or sourcing from other stores) is a factor affecting the customer experience; some customers may not be able to tolerate the wait and leave the store, resulting in lost orders.
[0003] The prerequisite for accurately predicting the quantity of goods consumed by customers is the accurate simulation and modeling of the customer's consumption and purchase process, i.e., the sales process. Simulation optimization algorithms are currently widely used in various industries, such as the dynamic optimization of traffic light durations and the optimal shape of vehicles from a dynamic energy-saving perspective. The purpose of process simulation is to use computers to simulate real-world environments under certain conditions and evaluate which processing schemes(s) better meet the optimization objectives of the process. For example, in the dynamic optimization of traffic light durations, when simulating vehicle and pedestrian flow, the efficiency corresponding to different traffic light duration settings is observed to select the duration scheme with the highest traffic efficiency.
[0004] Therefore, there is a need to improve existing inventory management by accurately predicting the sales process, determining the adequacy of inventory, and avoiding various sales losses. Summary of the Invention
[0005] The methods, apparatus, and computer storage media of the embodiments of this application are intended to solve, in whole or in part, at least one of the problems and / or needs mentioned above, and to achieve optimal inventory management of goods.
[0006] According to one aspect of this application, a method for determining a target inventory level for goods is provided, comprising:
[0007] Obtain historical sales data for the product;
[0008] Based on the historical sales data of the products, select the total sales quantity of the products within the predetermined time interval, and determine the sales time of the products with the total sales quantity and the sales quantity corresponding to the sales time;
[0009] Based on the sales time and sales quantity of the goods, the total sales quantity that ensures the sales loss of the goods within the predetermined time interval meets the preset loss conditions is determined as the target inventory level, where the sales loss of the goods includes the expiration loss of the goods and the order loss.
[0010] According to another aspect of this application, a device for determining a target inventory level of goods is provided, comprising:
[0011] The acquisition unit is configured to acquire historical sales data of the product;
[0012] The simulation unit is configured to select the total sales quantity of a product within a predetermined time interval based on historical sales data, and to determine the sales time of the product and the corresponding sales quantity for that sales time; and
[0013] The calculation unit is configured to determine the total sales quantity as the target inventory level based on the sales time and sales quantity of the goods, so that the sales loss of the goods in a predetermined time interval meets the preset loss conditions, wherein the sales loss of the goods includes the expiration loss of the goods and the order loss.
[0014] According to another aspect of this application, a computer-readable storage medium is provided that stores a computer program thereon, the computer program including executable instructions that, when executed by a processor, implement the method as described above.
[0015] According to yet another aspect of this application, an electronic device is proposed, including a processor and a memory for storing executable instructions of the processor, wherein the processor is configured to execute the executable instructions to implement the method described above.
[0016] The method and apparatus for determining target inventory levels of goods proposed in this application can accurately establish a probabilistic model of the sales process involving pre-prepared goods as a simulation environment for predicting and determining the optimal target inventory level. By calculating the minimum value of the loss function, which characterizes the sales loss of goods, within the predetermined time interval of interest, the optimal target inventory level is determined, finding an effective balance between cost savings and improved goods delivery efficiency, thereby enhancing the social and corporate benefits of the goods sales process. This method and apparatus for determining target inventory levels can simultaneously consider the time sensitivity and sales fluctuations of goods, making it particularly suitable for the sale of goods with short shelf lives, thus improving the user's consumption and shopping experience. Attached Figure Description
[0017] The above and other features and advantages of this application will become more apparent from a detailed description of exemplary embodiments thereof with reference to the accompanying drawings.
[0018] Figure 1 This is a schematic flowchart illustrating a method for determining a target inventory level of goods according to an embodiment of this application.
[0019] Figure 2 This is a schematic structural block diagram of a device for determining a target inventory level of goods according to an embodiment of this application.
[0020] Figure 3 This is a schematic block diagram of an electronic device for determining a target inventory level of goods according to an embodiment of this application. Detailed Implementation
[0021] Exemplary embodiments will now be described more fully with reference to the accompanying drawings. However, these exemplary embodiments can be implemented in many forms and should not be construed as limited to the embodiments set forth herein; rather, these embodiments are provided to make the content of this application comprehensive and complete, and to fully convey the concept of the exemplary embodiments to those skilled in the art. In the drawings, the dimensions of some elements may be exaggerated or modified for clarity. The same reference numerals in the drawings denote the same or similar structures, and therefore their detailed descriptions will be omitted.
[0022] Furthermore, the described features, structures, or characteristics can be combined in any suitable manner in one or more embodiments. Numerous specific details are provided in the following description to give a full understanding of embodiments of this application. However, those skilled in the art will recognize that the technical solutions of this application can be practiced without one or more of the specific details described, or other methods, elements, etc., can be employed. In other instances, well-known structures, methods, or operations are not shown or described in detail to avoid obscuring various aspects of this application.
[0023] This paper uses the food sales scenario in the catering industry, particularly the fast food industry, as an example to introduce the solution of this application, where the goods are mainly food or meals sold in catering stores. A significant characteristic of food products is their shelf life, which is generally short, such as less than one hour, or in some cases less than 30 minutes, 15 minutes, 10 minutes, or even a few minutes or seconds. For example, ice cream may melt in just a few seconds in summer, while French fries may not remain crispy for more than ten minutes after being taken out of the fryer. Those skilled in the art will understand that the solution proposed in this application for determining the target inventory level of goods is not only applicable to the catering industry but also to the sales scenarios of other goods, especially those with a shelf life, particularly a relatively short one. In addition to shelf-life requirements, these sales scenarios also involve situations where customer traffic, sales volume, or sales revenue fluctuates regularly or predictably over time, requiring advance preparation or preparation of goods (i.e., providing inventory). Therefore, inventory management is crucial for buffering sales fluctuations and peaks. In addition, different products have different shelf-life requirements and different sales process characteristics, requiring product providers to set up corresponding inventory management plans for different types of products.
[0024] Regarding the optimal inventory level problem, the academic and industrial communities have previously proposed the concept of safety stock. For example, the paper "Understanding safety stock and mastering its equations" proposes modeling commodity inventory by fitting the parameters of a Gaussian distribution based on periodic demand fluctuations. There are also some inventory level algorithms for other fields. For instance, Chinese patent application CN104573840A, entitled "Medical Consumables Prediction and Replenishment System and Calculation Method," proposes a method for calculating the replenishment quantity corresponding to different probabilities based on historical demand probabilities.
[0025] Safety stock solutions primarily target the storage of products or materials in industrial settings, where the shelf life of stored items often extends to several days or even months, making their availability relatively insensitive to time. However, applying safety stock principles to the food service industry leads to the overproduction of food in advance, resulting in significant waste as these pre-prepared items cannot be sold quickly enough.
[0026] The consumable replenishment plan proposed for the medical field mainly predicts the future consumption ratio and / or probability of consumables based on historical consumption data of different surgeries / tests. However, if the medical consumable inventory calculation plan is applied to the catering industry, the frequency and quantity of medical consumable consumption are far less than the frequency and quantity of food consumption, making it difficult to obtain an optimal inventory plan. The catering industry can obtain more accurate queuing data for different food items through large amounts of daily customer dining data from each store, enabling modeling of the sales process. However, the daily consumption frequency and quantity of each type of medical consumable cannot be compared to this. The method mentioned in CN104573840A mainly calculates the consumption probability based on the quantity of consumables consumed in the past 12 months, which cannot construct a more accurate simulation environment of the sales process on a daily, hourly, or even minute-by-minute basis. This results in low accuracy of the optimal inventory prediction results at the daily and hourly levels.
[0027] Safety stock solutions in the medical field not only suffer from the problem of inventory (consumables) being insensitive to the frequency, speed, and quantity of consumption, but also from differing responses to stockouts compared to other sectors. When emergency stock replenishment time exceeds the maximum allowable waiting time for surgery / examination, the solution in CN104573840A only issues a warning without considering order cancellation. In reality, in the medical consumables sector, when timely replenishment is not possible, surgery and examination appointments are typically suspended until the relevant consumables are available again in inventory, unlike in the food service industry where customers leave simply because their food needs to be prepared on-site and the wait is too long or there are too many people in line. Therefore, the aforementioned solution in the medical consumables sector does not provide a strategy for handling situations where the waiting cost exceeds the customer's or user's waiting limit, resulting in order losses.
[0028] In practice, the quantity of pre-prepared food, i.e., the inventory level, is typically set slightly higher than the actual demand or consumption. In the scenario of target inventory level prediction and determination for the goods involved in this application, particularly in the scenario of determining the inventory level of pre-prepared food provided by restaurants, the food inventory level is highly correlated with the shelf life of the food and the speed / frequency and quantity of consumer purchases. In this paper, the target inventory level is the goal of achieving optimal inventory management, i.e., the optimal inventory level. The shelf life determines that the difference between the predicted inventory level and the actual consumption quantity of food cannot be too large. When the difference is positive, it indicates that the food inventory is sufficient to meet the current consumer demand and there is a surplus; the storage time of the food must not exceed the shelf life. However, a fast consumption speed / frequency and / or excessive consumption quantity may cause the above difference to become negative, or even the absolute value of the negative difference to increase in the short term. When the difference is negative, it indicates that the food inventory is insufficient to meet the current consumer demand, and food preparation needs to be carried out on-site. If the difference is negative (or the difference between the rate / frequency and quantity of food consumption and the predicted food inventory is positive) and its absolute value increases over time, it indicates that the predicted food inventory is clearly insufficient to meet current user purchasing and consumption needs, food must be prepared on-site, and the shortage situation may become more severe.
[0029] In this paper, the consumption or purchase of goods can be understood as equivalent to the sale of goods; when a customer or user consumes or purchases a good, it is equivalent to the good being sold. Therefore, the speed / frequency and quantity of goods consumed or purchased can also be represented by the speed / frequency and quantity of goods sold, thus characterizing the actual sales process of the goods. Based on historical sales data, the sales process of goods is estimated or predicted for a future predetermined time period, thereby predicting or determining the inventory level needed to meet the sales demand for goods during that future predetermined time period.
[0030] Those skilled in the art will understand that when the inventory of goods is insufficient to meet current sales demand (also known as a stockout), users need to wait for the goods to be prepared on-site or for the goods to be replenished according to a predetermined replenishment strategy. The waiting time incurred by users while waiting for the goods to become available again can be referred to as the user's waiting cost. Waiting cost includes not only waiting time but also the number of users in the queue forming a waiting list for the goods requested in the user's order; that is, the number of users queuing for the goods. Users can measure their waiting cost by the length of time they wait for the goods, and they can also measure their queuing cost (which can also be converted into waiting time) by how many users are ahead of them or how many users' purchase requests will be fulfilled before they can receive the goods. Therefore, waiting cost is a parameter directly or indirectly related to waiting time.
[0031] According to embodiments of this application, a simulation environment can be established based on historical sales data of the product sales process, specifically supporting a model of the future sales process of pre-prepared products (represented by product inventory levels). The simulation model is used to simulate the product sales process in a store, for example, the sales process during a predetermined time interval. In this simulation environment, a loss function associated with product sales losses is created using the established sales process model. The value of the corresponding loss function is evaluated for different expected inventory levels, i.e., the degree of product sales loss during the product sales process is assessed. Finally, the expected inventory level of the product whose sales loss meets a preset loss condition within the time interval of interest is selected as the target inventory level; this target inventory level is the optimal inventory level. The preset loss condition can be the expected inventory level of the product with the minimum sales loss in the corresponding expected sales process, i.e., the sales loss of the target / optimal inventory level is the minimum among all expected inventory levels. The simulation environment generally targets the process of customers or users consuming in-store. Users purchase or consume the desired products of different types and quantities listed in the order by placing an order. The type and quantity of products in the order submitted by the user can be determined through experience or other calculation methods. The shelf life of each type of product can be predetermined or adjusted, and will not be detailed in this document. The shelf life is the maximum period a product can be stored in a warehouse. Products whose storage or inventory time exceeds the shelf life are considered expired and have no sales value, and are discarded. Products discarded due to expiration are recorded as expired losses, represented by the quantity of the product, and are part of the sales loss for the product during the predetermined time period of interest. Another part of the sales loss is the loss incurred by the store when, as mentioned above, the customer chooses not to place an order at the store because the waiting cost for preparing the product when it is out of stock exceeds the customer's maximum tolerable waiting cost (hereinafter referred to as the waiting cost threshold). This loss is referred to as order loss, expressed in terms of the quantity of the product corresponding to the type. Expiration losses involve cost-saving factors, while order losses involve product delivery efficiency and the shopping experience.
[0032] The reason for choosing sales loss as the loss function is that the purpose of determining the optimal target inventory level is to find an effective balance between cost savings and improved product delivery efficiency. Therefore, the difference between the inventory level and the demand level can be used as an intermediate variable.
[0033] The following reference Figure 1 This document presents an illustrative process for determining target inventory levels for goods.
[0034] The method mainly includes steps S110: establishing a model of the sales process of goods within a predetermined time interval of interest and acquiring relevant data; determining a loss function for calculating sales losses and calculating sales losses corresponding to different inventory levels of goods based on the sales process model; and selecting sales losses that meet preset loss conditions and their corresponding target inventory levels from the calculated sales losses. Prior to step S110, there may also be a step S101 to acquire historical sales data from the historical sales process of the goods.
[0035] According to the method for determining the target inventory level of goods in this application, after obtaining historical sales data of the goods, the actual sales process of the goods is simulated in step S110. Although this paper establishes a simulation environment by generating a probabilistic model of goods sales based on historical sales data of the goods' historical sales process, those skilled in the art will understand that other methods besides simulation methods can also be used to simulate the actual sales process of goods and determine the parameters related to the sales process. In addition to using a probabilistic model, other models that can accurately characterize the sales process of goods can also be used.
[0036] In step S110, a simulation environment is first established in sub-step S111, and a probabilistic model is selected to simulate the sales process. Next, in sub-step S112, the probabilistic model is used to calculate the sales time series data of the selected product within a predetermined time interval based on historical sales data of the product, for each simulation, the sales time series data corresponding to that total sales quantity. The sales time series data provides detailed information about the sales process, including the sales time of the product and the sales quantity of the product corresponding to that sales time. For sales scenarios offering multiple types of products, the total sales quantity can be selected for each type of product, and the corresponding product sales time and sales quantity can be calculated.
[0037] According to probability and statistics, the sales quantity of a commodity within a unit of time follows a Poisson distribution, as expressed by the following formula (1):
[0038]
[0039] Here, X represents the total sales quantity of the product within a predetermined time interval (e.g., a unit of time). Depending on the product type and the application scenario, different time intervals can be selected. For example, the predetermined time interval can be greater than or equal to 5 minutes, 10 minutes, 15 minutes, 30 minutes, or 1 hour. k represents the sales quantity of the product, which is an integer greater than or equal to 0. P is the probability that the sales quantity of the product within the predetermined time interval is k. The parameter λ, as the time parameter of the Poisson distribution, is related to the average sales quantity of the product within a unit of time. The average sales quantity of the product comes from the store's historical sales data and can be continuously updated. Historical sales data can be extracted for each type of product to obtain time series data of the sales time and the quantity of products sold during that sales time. For the purpose of simplifying calculations, the resolution of the time dimension of the historical data can be adjusted according to the setting of a unit of time or different predetermined time intervals to reduce the sample size of the sales data.
[0040] After establishing the probability model in sub-step S111, the sales process of the goods is simulated in step S112. Since the process of users arriving at the store to purchase and consume goods is a typical stochastic process, the sales process of the goods can be simulated based on the probability distribution calculated by formula (1) using methods that can characterize stochastic processes, thereby obtaining a simulation environment for generating and calculating the loss function related to sales losses. In the following text, the Monte Carlo method is used for simulation, but those skilled in the art should understand that other methods capable of simulating stochastic processes can also be used to construct the simulation environment.
[0041] In the Monte Carlo method, the total sales quantity of a specific product corresponds to the probability P of the Poisson distribution. Within the predetermined time interval (t, t+Δt) of interest. Sub-Monte Carlo sampling, obtained The timestamp was obtained from the simulation. The sales time of each product was recorded, and a simulation environment was established.
[0042] The above simulation addresses the ideal sales process, where one item is sold at a time. In reality, customers arriving at a store randomly may order more than one item of each product type. Therefore, the sales time and corresponding quantity settings in the Monte Carlo method can be adjusted to achieve the desired effect. Sub-Monte Carlo sampling obtained Second timestamp The sum of the number of goods sold (possibly greater than 1) corresponding to the sales time represented by each timestamp, that is, the total number of goods sold within the predetermined time interval. Furthermore, when multiple users arrive at the store and submit orders at the same time, or when users arrive at the store at different times but submit orders at the same time, the sum of the quantities of the same type of goods in these users' orders can be regarded as the sales quantity of the goods at the time of order submission (the time of sale).
[0043] For the total sales quantity X of the goods in formula (1), we can select those k values whose corresponding probability P values satisfy the probability conditions as the total sales quantity of the goods in the Monte Carlo method for simulation, without having to simulate and calculate the loss function value for all possible k values, thus reducing the amount of simulation data and computational burden. The probability conditions can be set, for example, so that only the k values corresponding to the probability P that are higher than a preset probability threshold (e.g., 90% or 0.9, 95% or 0.95, etc.) are eligible for simulation, or they can be set to sort according to the probability P values, and the k values corresponding to the top m (m is a natural number) probability values with the highest probability values are eligible for simulation.
[0044] The selection of the desired pre-order time interval (t, t+Δt) is related to the product's shelf life and peak sales periods determined based on experience or historical data, and is generally unrelated to the preparation time due to stockouts. Preparation time is typically calculated by multiplying the preparation time of a single product by the quantity required; for example, in a restaurant, it can be calculated using the on-site food preparation time. Product preparation can be sequential or parallel. When preparing a type of product in parallel, the preparation time for multiple parallel products is reduced accordingly, for example, by using the longest preparation time. For example, a fast-food restaurant can cook multiple similar foods simultaneously to meet multiple customer orders. Generally, preparation time is calculated separately for different types of products. For example, if a product has a very short shelf life (e.g., a few minutes, such as 15 minutes), a pre-order time interval of less than or equal to 15 minutes can be selected. For example, if a product experiences a sales peak between 11:30 and 12:30 every day (e.g., the busiest time for customers to have lunch at a restaurant), a predetermined time interval of 15 minutes or more (or 30 minutes, 10 minutes, or 5 minutes) can be set within this time interval. The optimal target inventory level for the product within this predetermined time interval can then be calculated to guide the store's product preparation plan.
[0045] According to embodiments of this application, multiple simulations can be performed for each selected total sales quantity k of the product, for example, n simulations (n being a natural number). Multiple simulations can avoid the random errors introduced by a single simulation, making the simulation environment more accurately simulate the actual situation of the product sales process that conforms to the probabilistic model. For multiple simulations, the calculated sales loss (i.e., the value of the loss function) can be taken as the average value of the multiple simulations (the sum of the loss function values divided by the number of simulations) to determine the average sales loss corresponding to the total sales quantity of the product, thereby determining the optimal target inventory level.
[0046] In sub-step S113, a simulation count threshold can be set for the simulation count n. Simulation continues for the total sales quantity k of the product until the accumulated simulation count reaches the minimum threshold; otherwise, the simulation stops. This avoids insufficient simulation counts from accurately simulating the product's sales process. Similarly, a maximum simulation count threshold (not shown in the attached diagram) can be set to prevent excessive simulations from consuming the system's computing and storage resources.
[0047] The selection of the number of simulations, n, is subject not only to a simulation number threshold but also to other constraints. As shown in sub-step S114, after reaching the simulation number threshold, the volatility of the loss function is further evaluated. The volatility of the average loss function value calculated based on the loss function from multiple simulations should converge to a constant (e.g., 0). That is, the volatility of the average loss function value (average sales loss) should gradually decrease to a constant so that the average loss function value converges to a certain loss value, which is called the minimum loss value. The fact that the volatility of the average loss function meets the requirement indicates that the simulation environment tends to be stable after multiple simulations and can accurately simulate and approximate the actual sales process of the product. Preset volatility conditions can be set for the volatility of the loss function. For example, when the average loss function value converges to the ε confidence interval of the set minimum loss value, the simulation for the selected total sales quantity k can be stopped to proceed to the next step; otherwise, the next simulation process continues.
[0048] In the simulation environment generated for each simulation of the total sales quantity k of the selected product, the method determines the loss function for calculating the sales loss in step S120, and calculates the value of the loss function based on the sales time and the corresponding sales quantity of the product.
[0049] Sales losses consist of two parts: expiration losses due to expired goods and order losses due to users not submitting orders because the waiting cost for preparing goods exceeds the waiting cost threshold when goods are out of stock. Therefore, the loss function is correspondingly derived from... Figure 1 The function consists of the overdue loss function calculated in sub-step S121 and the order loss function calculated in sub-step S122.
[0050] Taking the catering industry as an example, if food is not sold out by the expiration date, it will spoil and be discarded, resulting in expired losses or spoilage. Expired losses are mainly measured by monitoring the inventory time of each type of product from when it is ready to be put into storage.
[0051] For each type of product, sub-step S121 first monitors the remaining inventory quantity of the product in sub-step S1211. Only products that remain in inventory are likely to have an inventory period exceeding their shelf life; these products are characterized by their remaining inventory quantity. At each sales moment, the sales event of the product causes a change in the remaining inventory quantity of the product. Therefore, the remaining inventory quantity at each sales moment is equal to the difference between the initial inventory quantity at the beginning of the predetermined time interval of interest and the sum of the product sales quantities corresponding to all sales moments preceding that sales moment.
[0052] If the remaining inventory is zero at a certain sales moment (i.e., there are no goods in stock) or negative (this situation is generally unlikely, indicating that the sales volume at the previous sales moment exceeded the remaining inventory, resulting in a stockout), then all the goods in the inventory have been sold and there is no issue of goods expiring. Therefore, after sub-step S1211, sub-step S1212 iteratively checks whether the remaining inventory of the goods is greater than 0. Only if the remaining inventory is greater than 0 (the result is "yes") does it proceed to sub-step S1213 to monitor whether the goods have expired; otherwise (the result is "no"), it returns to sub-step S1211 to monitor the remaining inventory of the goods.
[0053] In sub-step S1213, the storage time of multiple items in the remaining inventory is timed separately, and the storage time of each item is compared with its shelf life. When the storage time of an item is greater than its shelf life (the judgment result is "yes"), the item is determined to be expired, resulting in an expiration loss. The expiration loss can be represented by the quantity of expired items. In the following sub-step S1214, the sum of the quantities of items whose storage time exceeds their shelf life is the value of the expiration loss. Sub-step S1213 can sequentially or in parallel determine whether multiple items in the remaining inventory are expired. If the storage time of all items is not greater than their shelf life, or if the storage time of other items after removing the items that have been judged to be expired is not greater than their shelf life (the judgment result is "no"), the method returns to sub-step S1212 to monitor the remaining inventory quantity.
[0054] In actual inventory management, goods can be sorted according to the time they entered the inventory, and priority should be given to selling goods that have been in the inventory for a relatively long time (i.e., entered the inventory earlier) to avoid the earliest goods entering the inventory from exceeding their shelf life due to prolonged storage.
[0055] If the remaining inventory at a given time is insufficient to meet the sales volume, a stockout occurs. A stockout necessitates on-site preparation of goods. If the wait time for customers is too long or the queue is too long, customers may choose not to shop at the store due to impatience or a poor shopping experience, resulting in the loss of both the customer and their potential order. The order loss function is calculated via sub-step S122.
[0056] In each simulation where the total sales quantity of goods is k, if the initial remaining inventory quantity at the start of the predetermined time interval is Y, then starting from the initial sales time, goods corresponding to the sales quantity at each sales time are sold sequentially from the Y inventory items. If the remaining inventory quantity y is greater than the sales quantity corresponding to the sales time, the user can directly purchase the goods in the inventory without waiting. In this case, the user neither spends time nor needs to queue to collect the goods, meaning the user's waiting cost is zero. When, at a certain sales time, the current remaining inventory quantity y is less than the sales quantity of goods at that sales time, meaning the goods in the inventory cannot immediately deliver the quantity of goods required in the user's order, a stockout event occurs. When goods are out of stock, the user needs to wait for the goods to be prepared on-site, just as customers in a fast food restaurant need to wait for the staff to prepare food on-site. For a certain type of goods, the on-site preparation time for each goods is T0. Then, when at least one item in a user's order requires on-site preparation, the time required for the user to wait for the complete delivery of the goods in the order should be T0 multiplied by the quantity of goods requiring on-site preparation. In practice, it's possible that before a user arrives at the store or submits their order, other users have already placed orders for the same type of goods. In this case, the user's waiting time needs to be added to the total waiting time for all previous users' orders to be delivered. If T... pre Let T0 be the sum of the preparation times (waiting times) of all orders placed by all users prior to the current user's current sales time. Then, the total waiting time for this user at the current sales time should be T0+T. pre Thus, for different initial remaining inventory quantities (i.e., initial inventory levels) Y, the total waiting time for each user when a product is out of stock can be obtained. For those waiting times that exceed the maximum acceptable waiting time for the user (i.e., the waiting time threshold), the user will leave the store and no longer submit an order. In this case, the value of the order loss function can be calculated, i.e., the order loss.
[0057] As mentioned above, ideally, we can assume that each customer arriving at the store at a specific time submits an order for a single item, or examine the simulated sales process by simulating the sale of one item at a time. Sub-Monte Carlo sampling Each sales moment (timestamp) can be used to simulate the sales process where each user submits an order for multiple items. Each sales moment corresponds to the time a user submits an order with multiple items, and the sales quantity corresponding to that sales moment is the total number of items in that user's order. Furthermore, the scenario of multiple users arriving at the store and / or submitting different orders at the same time can also be considered. In this case, the sales moment is the time these users arrive at the store and / or submit their orders, and the sales quantity corresponding to that sales moment is the total number of items in these users' orders. For example... Sub-Monte Carlo sampling Each sales moment (timestamp), among which
[0058] Accordingly, for each type of product, sub-step S122, which is used to calculate the order loss function, first determines in sub-step S1221 whether the remaining inventory quantity at each sales time is less than the sales quantity at that sales time. If the remaining inventory quantity is less than the sales quantity (the determination result is "yes"), it indicates that there is a product shortage, and the method proceeds to sub-step S1222; otherwise, the product is not in stock, and the user can directly obtain the required quantity of products in the order (the determination result is "no"), and the method continues to execute sub-step S1221 for the next user or the next sales time at that sales time.
[0059] After a stockout event is confirmed, the method calculates the total waiting cost for the current user to receive all goods in their submitted order in sub-step S1222. If no other users were waiting for the current user, the user's total waiting cost is the on-site preparation time required to deliver all goods in their submitted order at the current sales moment, calculated by multiplying T0 by the quantity of goods required. It should be noted that the quantity of goods required is the quantity of goods that need to be prepared on-site at the current sales moment, calculated as the difference between the quantity of goods required in the current user's order and the remaining inventory quantity. This is because some of the goods required in a user's order may be directly delivered from inventory, leaving only the remaining portion requiring on-site preparation. If at least one other user was waiting for goods at the current sales moment, it indicates that this type of goods was already out of stock before the user's arrival or order submission, and the stockout status persists at the current sales moment. In this case, the current user must wait until all the required quantities of goods in the previous user's order are delivered before their own goods are delivered, and the current user's total waiting time is T0+T.pre The waiting cost of previous users can be recursively calculated using the total waiting cost of those previous users at their respective sales moments. By working backwards to the sales moment when the first stockout occurred, the total waiting cost T for all previous sales moments can be calculated. pre .
[0060] After calculating the total waiting time for users at the current sales moment, the method continues in sub-step S1223 to determine whether multiple users have submitted orders at the current sales moment. When multiple users submit orders simultaneously or arrive at the store simultaneously (the result is "yes"), the total waiting cost for each user at the current sales moment needs to be determined; otherwise (the result is "no"), since only a single user has submitted an order at the current sales moment, the total waiting cost for other users does not need to be calculated. After calculating the total waiting cost for single users and multiple users respectively, the method proceeds to sub-step S1225, comparing the total waiting time for users at the current sales moment with the maximum acceptable waiting time for users (i.e., the waiting time threshold), to determine whether users will not submit orders and / or leave the store directly due to excessive waiting time. If the total waiting time is greater than the waiting time threshold (the result is "yes"), the user's order is lost. In the following sub-step S1226, the quantity of the required items in the user's planned order can be used as the value of the user's order loss function at this sales moment, i.e., the order loss value. Order losses need to be accumulated for each sales moment (which can be called the order loss for the current sales moment). The sum of the order losses for all sales moments in each simulation is the order loss for that simulation. In reality, when a user chooses not to submit an order, the quantity of goods in that order cannot be accurately predicted. Therefore, the order loss value can be recorded as 1, meaning that an order for one item is lost by default. If the total waiting time does not exceed the waiting time threshold (the judgment result is "no"), it means that at the current sales moment, the user can receive the on-site preparation of the waiting goods, and the method will repeat sub-step S1221 when the next sales moment arrives.
[0061] The above discussion focused on the scenario where waiting time is considered the waiting cost for users to wait for the on-site preparation of out-of-stock items. In actual sales, not only does the total waiting time affect the user's consumption or shopping experience, but the number of users in the queue waiting for the preparation of the items in their orders also impacts the user's consumption or shopping experience. The later a user's position in the queue, the longer their waiting time. Therefore, the user's waiting cost can also be represented by the number of users in the queue waiting for delivery, particularly the number of users who received their items before that user. In reality, when a user arrives at the store or intends to submit an order at the current sales moment, they are the last user in the queue; therefore, the user only needs to assess the number of users currently waiting for delivery in the queue. Accordingly, the total user waiting cost in sub-steps S1222 to S1225 is the sum of the number of users who experienced out-of-stock situations and were waiting for delivery at previous sales moments, and the waiting cost threshold is the maximum number of users in the queue that the user can accept. The total waiting time for the current user can also be calculated by the number of users preceding the current user in the user queue and the quantity of goods required in each user's order. In this case, both the waiting time and the number of users in the queue are equally effective in assessing whether a user will churn due to a decline in consumption or shopping experience; therefore, both can be considered specific forms of waiting cost. Those skilled in the art will understand that waiting cost can also take other specific forms.
[0062] Next, in sub-step S123, the value of the expiration loss function, which represents expiration loss, calculated in sub-step S1214, is added to the value of the order loss function, which represents order loss, calculated in sub-step S1226, to obtain the value of the total sales loss function, i.e., the sales loss (e.g., expressed in terms of the quantity of goods). Alternatively, different weights can be assigned to the two types of losses for weighted summation, reflecting the different contributions of losses in different situations to the overall sales loss.
[0063] It's important to note that the sales loss calculation above was performed for each product type. If there are multiple product types, and users submit orders including various product types, it's generally necessary to calculate expiration losses and order losses separately for each product type, and finally calculate the sales loss. Furthermore, if different types of products have dependencies or sequential requirements during preparation, the cumulative waiting costs for different product types must be considered to assess whether a user's order will be lost. For example, if a fast-food restaurant has at least two food items that require the same equipment for processing or preparation, and these items are simultaneously out of stock, the waiting time for multiple users with orders containing these types of food will become longer, or the number of users in the waiting queue will increase, making it easier for users to lose their orders.
[0064] As described in step S110, sales loss is calculated in each simulation for the total sales quantity k of each selected product. After the judgment results of sub-steps S113 and S114 are both "yes", the simulation loop process for the total sales quantity k of the product ends. Accordingly, multiple sales loss values and an average sales loss value corresponding to the total sales quantity k can be obtained. Next, in step S130, a final decision is made to select the total sales quantity k of the product that has a sales loss that meets the preset loss condition (e.g., its sales loss is minimized), and this total sales quantity k is used as the target inventory quantity or the target inventory quantity is determined based on this total sales quantity k. At this time, the target inventory quantity is the optimal inventory quantity.
[0065] Since the goal of determining the optimal target inventory level is to find an effective balance between cost savings and improved product delivery efficiency, the pre-defined loss condition for the final decision includes minimizing the average sales loss calculated in the simulation, i.e., minimizing the average value of the sales loss function. As mentioned above, the average sales loss corresponding to the total sales quantity k of the product is determined by dividing the sales loss calculated in each simulation by the number of simulations at the time the simulation stops. Since the minimum sales loss follows a normal distribution, using the average value of the sales loss function is sufficient to ensure that the optimal target inventory level is found through multiple simulations.
[0066] After determining the optimal target inventory level based on historical sales data, during peak sales periods (such as peak dining times at fast-food restaurants), the optimal target inventory level calculated in an offline simulation environment can be retrieved at predetermined time intervals for different product types. This calculated optimal inventory level is then used as the corresponding pre-prepared product quantity and provided to the store's inventory management system. Staff then prepare products in advance under the guidance of the inventory management system. For example, fast-food restaurant staff can prepare the optimal quantity of food in advance to cope with peak customer dining times, guided by the optimal target inventory level.
[0067] Figure 2 An apparatus 200 for determining a target inventory level of goods is shown according to an embodiment of this application. The apparatus 200 includes an acquisition unit 210, a simulation unit 220, and a calculation unit 230. The acquisition unit 210 is used to acquire historical sales data of the goods and perform tasks such as... Figure 1The function implemented in step S101 is as follows. This historical sales data comes from the historical sales process of the goods and can be stored locally at the store, on a network, or remotely on a server or in a database. Simulation unit 220 can be used to select the total sales quantity of goods within a predetermined time interval based on the historical sales data of the goods' historical sales process, and to determine, through simulation, the sales times at which these total sales quantities of goods were sold within the predetermined time interval, and the corresponding sales quantities at those times. Figure 1 The function implemented by step S110, which provides the simulation environment, is as follows. The calculation unit 230 can be used to determine the total sales quantity that ensures the sales loss of goods within a predetermined time interval meets a preset loss condition (e.g., minimizing sales loss) based on the sales time and quantity of goods provided in the simulation environment generated by the simulation unit 220, as the target inventory quantity. Figure 1 The functions implemented by steps S120 and S130 are described above. The simulation unit 220 can specifically implement the functions described above. Figure 1 The multiple sub-steps S111 to S114 are described above. The calculation unit 230 can specifically implement the above steps S121 to S123, and corresponding further sub-steps. Parts that are the same as or similar to those described above will not be detailed here.
[0068] The method and equipment proposed in this paper for determining target inventory levels of goods can accurately establish a probabilistic model of the sales process involving pre-prepared goods as a simulation environment for predicting and determining the optimal target inventory level. By calculating the minimum loss of the loss function representing the sales loss of goods within the predetermined time interval of interest, the optimal target inventory level is determined, finding an effective balance between cost savings and improved goods delivery efficiency, thereby enhancing the social and corporate benefits of the sales process. This method and equipment for determining target inventory levels can simultaneously consider the time sensitivity and sales fluctuations of goods, making it particularly suitable for the sale of goods with short shelf lives, thus improving the consumer and shopping experience.
[0069] For example, for large restaurant chains, especially for foods with short shelf lives and a large number of frequent sales records in the past, the solution provided in this application can be used to effectively conduct simulation modeling and achieve a good balance between reducing customer waiting time and reducing food preparation waste, thereby improving customer consumption experience and corporate and social efficiency.
[0070] It should be noted that although several modules or units of equipment for determining the target inventory level of goods are mentioned in the detailed description above, this division is not mandatory. In fact, according to embodiments of this application, the features and functions of two or more modules or units described above can be embodied in one module or unit. Conversely, the features and functions of one module or unit described above can be further divided and embodied by multiple modules or units. Components shown as modules or units may or may not be physical units; that is, they may be located in one place or distributed across multiple network units. Some or all of the modules can be selected to achieve the purpose of this application according to actual needs. Those skilled in the art can understand and implement this without inventive effort.
[0071] In exemplary embodiments of this application, a computer-readable storage medium is also provided, on which a computer program is stored, the program including executable instructions that, when executed by, for example, a processor, can implement the steps of the method for determining a target inventory level of goods as described in any of the above embodiments. In some possible implementations, various aspects of this application can also be implemented as a program product including program code that, when run on a terminal device, causes the terminal device to perform the steps described in the various exemplary embodiments of this application for the method of determining a target inventory level of goods.
[0072] The program product for implementing the above-described method according to embodiments of this application may employ a portable compact disc read-only memory (CD-ROM) and include program code, and may run on a terminal device, such as a personal computer. However, the program product of this application is not limited thereto. In this document, a readable storage medium may be any tangible medium that contains or stores a program that may be used by or in conjunction with an instruction execution system, apparatus, or device.
[0073] The program product may employ any combination of one or more readable media. A readable medium may be a readable signal medium or a readable storage medium. A readable storage medium may be, for example, but not limited to, an electrical, magnetic, optical, electromagnetic, infrared, or semiconductor system, apparatus, or device, or any combination thereof. More specific examples of readable storage media (a non-exhaustive list) include: an electrical connection having one or more wires, a portable disk, a hard disk, random access memory (RAM), read-only memory (ROM), erasable programmable read-only memory (EPROM or flash memory), optical fiber, portable compact disk read-only memory (CD-ROM), optical storage devices, magnetic storage devices, or any suitable combination thereof.
[0074] The computer-readable storage medium may include data signals propagated in baseband or as part of a carrier wave, carrying readable program code. Such propagated data signals may take various forms, including but not limited to electromagnetic signals, optical signals, or any suitable combination thereof. The readable storage medium may also be any readable medium other than a readable storage medium, capable of transmitting, propagating, or transmitting programs for use by or in connection with an instruction execution system, apparatus, or device. The program code contained on the readable storage medium may be transmitted using any suitable medium, including but not limited to wireless, wired, optical fiber, RF, etc., or any suitable combination thereof.
[0075] Program code for performing the operations of this application can be written in any combination of one or more programming languages, including object-oriented programming languages such as Java and C++, and conventional procedural programming languages such as C or similar languages. The program code can execute entirely on the user's computing device, partially on the user's device, as a standalone software package, partially on the user's computing device and partially on a remote computing device, or entirely on a remote computing device or server. In cases involving remote computing devices, the remote computing device can be connected to the user's computing device via any type of network, including a local area network (LAN) or a wide area network (WAN), or it can be connected to an external computing device (e.g., via the Internet using an Internet service provider).
[0076] In an exemplary embodiment of this application, an electronic device is also provided, which may include a processor and a memory for storing executable instructions of the processor. The processor is configured to perform the steps of the method for determining a target inventory level of goods in any of the above embodiments by executing the executable instructions.
[0077] Those skilled in the art will understand that various aspects of this application can be implemented as a system, method, or program product. Therefore, various aspects of this application can be specifically implemented in the following forms: a completely hardware implementation, a completely software implementation (including firmware, microcode, etc.), or a combination of hardware and software implementations, collectively referred to herein as a "circuit," "module," or "system."
[0078] The following reference Figure 3 To describe an electronic device 300 according to this embodiment of the present application. Figure 3 The electronic device 300 shown is merely an example and should not impose any limitations on the functionality and scope of use of the embodiments of this application.
[0079] like Figure 3As shown, the electronic device 300 is presented in the form of a general-purpose computing device. The components of the electronic device 300 may include, but are not limited to: at least one processing unit 310, at least one storage unit 320, a bus 330 connecting different system components (including storage unit 320 and processing unit 310), a display unit 340, etc.
[0080] The storage unit stores program code that can be executed by the processing unit 310, causing the processing unit 310 to perform the steps described in the method for determining the target inventory level of goods according to various exemplary embodiments of this application. For example, the processing unit 310 can perform actions such as... Figure 1 The steps are shown in the figure.
[0081] The storage unit 320 may include a readable medium in the form of a volatile storage unit, such as a random access memory unit (RAM) 3201 and / or a cache storage unit 3202, and may further include a read-only memory unit (ROM) 3203.
[0082] The storage unit 320 may also include a program / utility 3204 having a set (at least one) program module 3205, such program module 3205 including but not limited to: an operating system, one or more application programs, other program modules and program data, each or some combination of these examples may include an implementation of a network environment.
[0083] Bus 330 can represent one or more of several types of bus structures, including a memory cell bus or memory cell controller, a peripheral bus, a graphics acceleration port, a processing unit, or a local bus using any of the various bus structures.
[0084] Electronic device 300 can also communicate with one or more external devices 400 (e.g., keyboard, pointing device, Bluetooth device, etc.), and with one or more devices that enable a user to interact with electronic device 300, and / or with any device that enables electronic device 300 to communicate with one or more other computing devices (e.g., router, modem, etc.). This communication can be performed via input / output (I / O) interface 350. Furthermore, electronic device 300 can also communicate with one or more networks (e.g., local area network (LAN), wide area network (WAN), and / or public networks, such as the Internet) via network adapter 360. Network adapter 360 can communicate with other modules of electronic device 300 via bus 330. It should be understood that, although not shown in the figures, other hardware and / or software modules can be used in conjunction with electronic device 300, including but not limited to: microcode, device drivers, redundant processing units, external disk drive arrays, RAID systems, tape drives, and data backup storage systems.
[0085] Through the above description of the embodiments, those skilled in the art will readily understand that the exemplary embodiments described herein can be implemented by software or by combining software with necessary hardware. Therefore, the technical solutions according to the embodiments of this application can be embodied in the form of a software product, which can be stored in a non-volatile storage medium (such as a CD-ROM, USB flash drive, external hard drive, etc.) or on a network, including several instructions to cause a computing device (such as a personal computer, server, or network device, etc.) to execute the method for determining the target inventory level of goods according to the embodiments of this application.
[0086] Other embodiments of this application will readily occur to those skilled in the art upon consideration of the specification and practice of the disclosure herein. This application is intended to cover any variations, uses, or adaptations of this application that follow the general principles of this application and include common knowledge or customary techniques in the art not disclosed herein. The specification and examples are to be considered exemplary only, and the true scope and spirit of this application are indicated by the appended claims.
Claims
1. A method for determining a target inventory level for goods, comprising: Obtain the historical sales data of the product; Based on the historical sales data of the product, select multiple total sales quantities of the product within a predetermined time interval to simulate multiple sales processes of the product within the predetermined time interval, and determine the sales time of the product and the sales quantity corresponding to the total sales quantity of the product for each of the multiple sales processes. Based on the sales time and sales quantity of the goods corresponding to the multiple sales processes, a target inventory quantity is determined such that the sales loss of the goods in the predetermined time interval meets a preset loss condition. The sales loss of the goods includes the expiration loss of the goods and order loss. The order loss includes the loss contained in the order of the user who chooses not to submit an order at the store. The preset loss condition includes that the sales loss of the goods in the predetermined time interval of the total sales quantity of the goods determined as the target inventory quantity is the smallest among the sales losses corresponding to the selected multiple total sales quantities.
2. The method according to claim 1, characterized in that, The expired loss is determined through the following steps: The remaining inventory quantity of the product at each sales moment is determined by the difference between the initial inventory quantity of the product during the predetermined time interval and the sum of the sales quantity of the product before each sales moment; When the remaining inventory quantity is greater than zero, the inventory time of the goods in the inventory is timed; as well as The total number of goods whose inventory time exceeds the shelf life of the goods is taken as the expiration loss.
3. The method according to claim 2, characterized in that, The order loss was determined through the following steps: At each sales moment, When the remaining inventory quantity is less than the sales quantity at the current sales time, the total waiting cost at the current sales time is determined based on the sum of the waiting cost of the user who submitted the order at the current sales time and the waiting cost of all users who submitted orders before the current sales time. When the total waiting cost at the current sales moment is greater than or equal to the waiting cost threshold, the quantity of the goods in the order of the user who submitted the order at the current sales moment will be regarded as the order loss at the current sales moment; as well as The sum of the order losses for the current sales time at each of the aforementioned sales times is taken as the order loss.
4. The method according to claim 3, characterized in that, The waiting cost for a user who submits an order at the current sales time is determined by multiplying the quantity of goods that need to be prepared at the current sales time by the unit time for preparing the goods, wherein the quantity of goods that need to be prepared at the current sales time is determined based on the difference between the quantity of goods in the order of the user who submits an order at the current sales time and the remaining inventory quantity at the current sales time.
5. The method according to claim 4, characterized in that, For each of the multiple users who submit an order at the current sales time, the total waiting cost for the current sales time is determined, wherein the total waiting cost for the current sales time corresponding to each user is determined based on the sum of the waiting costs of all users who submitted orders before that user and the waiting costs of all users who submitted orders before the current sales time.
6. The method according to claim 3, characterized in that, The waiting cost is the waiting time, and the waiting cost threshold is the maximum waiting time that the user can accept.
7. The method according to claim 3, characterized in that, The waiting cost is the number of users in the user queue who are waiting for the goods in their submitted orders, and the waiting cost threshold is the maximum number of users in the user queue that the user can accept.
8. The method according to claim 1, characterized in that, Based on the historical sales data of the product, selecting the total sales quantity of the product within a predetermined time interval, and determining the sales time of the product and the sales quantity corresponding to the sales time for the total sales quantity, further includes: A probabilistic model for simulating the sales process of the product is established based on the historical sales data; and Select the total sales quantity whose probability satisfies the probability condition, simulate the sales process to determine the sales time of the product and the sales quantity corresponding to the sales time of the total sales quantity.
9. The method according to claim 8, characterized in that, The sales process was simulated using the Monte Carlo method.
10. The method according to claim 8, characterized in that, The historical sales data includes the average sales volume of the product per unit of time.
11. The method according to claim 8, characterized in that, Also includes: The sales process is simulated repeatedly for each total sales quantity, and the sales loss of the product in the predetermined time interval is determined based on the sales time and sales quantity obtained in each simulation. The average sales loss is determined based on the sales loss determined in each simulation and the number of simulations. When the volatility of the average sales loss meets a preset volatility condition, the simulation for the corresponding total sales quantity is stopped and the average sales loss is taken as the sales loss corresponding to the total sales quantity. as well as The target inventory level is selected as the total sales quantity that ensures the sales loss of the goods within the predetermined time interval meets the preset loss condition.
12. The method according to claim 1, characterized in that, Determine the corresponding target inventory level for different types of goods.
13. The method according to claim 1, characterized in that, Determine the corresponding target inventory level for different predetermined time intervals.
14. The method according to claim 1, characterized in that, The goods include food provided by restaurants.
15. An apparatus for determining a target inventory level for goods, comprising: An acquisition unit configured to acquire historical sales data of the product; The simulation unit is configured to select multiple total sales quantities of the product within a predetermined time interval based on the product's historical sales data to simulate multiple sales processes of the product within the predetermined time interval, and to determine the sales time of the product corresponding to the total sales quantity of the product and the sales quantity corresponding to the sales time for each of the multiple sales processes. as well as A calculation unit is configured to determine a target inventory quantity based on the sales time and sales quantity of the goods corresponding to the plurality of sales processes, such that the sales loss of the goods in the predetermined time interval satisfies a preset loss condition. The sales loss of the goods includes the expiration loss of the goods and order loss. The order loss includes the loss included in the order of the user who chooses not to submit an order at the store. The preset loss condition includes that the sales loss of the goods in the predetermined time interval of the total sales quantity of the goods determined as the target inventory quantity is the minimum among the sales losses corresponding to the selected plurality of total sales quantities.
16. A computer-readable storage medium having a computer program stored thereon, the computer program including executable instructions that, when executed by a processor, implement the method according to any one of claims 1 to 14.
17. An electronic device, characterized in that, include: processor; as well as Memory for storing the executable instructions of the processor; The processor is configured to execute the executable instructions to implement the method according to any one of claims 1 to 14.
Citation Information
Patent Citations
Pre-estimation medical consumable replenishment system and calculation method thereof
CN104573840A
An optimal bread delivery method and system under random distribution
CN109299971A
Sale stock simulator, article stock management system with built-in sale stock simulator, and sale stock simulation method correcting opportunity loss
JP2001265866A