Method and system for season planning and scheduling techniques using multiple planning period forecasts from Monte Carlo simulations

Abstract

The method may include: receiving historical data showing the demand for a product during multiple weeks within the past several years; determining the best-fitting gamma distribution for each week based on the historical data; performing a first simulation of the gamma distribution over the short-term planning period to generate a first estimated demand for the product over the short-term planning period; performing a second simulation of the gamma distribution over the long-term planning period to generate a second estimated demand for the product over the long-term planning period; determining a first inventory level of the product required to meet the first estimated demand at a first confidence level; determining a second inventory level of the product required to meet the second estimated demand at a second confidence level; and ordering a third inventory level that includes the minimum values ​​of the first and second inventory levels.

Description

Technical Field

[0001] (Cross - Reference to Related Applications) This application claims the benefit of U.S. Provisional Application No. 63 / 490,884, filed Mar. 17, 2023, the content of which is incorporated herein by reference in its entirety.

[0002] (Field of the Invention) This specification relates to inventory management, and more particularly, to methods and systems for seasonal planning and scheduling techniques that use multiple forecast periods for planning from Monte Carlo simulations.

Background Art

[0003] Maintaining an optimal amount of inventory for seasonal products based on demand uncertainty is important for companies to control inventory costs while maintaining service levels. Therefore, there is a need for improved methods of seasonal planning of inventory levels.

Summary of the Invention

[0004] In one embodiment, the method includes: receiving historical data showing the demand for a product over multiple periods within a few years in the past; determining a plurality of gamma distributions based on the historical data, including the gamma distribution that best fits each of the plurality of periods; performing a plurality of first simulations of the gamma distribution for a first number of future periods to generate a first estimated demand for each of the plurality of first simulations for each of the plurality of future periods of the first number; and performing a plurality of second simulations of the gamma distribution for a second number of future periods to generate a second estimated demand for each of the future periods of the second number. This may include, the future period of the second number being greater than the future period of the first number, determining for each period of the future period of the first number a first inventory level of the product necessary to meet the first estimated demand to be at least a first minimum percentage of the first simulation, determining for each period of the future period of the second number a second inventory level of the product necessary to meet the second estimated demand to be at least a second minimum percentage of the second simulation, wherein the second minimum percentage is less than the first minimum percentage, and ordering a third inventory level that includes the minimum of the first and second inventory levels.

[0005] In another embodiment, the computing device may include a processor that receives historical data showing product demand over multiple periods within a few years in the past; determines a plurality of gamma distributions based on the historical data, including the gamma distribution that best fits each of the plurality of periods; performs a plurality of first simulations of the gamma distribution for a first number of future periods, and for each of the plurality of first simulations, generates a first estimated demand for each period of the first number of future periods; performs a plurality of second simulations of the gamma distribution for a second number of future periods, and for each of the second estimated demand for each period of the second number of future periods The system is configured to generate a constant demand such that the future period of the second number is greater than the future period of the first number; for each period of the future period of the first number, determine a first inventory level of the product necessary to meet the first estimated demand to be at least a first minimum percentage of the first simulation; for each period of the future period of the second number, determine a second inventory level of the product necessary to meet the second estimated demand to be at least a second minimum percentage of the second simulation, such that the second minimum percentage is less than the first minimum percentage; and place an order for a third inventory level that includes the minimum values ​​of the first and second inventory levels. [Brief explanation of the drawing]

[0006] The embodiments shown in the drawings are for illustrative and illustrative purposes only and are not intended to limit the scope of the claims. A detailed description of the following exemplary embodiments can be understood in conjunction with the following drawings, in which similar structures are shown with the same reference numerals. [Figure 1] This figure schematically illustrates an exemplary computing device according to one or more embodiments shown and described herein. [Figure 2] This figure schematically shows multiple memory modules of the computing device system of Figure 1, according to one or more embodiments shown and described herein. [Figure 3] This figure shows an exemplary gamma distribution according to one or more embodiments shown and described herein. [Figure 4] This flowchart shows an exemplary method for operating the computing device of Figure 1 according to one or more embodiments shown and described herein. [Modes for carrying out the invention]

[0007] Embodiments disclosed herein describe methods and systems for season planning and scheduling techniques that use multiple planned period forecasts from Monte Carlo simulations. When supplying seasonal products, i.e., products used seasonally rather than throughout the year, it can be difficult for producers of those products to determine how much inventory to produce. If insufficient inventory is produced, producers may not be able to sell out their products and meet demand before the end of the season. However, if too much inventory is produced, producers may not be able to sell all of their inventory before the end of the season. This may require producers to bear the cost of storing the remaining inventory until the next season, or to dispose of the remaining inventory if it expires or is no longer usable in the next season. Estimating the amount of inventory required can be particularly difficult if demand for the product has substantial variability over the course of a season or between seasons (for example, if demand depends on weather or other unpredictable factors).

[0008] In embodiments disclosed herein, based on empirical studies, it is assumed that the gamma distribution provides a relatively accurate probability distribution of demand for a product. Therefore, the gamma distribution is determined using historical data spanning multiple years, showing past demand for the product between each week of a season, and the demand for each week of the season is estimated. The determined gamma distribution is then used to simulate the demand for the product over both the short-term planning period (e.g., the next few weeks) and the long-term planning period (e.g., the rest of the season). Based on the simulation, the amount of inventory needed to meet demand over the short-term and / or long-term planning periods can be determined with a certain level of confidence. Then, as disclosed herein, an appropriate amount of inventory can be produced based on the required amount.

[0009] Referring here to the drawings, Figure 1 is a schematic diagram illustrating an exemplary configuration of a computing device 100 according to embodiments disclosed herein. The computing device 100 may include various different types of devices (e.g., local computing systems, cloud computing systems, etc.). The computing device 100 may perform the operations of embodiments disclosed herein. In the illustrated embodiment, the computing device 100 includes one or more processors 102, a communication path 104, one or more memory modules 106, a data storage component 108, and network interface hardware 110, the details of which are described in the following paragraphs.

[0010] Each of the one or more processors 102 may be any device capable of executing machine-readable and executable instructions. Thus, each of the one or more processors 102 may be a controller, integrated circuit, microchip, computer, or any other physical or cloud-based computer device. The one or more processors 102 are coupled to a communication path 104 that provides signal interconnection between various modules of the computing device 100. Thus, the communication path 104 can connect any number of processors 102 to communicate with one another, enabling modules coupled to the communication path 104 to operate in a distributed computing environment. Specifically, each module can operate as a node capable of transmitting and / or receiving data. As used herein, the term “communicatively coupled” means that coupled components can exchange data signals with one another, such as electrical signals over a conductive medium, electromagnetic signals over air, or optical signals over an optical waveguide.

[0011] Therefore, the communication path 104 can be formed from any medium capable of transmitting signals, such as conductive wires, conductive traces, and optical waveguides. In some embodiments, the communication path 104 can facilitate the transmission of wireless signals such as WiFi, Bluetooth®, and Near Field Communication (NFC). Furthermore, the communication path 104 may be formed from a combination of media capable of transmitting signals. In one embodiment, the communication path 104 includes a combination of conductive traces, conductive wires, connectors, and buses that cooperate to enable the transmission of electrical data signals to components such as processors, memory, sensors, input devices, output devices, and communication devices. Additionally, it should be noted that the term “signal” means a waveform (e.g., electrical, optical, magnetic, mechanical, or electromagnetic) such as DC, AC, sine wave, triangular wave, square wave, or vibration.

[0012] The computing device 100 includes one or more memory modules 106 coupled to a communication path 104. One or more memory modules 106 may include RAM, ROM, flash memory, a hard drive, or any device capable of storing machine-readable and executable instructions so that the machine-readable and executable instructions can be accessed by one or more processors 102. Machine-readable and executable instructions may include, for example, machine language that can be executed directly by the processor, or logic or algorithms written in any programming language of any generation (e.g., 1GL, 2GL, 3GL, 4GL, or 5GL) that can be compiled or assembled into machine-readable and executable instructions and stored in one or more memory modules 106, such as assembly language, object-oriented programming (OOP), scripting language, or microcode. Alternatively, machine-readable and executable instructions may be written in a hardware description language (HDL), such as logic implemented via a field-programmable gate array (FPGA) configuration, an application-specific integrated circuit (ASIC), or an equivalent thereof. Therefore, the methods described herein can be implemented in any conventional computer programming language, either as pre-programmed hardware elements or as a combination of hardware and software components. The memory module 106 will be described in more detail below in relation to Figure 2.

[0013] Referring further to Figure 1, the exemplary computing device 100 includes a data storage component 108. The data storage component 108 may store data used by the computing device 100, such as historical demand data, as disclosed herein. The data storage component 108 may also store other data used by various components of the computing device 100.

[0014] Referring further to Figure 1, the computing device 100 includes network interface hardware 110 for communicatingly connecting the computing device 100 to an external computing device, such as a computing device that stores historical demand data. Thus, the network interface hardware 110 can transmit data to and / or receive data from various external computing devices. The network interface hardware 110 may include wired and / or wireless connections to one or more external computing devices. In other embodiments, the network interface hardware 110 can transmit data to and / or receive data from other computing devices.

[0015] The network interface hardware 110 may be any device that can be communicatively connected to the communication path 104 and can transmit and / or receive data over the network. Therefore, the network interface hardware 110 may include communication transceivers for transmitting and / or receiving any wired or wireless communication. For example, the network interface hardware 110 may include an antenna, a modem, a LAN port, a Wi-Fi card, a WiMax card, mobile communication hardware, near-field communication hardware, satellite communication hardware, and / or any wired or wireless hardware for communicating with external computing devices.

[0016] Referring here to Figure 2, one or more memory modules 106 of the computing device 100 include a history data receiving module 200, a history data smoothing module 202, a gamma distribution determination module 204, a short-term gamma distribution simulation module 206, a long-term gamma distribution simulation module 208, a required inventory determination module 210, a current inventory determination module 212, and an inventory ordering module 214. Each of the history data receiving module 200, the history data smoothing module 202, the gamma distribution determination module 204, the short-term gamma distribution simulation module 206, the long-term gamma distribution simulation module 208, the required inventory determination module 210, the current inventory determination module 212, and the inventory ordering module 214 may be a program module in the form of an operating system, an application program module, and other program modules, stored in one or more memory modules 106. Such program modules may include, but are not limited to, routines, subroutines, programs, objects, components, data structures, etc., for performing specific tasks or executing specific data types, as described below.

[0017] The historical data receiving module 200 can receive historical data showing the demand for seasonal products over several past years. In the illustrated example, the historical data receiving module 200 receives historical data related to the demand for aircraft de-icing fluid, which has seasonal demand during the winter and cold months of the year. However, in other examples, the historical data receiving module 200 can receive historical data related to other seasonal products.

[0018] The historical data receiving module 200 may receive historical data showing the demand for seasonal products over several past years. The number of years of historical data received by the historical data receiving module 200 may be equal to the number of years for which the historical data is available. In the illustrated example, the product from which the data is received is a seasonal product. Therefore, in the illustrated example, the historical data receiving module 200 receives demand data for several past years during the season in which demand exists (e.g., during winter). However, in other examples, the historical data receiving module 200 may receive year-round demand data for several past years.

[0019] In the illustrated example, the historical data receiving module 200 may receive historical data showing the demand for seasonal products during each week of a season over several past years (e.g., demand during each week of winter in 2022, demand during each week of winter in 2021, demand during each week of winter in 2020, etc.). In other examples, the historical data receiving module 200 may receive historical data showing the demand for seasonal products during other periods of a season over several past years (e.g., each day of a season or each month of a season in past years). In embodiments, the period that defines the season in which demand for seasonal products exists may be predefined (e.g., October 1st to March 31st). Thus, the historical data receiving module 200 may receive historical data for several past years during a given season period.

[0020] In the illustrated example, the historical data receiving module 200 may receive historical data indicating demand at multiple locations, as disclosed herein. In the embodiment, the seasonal product may be produced at multiple different factories or hubs, each of which may supply the product to customers within a specific geographical area. In the illustrated example, if the seasonal product is an aircraft de-icing fluid, the product may be supplied to airports located throughout the United States. In particular, multiple hubs that manufacture aircraft de-icing fluids may each supply the aircraft de-icing fluid to specific airports within a specific geographical area. Thus, the historical data receiving module 200 may receive demand data within each of such geographical areas. Thus, future demand can be predicted for each geographical area, as disclosed herein. As will be described in more detail below, the historical data received by the historical data receiving module 200 may be used to simulate future demand for the seasonal product, as disclosed herein.

[0021] Referring further to Figure 2, the historical data smoothing module 202 may perform smoothing of the data received by the historical data receiving module 200, as disclosed herein. As described above, the historical data receiving module 200 may receive historical data showing the demand for seasonal products during each week of a season (e.g., winter). That is, for each week of a season associated with a seasonal product, the historical data receiving module 200 may receive demand data for the first week of the season over the past several years, the second week of the season over the past several years, the third week of the season over the past several years, and so on. As will be described in more detail below, a gamma distribution may be determined for each week of the season based on the received historical data. Thus, each gamma distribution may represent the probability distribution of demand for seasonal products during a particular week of the season.

[0022] However, using historical data to generate a gamma distribution for each week of a season may not be the most accurate way to utilize historical data, especially when the amount of historical data is limited (e.g., when the number of past years with demand data is relatively small). In particular, it may be preferable to utilize historical data from multiple weeks (e.g., more than one week before and more than one week after a particular week) to determine the gamma distribution for each week of the season. In the illustrated example where the seasonal product is aircraft deicing fluid, demand tends to increase during extreme weather events (e.g., blizzards).

[0023] Such extreme weather events tend to be concentrated in time. Thus, if a blizzard occurred in the 7th week of that season in the first year of historical data and in the 8th week of that season in the second year of historical data, it can be predicted that future blizzards and subsequent increases in demand are likely to occur in the 7th or 8th week of that season in future years. Therefore, when determining the gamma distribution, it may be more accurate to consider the moving average of demand for each week based on historical data rather than simply using the historical data for each week of the season separately. This can help smooth the variability of demand over different years. In the illustrated example, the historical data smoothing module 202 determines a three-week moving average for each week for which historical data is received by the historical data receiving module 200. However, in other examples, the historical data smoothing module 202 may determine moving averages for different periods for each week for which historical data is received by the historical data receiving module 200. In still other examples, the historical data smoothing module 202 may utilize other methods to smooth the data received by the historical data receiving module 200.

[0024] Referring further to FIG. 2, the gamma distribution determination module 204 can determine a plurality of gamma distributions, as disclosed herein. The gamma distribution is a two-parameter family of continuous probability distributions. The gamma distribution can be defined by a shape parameter k and a scale parameter θ. FIG. 3 shows a plurality of exemplary gamma distributions having different shape parameters and scale parameters. In the example of FIG. 3, the x-axis represents the number of occurrences of an event (e.g., demand for a product), and the y-axis represents probability.

[0025] As described above, in an embodiment, it is assumed that the demand for seasonal products can be represented by a gamma distribution. That is, the probability distribution representing the demand for a seasonal product during any week of a season can be approximated by a gamma distribution. Further, the demand for a product during each week of a season can be approximated by different gamma distributions (e.g., gamma distributions having different values of the shape parameter k and / or the scale parameter θ). Thus, in an embodiment, the gamma distribution determination module 204 can determine the shape parameter k and the scale parameter θ for a plurality of gamma distributions based on the data received by the history data reception module 200 or the data generated by the history data smoothing module 202, as disclosed herein.

[0026] As described above, the historical data receiving module 200 can receive demand data for seasonal products over several past years. In particular, the historical data receiving module 200 can receive data showing the demand for seasonal products during each week of a season over several past years. Therefore, the gamma distribution determination module 204 can determine the parameters of the gamma distribution for each week of a season based on the historical data. For example, if the historical data receiving module 200 receives 10 years of historical demand data, the gamma distribution can determine the gamma distribution for each week of a season based on the 10 years of historical demand data. For example, the gamma distribution determination module 204 can determine the gamma distribution showing the demand for seasonal products during the first week of a season based on the historical data for the first week of that season in each year of the 10 years of historical demand data. The gamma distribution determination module 204 can determine the gamma distribution showing the demand for seasonal products during the second week of a season based on the historical data for the second week of that season in each year of the 10 years of historical demand data. The gamma distribution determination module 204 can similarly determine the gamma distribution showing the demand for seasonal products during each week of a season, based on historical data for each week of that season within each year of 10 years of historical demand data. In some examples, the gamma distribution determination module 204 can determine the gamma distribution based on data generated by the historical data smoothing module 202 (e.g., moving average demand data) rather than the raw data received by the historical data receiving module 200.

[0027] In some embodiments, the gamma distribution determination module 204 may determine the parameters of a gamma distribution to best fit appropriate data (e.g., historical data associated with a specific week of a season). In some examples, the gamma distribution determination module 204 may determine shape parameter k and scale parameter θ to generate a gamma distribution for that week of a season with least squares error by comparing it with historical data for that specific week of a season. For example, the gamma distribution determination module 204 may consider initial shape parameter k and scale parameter θ and determine the sum of squares of the differences between a gamma distribution with initial shape parameter k and scale parameter θ and historical data for a suitable week of that season. The gamma distribution determination module 204 may then vary the shape parameter k and scale parameter θ to minimize the sum of squares and determine the best-fitting gamma distribution. In other examples, the gamma distribution determination module 204 may use other methods to best fit the historical data for a specific week of a season to a gamma distribution.

[0028] As described above, the gamma distribution determination module 204 may determine multiple gamma distributions using historical demand data from several past years, each gamma distribution representing a probability distribution indicating the demand for seasonal products during a particular week of the season. Thus, the gamma distribution determination module 204 may determine different gamma distributions for each week of the season. In some examples, the gamma distribution determination module 204 may determine different gamma distributions for different geographical regions. For example, the gamma distribution determination module 204 may determine different gamma distributions for each week of the season for each geographical region where historical demand data is received by the historical data receiving module 200. The determined gamma distributions can then be used to determine how much of the seasonal product to produce, as will be explained in more detail below.

[0029] Referring back to Figure 2, the short-term gamma distribution simulation module 206 and the long-term gamma distribution simulation module 208 can simulate one or more gamma distributions determined by the gamma distribution determination module 204 over the short-term and long-term planning periods, respectively, as disclosed herein.

[0030] After determining the gamma distribution representing the expected demand for seasonal products between weeks of the season, the appropriate gamma distribution can be used to estimate future week-to-week demand with a certain level of confidence. However, simply estimating the demand for seasonal products next week may be insufficient to determine the quantity of products to produce or store. For example, the lead time for producing or otherwise procuring additional product inventory may be longer than one week. Therefore, it may be desirable to forecast the demand for products several weeks in advance when deciding how much product to produce or procure. Furthermore, as mentioned above, if inventory of seasonal products remains at the end of the season, it is most likely that those products will not be able to be sold until the next season. Therefore, there may be costs associated with storing the products until the next season. In addition, some seasonal products may not be usable in the next season and thus may go to waste. Therefore, while it may be desirable to maintain sufficient inventory of seasonal products to meet seasonal demand, it may also be desirable not to have so much inventory that a large amount of product remains unsold at the end of the season.

[0031] Accordingly, in the embodiments, the short-term gamma distribution simulation module 206 may simulate the gamma distribution over a short-term planning period (e.g., the next few weeks), and the long-term gamma distribution simulation module 208 may simulate the gamma distribution over a long-term planning period (e.g., the remainder of the season). The results of these simulations may be used to determine how much product to produce, as disclosed herein.

[0032] The short-term gamma distribution simulation module 206 can simulate multiple gamma distributions determined by the gamma distribution determination module 204 for the next few weeks. In some examples, the number of weeks in which the simulation is performed may correspond to the number of weeks required to produce or procure seasonal products and deliver them to a specific location. For example, if it takes three weeks to produce inventory and deliver it to a specific location, the short-term gamma distribution simulation module 206 may perform a simulation of the gamma distribution related to the next three weeks of that season.

[0033] For example, if the simulation is run before, for instance, the fourth week of the season, and it takes three weeks to produce and deliver inventory, the short-term gamma distribution simulation module 206 may run simulations of the gamma distribution associated with the fourth, fifth, and sixth weeks of the season. In particular, a large number of simulations (e.g., 10,000 simulations) may be run, and each simulation may predict the demand for the fourth, fifth, and sixth weeks of the season based on the simulation results. The simulations run by the short-term gamma distribution simulation module 206 may be Monte Carlo simulations, but each simulation of the gamma distribution includes generating random numbers and determining demand based on the gamma distribution and the generated random numbers.

[0034] The gamma distribution simulations for weeks 4, 5, and 6 of the season can be run together. That is, the first simulation can predict the demand for week 4 based on the week 4 gamma distribution and the first generated random number, the demand for week 5 based on the week 5 gamma distribution and the second generated random number, and the demand for week 6 based on the week 6 gamma distribution and the third generated random number. The three predicted demand levels (predicted demand levels for weeks 4, 5, and 6) can be summed to determine the total demand for the seasonal product over weeks 4, 5, and 6 related to the first simulation. Then, the second simulation can be run in a similar manner to predict the demand for weeks 4, 5, and 6, and the total demand over all three weeks, for the seasonal product related to the second simulation. This can be repeated for the total number of simulations to be run (e.g., 10,000 simulations). Next, the total demand for seasonal products for weeks 4, 5, and 6 (or another short-term planning period) is determined for each of the multiple simulations.

[0035] Once the total demand for the short-term planning period is determined for each of the multiple simulations, the computing device 100 can determine the demand level required to meet a specific service or reliability level, as will be disclosed in more detail below. For example, the computing device 100 may determine the amount of product inventory needed to meet demand 98% of the simulation to meet a 98% confidence level. This is the amount of inventory that has a 98% probability of meeting demand for the next three weeks. However, the 98% confidence level or service level is merely an example, and different confidence intervals may be used in other examples. The determination of the amount of product to be produced based on this inventory level will be described in more detail below with respect to the required inventory determination module 210.

[0036] Referring further to Figure 2, the long-term gamma distribution simulation module 208 can simulate multiple gamma distributions determined by the gamma distribution determination module 204, corresponding to each week of the remaining season. The long-term gamma distribution simulation module 208 can operate similarly to the short-term gamma distribution simulation module 206, except that it simulates more gamma distributions over a longer planning period. For each simulation performed by the long-term gamma distribution simulation module 208, the total amount of inventory needed to meet the projected demand for the entire remaining season can be determined. After performing numerous simulations (e.g., the same number of simulations performed by the short-term gamma distribution simulation module 206), the computing device 100 can determine, with a certain level of confidence, the amount of product inventory needed to meet the demand for the remaining season. This will be further explained below with respect to the required inventory determination module 210.

[0037] In some examples, the short-term gamma distribution simulation module 206 and the long-term gamma distribution simulation module 208 may simulate gamma distributions associated with different geographical regions. In these examples, the gamma distribution determination module 204 may generate one gamma distribution for each geographical region for each week of the season, as described above. Thus, in these examples, each simulation performed by the short-term gamma distribution simulation module 206 may simulate the gamma distribution for each week over the short-term planning period (e.g., the next three weeks) for each geographical region having a gamma distribution. The short-term gamma distribution simulation module 206 may then determine the total inventory required to collectively meet the projected demand for all locations over the short-term planning period.

[0038] The Long-Term Gamma Distribution Simulation Module 208 can similarly simulate the gamma distribution for each location each week over a long-term planning period (e.g., the entire remaining season). The Long-Term Gamma Distribution Simulation Module 208 can similarly determine the total inventory required to collectively meet the predicted demand for all locations over the long-term planning period. By determining the total inventory needed to meet the demand for each location, inventory can be moved between geographical areas if there is a shortage of inventory in one area but a surplus in another.

[0039] Referring further to Figure 2, the required inventory determination module 210 can determine the required amount of inventory based on simulations performed by the short-term gamma distribution simulation module 206 and the long-term gamma distribution simulation module 208, as disclosed herein. As described above, the short-term gamma distribution simulation module 206 may determine the amount of inventory required to meet demand over the short-term planning period for each of a plurality of simulations, and the long-term gamma distribution simulation module 208 may determine the amount of inventory required to meet demand over the long-term planning period for each of a plurality of simulations. Therefore, in the embodiment, the required inventory determination module 210 may determine the amount of inventory required to meet demand over the short-term planning period at a first confidence level, or it may determine the amount of inventory required to meet demand over the long-term planning period at a second confidence level.

[0040] Since the long-term planning period extends further into the future than the short-term planning period, if the first confidence level is equal to the second confidence level, the amount of inventory needed to meet demand over the long-term planning period will inevitably be greater than the amount of inventory needed to meet demand over the short-term planning period. However, because there is greater uncertainty over the long-term planning period than over the short-term planning period, the second confidence level associated with the long-term planning period may be lower than the first confidence level associated with the short-term planning period.

[0041] For example, the required inventory determination module 210 may determine a first inventory quantity needed to meet demand over a short-term planning period with at least a 98% confidence level (e.g., an inventory level that satisfies demand in 98% of simulations performed by the short-term gamma distribution simulation module 206), and may determine a second inventory quantity needed to meet demand over a long-term planning period with at least a 90% confidence level (e.g., an inventory level that satisfies demand in 90% of simulations performed by the long-term gamma distribution simulation module 208). Since the second confidence level is lower than the first, the inventory quantity needed to meet demand over a short-term planning period may be greater or less than the inventory quantity needed to meet demand over a long-term planning period, depending on the specific confidence levels selected, the lengths of the short-term and long-term planning periods, and the details of the gamma distribution. While 98% and 90% confidence levels are specified herein, it should be understood that any other confidence levels may be selected in other examples.

[0042] In one embodiment, after the required inventory determination module 210 determines a first inventory quantity needed to meet demand over a short-term planning period at a first confidence level and a second inventory quantity needed to meet demand over a long-term planning period at a second confidence level, the required inventory determination module 210 may determine the smaller of the first and second inventory quantities as the required inventory quantity. This ensures that sufficient inventory will be available to meet demand over either the short-term or long-term planning period at an appropriate confidence level. Therefore, by selecting the smaller of the first and second inventory quantities as the required inventory quantity, it is possible to balance the desire to ensure that inventory does not run out before the end of the season with the desire to ensure that there is no excess inventory remaining at the end of the season. However, in some examples, the required inventory determination module 210 may determine the larger of the first and second inventory quantities as the required inventory quantity.

[0043] Referring further to Figure 2, the current inventory determination module 212 can determine the amount of current inventory held by the producer of the seasonal product. In the illustrated example, where the seasonal product is aircraft de-icing fluid, the aircraft de-icing fluid may be stored in one or more tanks, each of which has sensors to monitor the amount of aircraft de-icing fluid stored in it. Thus, in these examples, the current inventory determination module 212 may receive tank telemetry data indicating how much aircraft de-icing fluid is currently stored. However, in other examples, the current inventory determination module 212 may receive other types of data indicating the current inventory level of the seasonal product.

[0044] Referring further to Figure 2, the inventory ordering module 214 may order a quantity of seasonal products equal to the difference between the required inventory quantity determined by the required inventory determination module 210 and the amount of on-hand inventory determined by the current inventory determination module 212. In some examples, the inventory ordering module 214 may transmit a request for an appropriate quantity of seasonal products to be produced (e.g., by a factory). In other examples, the inventory ordering module 214 may transmit a request for an appropriate quantity of seasonal products to be ordered or otherwise procured. This allows producers of seasonal products to produce or procure sufficient stock of seasonal products to meet forecast demand over either the short-term or long-term planning period, as described above. In some examples, the current inventory determination module 212 may be omitted, and the inventory ordering module 214 may simply order the required inventory quantity determined by the required inventory determination module 210.

[0045] Figure 4 shows a flowchart of an exemplary method for determining the quantity of seasonal product inventory to order, which may be performed by the computing device 100. In step 400, the historical data receiving module 200 receives historical data. As described above, the historical data received by the historical data receiving module 200 may show the demand for seasonal product during each week of the season associated with the seasonal product for several past years. In some examples, the historical data receiving module 200 may receive historical data associated with multiple locations or geographical areas.

[0046] In step 402, the historical data smoothing module 202 smooths the historical data received by the historical data receiving module 200. In the illustrated example, the historical data smoothing module 202 determines a three-week moving average of the received historical data. However, in other examples, the historical data smoothing module 202 may determine a moving average over different time lengths, or it may perform different types of data smoothing.

[0047] In step 404, the gamma distribution determination module 204 determines the gamma distribution associated with the demand for seasonal products during each week of the season, based on the historical data received by the historical data receiving module 200. In some examples, the gamma distribution determination module 204 may determine the gamma distribution associated with the demand for seasonal products during each week of the season in each of several locations or geographical areas.

[0048] In step 406, the short-term gamma distribution simulation module 206 performs a simulation of the gamma distribution over a future short-term planning period. In particular, as described above, the short-term gamma distribution simulation module 206 may use random number generation and Monte Carlo simulation to perform multiple simulations of the gamma distribution for a future week or longer, and for each simulation, it may determine the amount of seasonal product inventory needed to meet the demand for a future week or longer.

[0049] In step 408, the long-term gamma distribution simulation module 208 performs simulations of the gamma distribution over the future long-term planning period. Specifically, as described above, the long-term gamma distribution simulation module 208 uses random number generation and Monte Carlo methods to perform multiple simulations of the gamma distribution for each remaining week of the season, and for each simulation, it determines the amount of seasonal product inventory needed to meet the remaining demand of the season.

[0050] In step 410, the required inventory determination module 210 determines the required inventory quantity for seasonal products. In particular, as described above, the required inventory determination module 210 may select the smaller of the inventory quantity required to satisfy the short-term planning period determined by the short-term gamma distribution simulation module 206 and the inventory quantity required to satisfy the long-term planning period determined by the long-term gamma distribution simulation module 208.

[0051] In step 412, the current inventory determination module 212 determines the current inventory of the seasonal product. As described above, in the illustrated example, the current inventory determination module 212 may receive tank telemetry data indicating the amount of aircraft de-icing fluid stored in one or more tanks. However, in other examples, the current inventory determination module 212 may determine the current inventory of the seasonal product in other ways.

[0052] In step 414, the inventory ordering module 214 orders the inventory quantity of seasonal products. In one example, as described above, the inventory ordering module 214 may order an amount of seasonal products equal to the difference between the required inventory quantity determined by the required inventory determination module 210 and the current inventory quantity determined by the current inventory determination module 212. In another example, the inventory ordering module 214 may simply order the inventory quantity determined by the required inventory determination module 210.

[0053] It should be understood here that the embodiments described herein concern methods and systems for maintaining inventory of seasonal products. Gamma distributions may be generated based on historical demand data to represent the expected demand for seasonal products during each week of the season. These gamma distributions may be used to simulate future demand for seasonal products over both short-term and long-term planning periods with different confidence levels. By ordering sufficient product inventory to meet the lower of these demand levels, the embodiments disclosed herein can avoid excess inventory at the end of the season while maintaining an inventory level that balances the desire to maintain sufficient inventory to meet demand.

[0054] It should be noted that in this specification, the terms “substantially” and “about” may be used to describe the degree of inherent uncertainty that may arise from any quantitative comparison, value, measurement, or other expression. These terms are also used in this specification to describe the extent to which a quantitative expression may deviate from the stated standard without altering the fundamental function of the subject matter in question.

[0055] While specific embodiments are illustrated and described herein, it should be understood that various other changes and modifications may be made without departing from the spirit and scope of the claimed subject matter. Furthermore, although various aspects of the claimed subject matter are described herein, such aspects do not need to be used in combination. Accordingly, the appended claims are intended to encompass all such changes and modifications that fall within the scope of the claimed subject matter.

Claims

1. It is a method, Receiving historical data showing product demand over multiple periods within the past several years, Based on the aforementioned historical data, determine a plurality of gamma distributions, including the gamma distribution that best fits each of the plurality of periods, Perform a plurality of first simulations of the gamma distribution for a future period of the first number, and generate a first estimated demand for each of the plurality of first simulations for each period of the future period of the first number. Performing a plurality of second simulations of the gamma distribution for a future period of the second number to generate a second estimated demand for each period of the future period of the second number, wherein the future period of the second number is greater than the future period of the first number. For each future period of the first number, the first inventory of the product necessary to meet the first estimated demand is determined to be at least the first minimum percentage of the first simulation, For each future period of the second number, the second inventory of the product necessary to meet the second estimated demand is determined to be at least a second minimum percentage of the second simulation, wherein the second minimum percentage is smaller than the first minimum percentage. A method comprising: ordering a third inventory quantity that includes the minimum of the first inventory quantity and the second inventory quantity.

2. The method according to claim 1, wherein the future period of the second number includes the remainder of the season associated with the product.

3. The method according to claim 1, wherein each of the plurality of periods includes one week.

4. The aforementioned historical data is smoothed to generate smoothed historical data, Based on the smoothed historical data, the plurality of gamma distributions are determined, The method according to claim 1, further comprising:

5. The historical data is smoothed by determining the moving average of the demand for the product over the multiple periods within the past multiple years, based on the historical data. The plurality of gamma distributions are determined based on the moving average, The method according to claim 4, further comprising:

6. The method according to claim 1, wherein the historical data shows the demand for the product during the multiple periods within the multiple past years in multiple geographical areas.

7. The method according to claim 6, further comprising determining the plurality of gamma distributions, including the best-fitting gamma distribution, for each of the plurality of periods and for each of the plurality of geographical regions, based on the historical data.

8. The method according to claim 1, further comprising using the least squares error method to determine the plurality of gamma distributions, including the best-fitting gamma distribution for each of the plurality of periods, based on the historical data.

9. The method according to claim 1, further comprising performing the plurality of first simulations of the gamma distribution for a future period of the first number using random number generation and Monte Carlo simulation.

10. To determine the current inventory of the aforementioned product, Determining a fourth inventory quantity that includes the difference between the third inventory quantity and the current inventory quantity, Ordering the aforementioned fourth inventory quantity, The method according to claim 1, further comprising:

11. Receiving tank telemetry data indicating the quantity of the product in one or more storage tanks, Based on the tank telemetry data, the current inventory of the product is determined. The method according to claim 10, further comprising:

12. A computing device comprising a processor, wherein the processor is Receiving historical data showing product demand over multiple periods within the past several years, Based on the aforementioned historical data, determine a plurality of gamma distributions, including the gamma distribution that best fits each of the plurality of periods, Perform a plurality of first simulations of the gamma distribution for a future period of the first number, and generate a first estimated demand for each of the plurality of first simulations for each period of the future period of the first number. Performing a plurality of second simulations of the gamma distribution for a future period of the second number to generate a second estimated demand for each period of the future period of the second number, wherein the future period of the second number is greater than the future period of the first number. For each future period of the first number, the first inventory level of the product necessary to meet the first estimated demand is determined to be at least the first minimum percentage of the first simulation, For each future period of the second number, the second inventory of the product necessary to meet the second estimated demand is determined to be at least a second minimum percentage of the second simulation, wherein the second minimum percentage is smaller than the first minimum percentage. A computing device configured to place an order for a third inventory quantity that includes the minimum of the first inventory quantity and the second inventory quantity.

13. The computing device according to claim 12, wherein the future period of the second number includes the remainder of the season associated with the product.

14. The computing device according to claim 12, wherein each of the plurality of periods includes one week.

15. The aforementioned processor, The historical data is smoothed by determining the moving average of the demand for the product over the multiple periods within the past multiple years, based on the historical data. The process involves determining the plurality of gamma distributions based on the aforementioned moving average. The computing device according to claim 14, further configured as follows.

16. The computing device according to claim 12, wherein the historical data indicates the demand for the product during the multiple periods within the multiple past years in multiple geographical areas.

17. The computing device according to claim 16, wherein the processor is further configured to determine the plurality of gamma distributions, including the best-fitting gamma distribution, for each of the plurality of periods and for each of the plurality of geographic regions, based on the historical data.

18. The computing device according to claim 12, wherein the processor is further configured to use the least squares error method to determine the plurality of gamma distributions, including the best-fitting gamma distribution for each of the plurality of periods, based on the historical data.

19. The computing device according to claim 12, wherein the processor is further configured to perform the plurality of first simulations of the gamma distribution for future periods of the first number using random number generation and Monte Carlo simulation.

20. The aforementioned processor, To determine the current inventory of the aforementioned product, Determining a fourth inventory quantity that includes the difference between the third inventory quantity and the current inventory quantity, To order the fourth quantity of inventory mentioned above, The computing device according to claim 12, further configured as follows.

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