Inventory Allocation and Pricing Optimization System

Abstract

An embodiment optimizes inventory allocation for a retail item, the retail item being allocated from a plurality of different fulfillment centers to a plurality of different customer groups. An embodiment receives historical sales data for the retail item and estimates demand model parameters. An embodiment generates a network including first nodes corresponding to the fulfillment centers, second nodes corresponding to the customer groups, and third nodes between the first and second nodes, each of the third nodes corresponding to one of the second nodes. An embodiment generates feasible initial inventory allocations from the first nodes to the second nodes and solves a minimum cost flow problem for the network to generate an optimal inventory allocation.

Description

[Technical Field]

[0001] Field One embodiment is generally directed towards computer systems, and in particular towards computer systems for determining optimized pricing and inventory allocation for products. [Background technology]

[0002] Background information A retailer or any seller of a product will likely need to make a decision at some point in the sales cycle regarding when and by how much to lower the price of the product, possibly through promotions. Price reductions can be a major part of product item lifecycle pricing. A typical retailer might reduce the price of an item by 20% to 50% (i.e., permanently discount it), generating approximately 30% to 40% of the revenue at the discounted price.

[0003] Optimized pricing reduction decisions maximize profits by taking into account inventory constraints and the impact of demand dependence on time, price, and inventory. Optimized reductions can bring inventory to a desired level not only during regular-priced sales but also during discounted sales, maximizing total gross profit over the entire product lifecycle. However, price optimization systems typically do not take into account inventory allocation and its impact on pricing across many potential locations. Summary of the Invention

[0004] overview An embodiment optimizes inventory allocation of a retail item, the retail item being allocated from a plurality of different fulfillment centers to a plurality of different customer groups. An embodiment receives historical sales data for the retail item and estimates demand model parameters. An embodiment generates a network including first nodes corresponding to the fulfillment centers, second nodes corresponding to the customer groups, and third nodes between the first and second nodes, each of the third nodes corresponding to one of the second nodes. An embodiment generates feasible initial inventory allocations from the first nodes to the second nodes and solves a minimum-cost flow problem for the network to generate an optimal inventory allocation. [Brief explanation of the drawings]

[0005] [Figure 1] FIG. 1 is a block diagram of an exemplary retail chain having multiple warehouses, according to an embodiment. [Figure 2] FIG. 1 is a block diagram of a computer server / system according to an embodiment of the present invention. [Figure 3] FIG. 1 illustrates a network according to an embodiment of the present invention, including three layers of nodes. [Figure 4] FIG. 3 is a flow diagram of the functionality of the inventory and price optimization module of FIG. 2 according to one embodiment. DETAILED DESCRIPTION OF THE INVENTION

[0006] Detailed Description One embodiment is an optimization system for optimizing profits or revenues for a retail chain with multiple locations, each served by multiple inventory warehouses. The embodiment optimizes both inventory allocation among warehouses as well as product pricing.

[0007] Embodiments are directed to a system or method for maximizing profits or revenues for a retail chain that manages multiple locations supplied by multiple warehouses. The retail chain may include an e-commerce operation. Each warehouse may be connected to multiple locations, and each location may be supplied by multiple warehouses.

[0008] FIG. 1 is a block diagram of an exemplary retail chain 50 having multiple warehouses, according to an embodiment. As shown, the multiple retail locations 54-56 may be in the form of brick-and-mortar retail stores or retail price zones, which may include multiple geographically consistent brick-and-mortar retail stores (or single stores) that use the same pricing. For example, a price zone may be based on a geographic location, such as all retail stores in the Washington, D.C., area or all retail stores within a 25-mile radius. Each price zone is supplied by one or more warehouses 52, 53 (also referred to as fulfillment centers ("FCs")). When a single warehouse provides inventory for multiple price zones, in an embodiment, this inventory will be allocated among the various price zones. For example, warehouse 52 may have 60% of its inventory assigned to price zone 54 and 40% of its inventory assigned to price zone 55. Similarly, warehouse 53 may have 70% of its inventory assigned to price zone 55 and 30% of its inventory assigned to price zone 56. For purposes of this disclosure, each warehouse and price zone combination may be referred to as an arc or one or more links.

[0009] Allocating inventory to a price zone means that the inventory will only be sold within that price zone. Furthermore, since each price zone is generally supplied from multiple warehouses, inventory can be allocated to a given price zone from multiple warehouses. It should be noted that the allocations described in this model do not necessarily imply physical shipments. In many situations, inventory is virtually allocated for planning purposes to provide input to price zone-specific price optimization, which aims to maximize the profit derived from selling the entire inventory allocated to a price zone at that store. However, as disclosed below, changing inventory allocations may result in transporting inventory to different stores or price zones than before (e.g., via truck transport).

[0010] The embodiment is applicable to e-commerce environments. A typical e-commerce retailer generally fulfills orders from multiple geographically dispersed warehouses or fulfillment centers (FCs), so the cost of shipping an order to a customer can vary significantly by FC. At the same time, as an item approaches the end of its lifecycle, its inventory level often varies considerably by FC. Therefore, maximizing gross profit involves both allocating FCs to customers to balance the load across FCs and pricing items based on each customer's price elasticity and cost of service.

[0011] In contrast, more traditional brick-and-mortar retailers also supply stores from multiple warehouses. Stores are typically divided into so-called price zones, allowing retailers to implement flexible pricing policies that offer different prices in price zones with varying price sensitivities. Both e-commerce and brick-and-mortar implementations involve multiple supply centers and customer groups with diverse demand parameters and service costs.

[0012] Embodiments of the present invention are particularly directed to items with a limited life cycle, such as fashion goods or electronics. These items lose nearly all value after a certain period of time because they must be replaced with new versions of the product. As such items approach the end of their lifespan, their inventory is typically not replenished. If inventory levels at the beginning of the period are high enough that they cannot be sold at the current price by the end date, a price reduction is applied.

[0013] FIG. 2 is a block diagram of a computer server / system 10 according to an embodiment of the present invention. While shown as a single system, the functionality of system 10 may be implemented as a distributed system. Additionally, the functionality disclosed herein may be implemented on separate servers or devices that may be coupled together via a network. Additionally, one or more components of system 10 may not be included. System 10 may centrally provide functionality for all entities in FIG. 1, or multiple systems 10 may be located at one or more of the entities, with information and computations integrated to provide a holistic pricing and inventory allocation solution.

[0014] System 10 includes a bus 12 or other communication mechanism for communicating information and a processor 22 coupled to bus 12 for processing information. Processor 22 may be any type of general-purpose or special-purpose processor. System 10 also includes memory 14 for storing information and instructions executed by processor 22. Memory 14 may be comprised of any combination of random access memory ("RAM"), read-only memory ("ROM"), static storage such as a magnetic or optical disk, or other types of computer-readable media. System 10 also includes a communication device 20, such as a network interface card, for providing access to a network. Thus, users can connect with system 10 directly, remotely over a network, or otherwise.

[0015] Computer-readable media may be any available media that is accessible by processor 22 and includes both volatile and nonvolatile media, removable and non-removable media, and communication media. Communication media may include computer-readable instructions, data structures, program modules, or other data in a modulated data signal such as a carrier wave or other transport mechanism and includes any information delivery media.

[0016] Processor 22 is further coupled to a display 24, such as a liquid crystal display ("LCD"), via bus 12. A keyboard 26 and a cursor control device 28, such as a computer mouse, are further coupled to bus 12 to enable a user to interact with system 10.

[0017] In one embodiment, memory 14 stores software modules that provide functionality when executed by processor 22. These modules include an operating system 15 that provides operating system functionality to system 10. These modules further include an inventory and price optimization module 16 that jointly optimizes inventory allocation and markdown pricing of retail items, as well as all other functionality disclosed herein. System 10 may be part of a larger system. Thus, system 10 may include one or more additional functional modules 18 to include additional functionality, such as a retail management system (e.g., Oracle Retail Offer Optimization Cloud Service or Oracle Retail Advanced Science Engine (“ORASE”) from Oracle Corporation) or an enterprise resource planning (“ERP”) system or inventory management system. Database 17 is coupled to bus 12 to provide centralized storage for modules 16 and 18 and to store customer data, product data, transaction data, etc. In one embodiment, database 17 is a relational database management system (“RDBMS”) capable of managing stored data using structured query language (“SQL”). In one embodiment, a specialized point of sale ("POS") terminal 100 generates transactional and historical sales data (e.g., data regarding transactions for each item / SKU at each retail store) that is used for price and inventory optimization. The POS terminal 100 itself may include additional processing capabilities for optimizing pricing and inventory allocation according to one embodiment, and can operate by itself, or in conjunction with the other components of FIG. 2, as a specialized inventory and pricing optimization system.

[0018] In one embodiment, particularly when there are many retail stores, many items, and a large amount of historical data, the database 17 is implemented as an in-memory database ("IMDB"). An IMDB is a database management system that relies primarily on main memory for storing computer data. An IMDB is contrasted with a database management system that utilizes disk storage mechanisms. Main-memory databases are faster than disk-optimized databases because disk access is slower than memory access, the internal optimization algorithms are simpler, and fewer CPU instructions are executed. By accessing data in memory, seek time is eliminated when querying data, resulting in faster and more predictable performance than disks.

[0019] In one embodiment, the database 17, implemented as an IMDB, is implemented based on a distributed data grid. A distributed data grid is a system in which a collection of computer servers collaborate in one or more clusters to manage related operations such as information and computation within a distributed or clustered environment. A distributed data grid can be used to manage application objects and data shared across servers. Distributed data grids offer slow response times, high throughput, predictable scalability, continuous availability, and information reliability. In a specific example, a distributed data grid such as Oracle's "Oracle Coherence" data grid achieves higher performance by storing information in memory and utilizes redundancy by making synchronized copies of information across multiple servers, thus ensuring system resilience and continuous data availability even in the event of server failure.

[0020] In one embodiment, System 10 is a computing / data processing system that includes applications for an enterprise organization or a collection of distributed applications, and may also implement logistics, manufacturing, and inventory management functions. The applications and computing system 10 may be configured to work with a cloud-based networking system, a Software-As-A-Service ("SaaS") architecture, or other types of computing solutions, or may be implemented as a cloud-based networking system, a SaaS architecture, or other types of computing solutions.

[0021] Known approaches to solving various aspects of price reduction and related optimization problems stemming from demand uncertainty generally assume that demand parameters are fixed and model demand uncertainty as fluctuations in demand realization. However, it is necessary to take into account uncertain demand parameters. For example, when addressing the problem of retail item price reductions for various retailers, each retailer generally implements several rules that are basically aimed at preventing mispricing, particularly underpricing and early-season stockouts, resulting from erroneous estimations of the price elasticity of demand. For example, a retailer might limit the percentage of a single price reduction or impose limits on the minimum time between the earliest price reduction and / or two consecutive price reductions. The latter two limits are intended to better learn demand and price sensitivity before taking further action.

[0022] More recently, retailers, especially those with online channels, have begun to use price randomization to find better estimates of customer demand parameters. Nevertheless, uncertainty always exists in demand parameters, especially price elasticity, which is typically the most difficult parameter to estimate. Furthermore, solving the markdown optimization problem requires a comprehensive forecasting model that accounts for various exogenous and endogenous influences that retailers commonly face, such as holiday-driven changes in customer demand, the presence of similar items that result in demand shifting (i.e., demand cannibalization), and pricing and promotion effects.

[0023] In contrast, one embodiment first constructs a markdown optimization model as a basic markdown problem for a single customer group served by the same FC. Another embodiment constructs a model in which multiple FCs serve multiple customer groups at a specific service cost and includes a minimum-cost network flow approach to solving the joint inventory allocation and markdown optimization problem. Both embodiments include a closed-form solution and a steepest descent algorithm for a log-linear demand model and a uniform distribution of price elasticity parameters, allowing for a straightforward, realistic implementation.

[0024] Joint inventory allocation and price reduction optimization problem One embodiment considers a markdown problem associated with multiple warehouses or fulfillment centers ("FCs") that supply goods to various groups of customers. The customers may be individual customers, such as online shoppers or customer groups, that share the same demand parameters, or more generally, stores or groups of stores. The demand model parameters are assumed to be unknown precisely but are measurable within certain limits. Each customer is assumed to have demand modeled as a function of product price with parameters that follow a known joint distribution. The problem solved by the embodiment is to determine the best price to maximize the expected profit derived from selling a given amount of product inventory located at multiple FCs that accounts for the costs of handling the product and shipping the product to the customer group. It is also assumed that the sales period is bounded by a specific end date, after which the product is withdrawn at a price close to zero. It is further assumed that there is no product replenishment at the FC level during the sales period, but that products are replenished at the customer group level as demand arises. So, if a customer group represents a brick-and-mortar store, the model will ignore situations where the store's on-hand inventory is shipped but not sold, resulting in shipping costs with no revenue.

[0025]

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[0026] The first assumption does not allow demand to be modeled as a piecewise linear function, while the second assumption is a constant elastic power law demand model (e.g., d(p)=αp). -β ,β=const>0). The time and price parameters and demand output are considered to be continuous variables, and their inclusion in the model can be directly replaced by addition, so this does not limit the practical applicability of the model.

[0027] Basic price reduction optimization problem: A single customer group supplied from a single franchise. To demonstrate the embodiment of price reduction optimization under parameter uncertainty, a basic price reduction optimization problem for a single customer or a homogeneous customer population supplied by the same FC is presented. In this problem, there is assumed to be S inventory items that must be sold within a time horizon T. There is no replenishment during this period, and all unsold inventory by the end time T is retrieved at a negligibly low, nonzero price. This problem is constructed as finding the optimal pricing policy, i.e., the price of an item as a function of time, p:t → p(t), t ∈ [0, T). In general, the price policy function should satisfy several price reduction constraints, the most important of which is non-increasing. Other examples of these constraints are finite price reductions during price reduction events and finite intervals between reductions. The set of permitted price policies is denoted by P. Assume there is a demand function d(t, p; θ) for a pricing policy p ∈ P at time t that also depends on a function parameter vector θ. Because it is impossible to measure the exact parameter values ​​in practice, θ is assumed to be a realization of a random variable Θ that follows the distribution given by the pdf f(θ) with range dom(f). θ may include components such as the price elasticity of demand, promotional lift, and sensitivity to the benchmark price.

[0028] In general, demand as a function of time depends on ex ante pricing decisions. For example, ex ante pricing decisions can be ex ante promotions that change the customer reference price point or customer perception of fair price, as well as influencing future demand through the "pantry loading" effect. Another example is the effect of stock-outs, where ex ante sales can negatively impact current demand by reducing current inventory levels.

[0029] Since inventory is finite, the sell-off time T0 for a given pricing policy can be defined as the time when inventory is depleted under the current pricing policy. It is found as the solution to the following equation:

[0030]

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[0031] Note that in some combinations of demand models and pricing policies, sales may continue indefinitely. In this case, T0 = ∞. The end of sales time T1 = min(T, T0) is defined as the earlier of either the time when the seller runs out of stock or the time when time runs out.

[0032] The total revenue under pricing policy p can be expressed as:

[0033]

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[0034] In this case, the expected revenue can be expressed as:

[0035]

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[0036] The price reduction optimization problem is to find the optimal pricing policy p that will maximize expected revenue. * The goal is to seek this.

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[0038] Generally, solutions to the above problem may not be computationally feasible when the dimension of the parameter vector θ is relatively high, but they are applicable to practical cases when only one or two components of the demand function parameters are uncertainly estimated. In many practical cases, for several reasons, the price sensitivity or price elasticity parameter is the most difficult to estimate. For example, if no price changes for a product are observed, price elasticity can only be estimated by observing similar products. Another example is when discounting occurs during a seasonal decline in product demand. In this case, if low prices correlate with low product demand due to so-called endogeneity, the price sensitivity coefficient can be estimated with a much lower absolute value, or even with the opposite sign. Common practices in this case are to consider estimating a wider set of products or to apply various endogeneity mitigation measures. In both of these examples, the price elasticity estimate will be within a specific range. One embodiment disclosed below obtains an empirical distribution function of the coefficient estimates. The following shows how the embodiment can be applied to a widely used special case of the log-linear demand model.

[0039] Special cases of log-linear demand models and uniform distribution of price coefficients We consider here one of the simplest demand models, the log-linear demand model, which is constructed as follows:

[0040]

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[0041] Note that the first-order optimality condition for the revenue-maximizing price is equivalent to the price elasticity of demand being equal to one.

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[0043] Also, prices are set to maximize revenue when inventory is high enough relative to base demand α and the length of the sales period, or:

[0044]

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[0045] In this case, some of the inventory remains unsold. The above can be summarized in the following formula:

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[0047] In an optimal solution to a deterministic markdown optimization problem with an arbitrary demand function, the optimal pricing policy is one that ensures that inventory is not completely sold out before the end of the sales period; otherwise, prices can be raised so that the same amount of inventory yields higher revenues.

[0048] When the price coefficient β is not known precisely, it can be seen that underpricing an item when the value of β is overestimated and ensuring that the stock is depleted before the end of the season will result in a greater loss of revenue than overpricing the product when the value of β is underestimated by the same amount. The following specific distribution case illustrates this. Let the price coefficient β be a realization of a random variable with uniform distribution β~U(β1,β2). For a fixed price p, the value of the parameter β at which the stock is depleted within the sales period T is denoted as β0.

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[0050] At the value of β in the [β1, β0] interval, the inventory is sold out, generating revenue pS. At the value of β in the [β0, β2] interval, the inventory is not depleted, so sales per unit time are αTe -βpIf β0<β1, the inventory is never depleted. If β0>β2, the inventory is always sold out. Combining the above, the revenue defined in equation (1) above can be expressed as follows:

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[0052] If the value of β is known exactly, ie, β1=β2=β, the last line in equation (8) can be calculated as follows:

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[0054] This is consistent with the revenue equation for the revenue-maximizing price disclosed earlier.

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[0056] The price defined in equation (10) can be thought of as the modified clearance price ("ICP") defined in the first line of equation (5). When the price coefficient is uncertain, the modified ICP is greater than the ICP in the deterministic case for any β∈[β1, β2).

[0057] A comparison can be made between the conditions in equation (11) and those used to apply ICP in equation (5). First, the right-hand side of equation (11) converges to 1 when Δβ→0. Second, it can be seen that when β2>β1,

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[0059] This can be interpreted as requiring higher levels of inventory to apply ICP when the price coefficient is not known exactly.

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[0061] Similar to the revenue-maximizing optimal price in the second line of equation (5), the optimal price defined in equation (12) does not depend on inventory. That is, in this case, the optimal markdown solution will have some unsold inventory at the end date. Also,

[0062]

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[0063] This coincides with the optimal price defined in equation (5).

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[0065] Finally, the solution for optimal discount pricing when the price coefficients are uniformly distributed in the interval [β1, β2] can be summarized as follows:

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[0067] Joint inventory allocation and price reduction optimization problems for multiple customer groups supplied from multiple fulfillment centers. Generally, the demand for an item with a finite lifespan will be met by several fulfillment centers (FCs). Demand typically originates from several distinct groups with varying demand parameters. For example, these groups may be determined by geographical locations with various socioeconomic characteristics that affect price elasticity. An embodiment can determine the optimal down-pricing for an item when inventory is spread across several FCs. In this embodiment, inventory at all FCs has the same end date, after which the inventory is recovered at a price close to zero. The costs associated with sales from each FC to each customer group may also be individual. In the example of geographically dispersed customer groups, the cost may be the delivery cost from one FC to a certain geographical location.

[0068] A typical case of multiple customer groups supplied by multiple fulfillment centers (FCs).

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[0070] In the formula, B m This is the inventory quantity at FCm. In other words, the constraint in equation (15) determines the upper bound on the inventory delivered from FCm.

[0071] Generally, allocating more inventory to be sold to customers does not decrease revenue, because excess inventory is always likely to remain unsold. On the other hand, in order to generate more revenue by selling more inventory within a given period, the selling price should be lowered, which reduces the marginal profit of inventory allocation. Mathematically, the second derivative of the optimally priced revenue as a function of allocated inventory is negative, which means the function is concave. Thus, after changing the sign of the objective function in equation (14), the optimization problem in equations (14-17) becomes equivalent to a well-studied minimum-cost network flow problem with convex costs, for which a known solution exists.

[0072] In contrast, the embodiment implements a novel algorithm ("Algorithm 1") disclosed below for iteratively solving the optimal inventory allocation problem. Algorithm 1 takes the following hyperparameter δ0 to determine the initial step length.

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[0076] If the network is non-degenerate, links between the upper and middle layers that have non-zero flow, i.e., as follows, cannot form a cycle.

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[0078] For example, in the network shown in Figure 3, at most three of the four links 310-313 in the upper layer cannot have positive flow. This can be proven by considering the fact that a non-zero flow cycle has a positive cost in one direction, meaning that reducing the flow along this cycle improves the objective function, indicating suboptimality of the solution. One implication of this observation is that the number of links between FCs 300, 301 and intermediate integration nodes 302, 303 does not exceed |M| + |L| - 1 if shipping costs are sufficiently different. Another observation is that each customer group is supplied by at least one FC. Since the demand function remains positive at any price, and therefore at any delivery cost value, there is always a positive inventory allocation (even if very small), making this allocation profitable. In other words, if there is zero inventory allocation, a sufficiently small reallocation from another customer group will have an overall positive marginal benefit. One implication of this observation is that the number of customer groups served by two or more FCs is, at most, one less than the number of FCs.

[0079] These properties of the optimal solution in the embodiment provide the following: In many supply chain examples, the number of FCs is significantly smaller than the number of customer groups, so it is necessary to impose additional constraints on supply planning to improve robustness. One such measure could be to impose hard or soft constraints on link capacities.

[0080] Most minimum-cost flow algorithms also calculate so-called node potentials or dual costs for nodes with binding supply constraints. One interpretation of dual costs is the improvement of the objective function per unit of extra supply at the node. This information can be useful when there are additional opportunities to move inventory between nodes. Usually, it involves significant fixed costs, making the problem a so-called "network design" problem. The solution can serve as a further decision tool for planning load balancing between FCs.

[0081] Multiple customer groups supplied by multiple franchise centers when price factors are uniformly distributed.

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[0083] Hierarchical Demand Model Several approaches for estimating demand model parameters are available in embodiments. Demand modeling can be considered a general predictive analytics problem, but models must exhibit certain characteristics that narrow the model selection. A key limitation stems from the fact that demand is a monotonically decreasing function of product price, making most commonly used machine learning approaches, such as ensemble methods or deep learning neural networks, inapplicable. Therefore, embodiments are limited to two main groups of parametric methods: discrete choice models based on multinomial logit ("MNL") and regression methods using generalized linear models ("GLM"). The latter includes log-linear regression, Poisson regression, and negative binomial regression. In both groups, forecasts are based on a linear function of several attributes, including price, seasonality or seasonal time shocks, promotional lift, and post-promotion fatigue or pantry loading. MNL-based methods consider this linear function as product utility to forecast demand as market share. Their common disadvantage is their reliance on estimating so-called "no-purchase" option coefficients, which are usually unobservable variables. On the other hand, these methods account for demand shifting between similar products and perform well for product categories with high substitutability. GLM-based methods usually do not explicitly model demand shifting. However, recently emerging models can use similarity in customer attributes such as brand, color, and size to explain the existence of similar products and their impact on demand cannibalization.

[0084] The main obstacle in applying these methods to predict sales of a specific item at a specific store or by a specific customer group is that most of these sales are very small, resulting in a very low signal-to-noise ratio. Also, price changes may be very rare and within a very small range, further complicating the estimation of price sensitivity. Furthermore, the sales history of an individual item may contain too few observations to provide sufficient statistical power for the estimation of some parameters. All these factors make parameter estimation highly unreliable when based on data from sales of isolated items. However, this can be mitigated by considering multiple items sharing similar parameters or the same item sold at different locations. Locations and product items typically form a hierarchy, ranging from the entire chain down to price zones and individual stores when considering a location hierarchy, and from the entire chain down to departments, categories, classes, and individual items when considering a product hierarchy. When combined with clustering of items at lower levels of product classification, this hierarchy provides a useful tool for estimating demand model parameters at hierarchical levels with sufficient statistical power. In addition to constructing clusters of similar items for parameter estimation, known approaches provide techniques for determining at what level each parameter is estimated.

[0085] Embodiments develop estimation methods that exploit the existing hierarchical structure and the clusters constructed for estimation purposes. The output of these methods is a probability distribution of some of the parameter estimates.

[0086] Demand Model Assumptions Embodiments assume the availability of general sales data aggregated over a short period of time, such as a day or a week (i.e., historical sales data), rather than transaction-level data reflecting individual purchases. That is, for each item i, a triplet (s it ,pit ,r it ), where the triplets respectively represent sales, price, and a binary promotion flag over a dated period t. Often, zero sales are not part of the data, and additionally, out-of-stock ("OOS") periods are not explicitly flagged. The combination of these two factors makes it impossible to distinguish between zero demand and OOS observations. Also, sometimes promotions are not explicitly indicated, or there can be several types of promotions with different promotional lifts indicated by the same flag. Embodiments can use heuristics, disclosed below, to distinguish between these cases.

[0087] It is also assumed that the product hierarchy is known and sufficiently reflects the similarities between retail items. Furthermore, multiple items with different magnitudes of demand and prices can be pooled together. It is assumed that text descriptions of items exist in historical sales data and that attributes can be extracted from those text descriptions.

[0088] Demand Model Attributes Below we describe the attributes along with the demand output variables and how they are used by the model. We also describe some pre-processing steps that are performed to form the pool of observations at higher levels of the hierarchy. The notation x i (t) is used to represent the value of variable x observed for product i at time t.

[0089] Demand: Since items pooled together may behave similarly but have different average demands (e.g. for the same item in different stores), it is necessary to estimate a so-called base demand, which can be approximated by the average demand if item price changes are not large, or can be estimated as an intercept-type constant.

[0090] For slow-selling products, because it is not possible to distinguish between periods of zero demand and product unavailability when periods of zero inventory are not reliably identified in the data or appear as missing data, embodiments consider a sufficiently long sequence of periods of missing or zero sales to be OOS. The length threshold is determined by a probability threshold for encountering a certain number of consecutive periods of zero demand and is calculated as follows:

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[0092] where λ is the parameter of the Poisson distribution. i Since (t) is effectively truncated to zero, the maximum likelihood estimate of the parameter λ is obtained by solving:

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[0094] The threshold probability value is typically chosen to be around 0.01, meaning that the probability of a sequence of zero-demand periods having a length exceeding the threshold due to zero demand does not exceed 1%. For example, if the sample mean of observed zero-truncated demand is 2.3, the estimated mean demand is about 2, meaning that the probability of zero demand in three or more consecutive periods is less than 1%. Therefore, it is reasonable to assume that these are likely to be OOS periods.

[0095] Price: To pool together similar items with different prices, such as different size packages of the same product, their price values ​​are replaced with the average price below or the relative deviation from the initial undiscounted price.

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[0097] The estimated coefficient on this variable is the price elasticity of demand, if demand is modeled as exponentially dependent on price.

[0098] Promotion Flags: Promotions come in many different types and flavors, so ideally, there should be a vector of promotion flags that reflects which campaigns were run and which promotional tools were used in each case. However, few retailers keep historical records of promotions. Sometimes there is no indication of promotions at all. In this case, promotions can be separated from regular sales by running a clustering algorithm in the price-demand space. An embodiment uses the promotion flag variable as a i It is expressed as (t).

[0099] Post-promotion: This is a well-known effect caused by so-called promotion fatigue, where pantry loading leads to a temporary decrease in sales after a promotion period. This variable is defined as 0-1 or Boolean, indicating whether there was a promotion in the previous week.

[0100] Similarity: This is a set of variables that reflect how much the demand for this item is cannibalized by other items in the current product mix and their prices. The embodiment defines two variables: one for the sum of product mix item similarities, and the other for the sum of item prices weighted by similarity. The latter reflects the competitive effect of other item prices. The similarity between items is calculated based on item attributes extracted from their text descriptions. The embodiment defines the similarity variable and the price similarity variable as u, respectively. i (t) and v i It is expressed as (t).

[0101] Seasonality: Because the timing of most peak sales periods is determined by annual holidays, some of which follow a lunar rather than solar calendar (e.g., Easter) and others that fall on different days each year (e.g., Thanksgiving), the corresponding periods are indicated by the occurrence of the holidays rather than by calendar dates. Also, in most cases, peak sales occur in the week preceding the holiday, and the holiday and post-holiday periods are characterized by a sales decline. Therefore, embodiments define three-week seasonality variables for each holiday. Given that the week associated with each holiday is denoted by subscript h, embodiments define a set of dummy variables w that indicate whether period t is a period associated with a holiday. h Define (t).

[0102] An embodiment expresses the vector of explanatory variables as follows:

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[0104] An embodiment expresses the vector of coefficients as follows:

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[0106] If demand is modeled as a Poisson distribution with mean value as follows:

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[0108] The probability mass function is given by:

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[0110] A set of T observations (d i (t),x i Considering (t), t=1,...T, the embodiment uses regularized regression to estimate the β coefficient by maximizing the difference between the logarithm of the likelihood and the regularized term.

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[0112] In the equation, α is the regularization penalty parameter estimated by cross-validation. This technique, similar to ridge regression, can reduce overfitting.

[0113]

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[0114] Hierarchical estimation The embodiment uses a hierarchical approach to estimate the coefficients of the demand model defined above. It assumes there are at least three levels of hierarchy: categories (approximately 100–1,000 individual SKUs / UPC items), classes (approximately 10–100 items), and individual items that may include several SKUs / UPCs with varying sizes / colors but identical styles. While terminology may differ between retailers, this hierarchy is almost always present. The majority of the demand model coefficients are based on base demand β. 0 are estimated at the class level except for the base demand β 0is estimated at the item level. Price elasticities are also estimated at the class level, except for classes with strong seasonality. In those classes, postseasonal demand declines often coincide with significant price discounts, to the extent that a positive correlation between price changes and demand changes can result in a positive sign for the estimated price coefficient. This is a well-known endogeneity effect when correlation exists between explanatory variables and error terms (or unobserved factors) in the model. Several known solutions have been proposed to correct for this (e.g., solutions for automobile prices and airline prices). However, each of these and other approaches depends on the availability of so-called instrumental variables and requires special knowledge of product characteristics, which is not always available. Instead, embodiments estimate price elasticities using other products from the same category that do not exhibit strong seasonality, or other products at higher levels in the hierarchical tree if necessary.

[0115] Uncertainty Estimation Embodiments estimate parameter uncertainty using two methods: one based on the "Hessian" at the maximum of the log-likelihood function, and one using Markov Chain Monte-Carlo ("MCMC") methods.

[0116] Hessian-based: The Newton-Raphson method effectively approximates the log-likelihood function as a paraboloid whose shape is determined by the Hessian of the function, so that the variance of the parameter estimate can be calculated as the negative of the diagonal elements in the inverse Hessian, providing a means for constructing confidence intervals by assuming a normal distribution around this estimate. For example, a 95% confidence interval can be found as follows:

[0117]

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[0118] • MCMC-based: The embodiment utilizes Markov Chain Monte Carlo ("MCMC") sampling. The samples are derived from a prior distribution having a distribution of the next sample that depends on the last sample, forming a Markov chain that converges to the following posterior distribution.

[0119]

number

[0120] At higher hierarchical levels, parameters are estimated using prior distributions that do not provide much information. At lower levels, the prior distribution is posterior to that of higher levels. Item-level posterior distributions are used to model parameter uncertainty.

[0121] From the perspective of practical implementation, these two methods have advantages and disadvantages. The Newton-Raphson MLE method is relatively fast but can be computationally unstable. On the other hand, MCMC-type methods are usually stable but can be computationally slow, especially for large samples. In some practical implementations, it may be beneficial to use a hybrid approach by applying the Newton-Raphson method at higher hierarchical levels and MCMC at the item level, using a Gaussian prior obtained from the resulting Hessian at the higher levels.

[0122] Figure 4 is a flow diagram of the functionality of inventory and price optimization module 16 of Figure 2, according to one embodiment. In one embodiment, the functionality of the flow diagram of Figure 4 is implemented by software stored in memory or other computer-readable or tangible medium and executed by a processor. In other embodiments, the functionality may be performed by hardware (e.g., by using an Application Specific Integrated Circuit ("ASIC"), a Programmable Gate Array ("PGA"), a Field Programmable Gate Array ("FPGA"), etc.), or any combination of hardware and software.

[0123] In one embodiment, the functionality of Figure 4 controls the amount of inventory (e.g., of items at a single store) that is electronically ordered by a computerized inventory system (e.g., by a computerized inventory control and demand forecasting system). The functionality of Figure 4 may also control the amount of inventory (e.g., of items at a single store) that is allocated by the computerized inventory system. Furthermore, the functionality of Figure 4 may control adjustments to the amount of inventory (e.g., of items at a single store) by the computerized inventory system.

[0124] At 402, historical sales data or sales history is received for a retail item for which optimized prices and inventory allocations are to be determined. The retail item is shipped from multiple possible warehouses / fulfillment centers (i.e., supply nodes) to multiple possible customer groups / retail stores (i.e., receiving nodes). In one embodiment, the item is a finite lifespan item. In an embodiment, sales history of similar items is also received to capture the impact of demand shifting and infer parameter estimates when the sales history of a given item is not complete.

[0125] In one embodiment, the sales history of an item is weekly or daily sales data over a longer period, such as three months to a year, and is SKU / store level data. In other embodiments, the historical sales data is sales transaction data aggregated over a shorter period, such as a week or a day. For each item i, a triplet (s it ,p it ,r it ), where triples represent sales, price, and a binary promotion flag, respectively, over a dated period t. Often, zero sales are not part of the data, and additionally, out-of-stock ("OOS") periods are not explicitly flagged.

[0126] At 404, demand model parameters and corresponding confidence or tolerance intervals are estimated. In one embodiment, the estimated parameters include price elasticity or general price sensitivity coefficients, promotional lift impact, post-promotion fatigue impact, similarity to other products, and seasonality coefficients. For each parameter, parameter uncertainty is estimated. In one embodiment, a Hessian-based confidence interval is used as the parameter uncertainty measure. In one embodiment, an MCMC-based parameter uncertainty is calculated as the tolerance interval based on the observed variance of the underlying Markov chain. Thus, embodiments use confidence intervals when a Hessian can be calculated and tolerance intervals when using an MCMC approach.

[0127] At 406, a network of supply nodes (e.g., warehouses or FCs) for consumer connection is designed (e.g., the network shown in FIG. 3). This network includes three layers of nodes, namely an upper layer, a middle layer, and a lower layer. Nodes in the upper layer (e.g., nodes 300, 301 in FIG. 3), referred to as "supply nodes", correspond to FCs, and middle-level nodes (e.g., nodes 302, 303 in FIG. 3) and lower-level nodes (e.g., nodes 304, 305 in FIG. 3) correspond to customer groups. Each node in the upper layer is connected to each node in the middle layer by links (e.g., links 310, 311, 312, 313 in FIG. 3) if the supply from the corresponding FC can be used to satisfy the demand in the corresponding customer group. Further, each node in the middle layer (i.e., the "imaginary" nodes) is connected to the lower-layer nodes of the same customer group by links (e.g., links 314 and 315 in FIG. 3). Thus, in an embodiment, there is always a one-to-one relationship between the middle nodes and the customer group nodes.

[0128]

Number

[0129] At 410, if n < N and the termination criterion is not met, an incremental step δ n = δ0In is set and the minimum cost flow problem of the network of 406 is solved using, for example, Algorithm 1 disclosed above. Then, the inventory allocation is updated using the flow on the links. Algorithm 1 is executed for a predetermined number of steps (represented by N), but may end earlier if the improvement of the objective function between steps is below a specific threshold.

[0130] At 412, an optimal solution is obtained and reported. The optimal solution includes recommended inventory allocations and sales prices among the customer groups. Continuing with the above example, the optimal inventory allocation may be 100 units from FC1 to customer group 1, 20 units from FC2 to customer group 1, and 50 units from FC2 to customer group 2. The price at customer group 1 is $8, and the price at customer group 2 is $9. Note that in this example, the marginal revenue at both customer groups is approximately the same as the per-unit delivery cost from FC2 to those groups, so the 30 units at FC2 are unsold. Therefore, allocating each additional unit of inventory would result in a profit loss.

[0131] As a result of embodiments of the present invention, some inventory at a warehouse will be reallocated from one customer group to another. This may be a "virtual" reallocation because the inventory may not yet have been shipped to the respective price zone. However, the result of the functionality of FIG. 4 is that some inventory that would otherwise be shipped to another customer group is now shipped to one customer group or price zone. As a result, the logistics and inventory management systems at each warehouse cause some inventory to be shipped using transportation mechanisms such as trucks. The entire process can be automated with automated transportation vehicles such as self-driving trucks, automated truck loaders, etc., all of which respond to electronic signals from system 10 of FIG. 2.

[0132] As disclosed, the embodiments compensate for parameter uncertainties in generating practically applicable normative solutions based on parametric predictive models, because in most applications, it is impossible to obtain sufficiently accurate estimators of the model parameters. Along with a new formulation of the joint price reduction and distributional optimization problem based on explaining the uncertainty of demand parameters rather than probabilistic demand fluctuations, the embodiments are directed toward a novel solution approach that can be readily implemented by a wide variety of retail chain operators offering products with finite lifespans.

[0133] The embodiments disclose a network flow optimization model that can be used as a decision-making tool to provide further management insights in situations where retailers can benefit from further one-off tasks such as load balancing between FCs by improving fault tolerance in the supply chain between FCs and retail locations by transporting large volumes of inventory at a fixed cost or by increasing connection density.

[0134] The embodiment optimizes retail price reduction recommendations when demand model parameters are not precisely known (which is generally when demand parameters are estimated based on historical sales data). The embodiment further applies when a retailer has multiple warehouses or fulfillment centers that must supply product items to multiple locations or customer groups with various demand parameters, particularly price sensitivity.

[0135] Embodiments solve a markdown pricing optimization problem under parameter uncertainty. The embodiments assume that a retailer enables price differentiation among multiple customer groups with varying demand parameters. These groups may generally be supplied by multiple warehouses or fulfillment centers at varying costs. As in the markdown phase of a retail item's lifecycle, the retailer is assumed to have a finite amount of inventory in each warehouse that must be sold by a specific end date without further replenishment. The objective of the embodiments is to maximize gross profit, defined as total revenue minus total costs.

[0136] Because demand parameters cannot be accurately estimated in most practical situations, embodiments optimize the expected value of profit based on a given distribution of demand parameters. For general demand models and general distributions of demand parameters, embodiments provide a framework for finding optimal pricing policies that have the largest expected value of total profit. Embodiments can be further effectively implemented when there is a computationally tractable procedure for calculating the derivative of optimal expected revenue as a function of the inventory allocated to each customer group. The problem then reduces to a well-known minimum-cost network flow with convex arc costs that can be solved in a relatively small number of iterations.

[0137] Additionally, for a single customer group served by a single warehouse, embodiments include closed-form solutions for the case of a log-linear demand model and uniform distribution of the price elasticity parameter. For multiple customer groups served by multiple warehouses, embodiments provide closed-form expressions for arc costs and their derivatives in a minimum-cost network flow formulation, allowing for rapid problem solving.

[0138] Embodiments provide a novel approach to solving the markdown problem by taking into account parameter uncertainty. Embodiments provide a novel closed-form solution for a basic formulation with a log-linear demand model and uniform price elasticity parameter distribution when there is a single customer group (e.g., a brick-and-mortar store) but no shipping and handling costs. Embodiments provide a natural generalization to the case of multiple customer groups supplied by multiple warehouses by reducing the problem to repeatedly solving a minimum-cost network flow problem.

[0139] Embodiments overcome known solution asymmetries in the results of markdown processes due to inherent inaccuracies in price elasticity estimation. That is, if price elasticities are overestimated and markdown prices are set too low, retailers will run out of stock before the end of the selling season and lose revenue. In the opposite situation, if prices are set too high, retailers will have some unsold inventory but will lose less revenue. Thus, conventional wisdom is to markdown at a price lower than that based on the average of estimated parameters. In contrast, embodiments provide a quantification tool for determining optimized markdown price recommendations.

[0140] Although several embodiments have been specifically shown and / or described herein, it will be understood that variations and modifications of the disclosed embodiments are encompassed within the scope of the appended claims in accordance with the above teachings without departing from the spirit and intended scope of the invention.

Claims

1. 1. A method for optimizing inventory allocation of retail items, the retail items being allocated to a plurality of different customer groups from a plurality of different fulfillment centers, the method comprising: receiving, by one or more processors, historical sales data for the retail item; the one or more processors estimating demand model parameters based on the historical sales data; generating a network including a plurality of first nodes, each corresponding to one of a plurality of said fulfillment centers (FC m), a plurality of second nodes, each corresponding to one of a plurality of said customer groups, and a plurality of third nodes, each between one of the plurality of said first nodes and one of the plurality of said second nodes, wherein said customer groups share the same said demand model parameters, each of said plurality of third nodes aggregates allocations between a corresponding first node and said second node, and a plurality of arcs connect each fulfillment center with each customer group reachable from said corresponding fulfillment center, said method further comprising: [Equation 1] the one or more processors solving a minimum cost flow problem for the network to generate an inventory allocation; The step of generating the network comprises: The method includes the step of the one or more processors connecting each of the plurality of first nodes to each of the plurality of third nodes if supply from a corresponding fulfillment center can meet demand in a corresponding customer group.

2. The method of claim 1 , wherein the demand model parameters include one or more of price elasticity, similarity to other products, or seasonality coefficients. [Request Item 3] [Number 2] [Request Item 4] [Number 3]

5. The method of claim 1 , further comprising the step of transferring a first quantity of the retail item from a first fulfillment center to a first customer group in response to the generated inventory allocation.

6. A program causing one or more processors to execute the method according to any one of claims 1 to 5.

7. 1. A system for optimizing inventory allocation of retail items, the retail items being allocated to a plurality of different customer groups from a plurality of different fulfillment centers, the system comprising: one or more processors; and a storage device storing instructions; The instructions cause the one or more processors to perform the method of any one of claims 1 to 5.

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