Patent Publication Number: US-2011054984-A1

Title: Stochastic methods and systems for determining distribution center and warehouse demand forecasts for slow moving products

Description:
CROSS REFERENCE TO RELATED APPLICATIONS 
     This application is related to the following co-pending and commonly-assigned patent applications, which are incorporated by reference herein: 
     application Ser. No. 10/737,056, entitled “METHODS AND SYSTEMS FOR FORECASTING FUTURE ORDER REQUIREMENTS” by Fred Narduzzi, David Chan, Blair Bishop, Richard Powell-Brown, Russell Sumiya and William Cortes; filed on Dec. 16, 2003; 
     application Ser. No. 10/875,456, entitled “METHODS AND SYSTEMS FOR SYNCHRONIZING DISTRIBUTION CENTER AND WAREHOUSE DEMAND FORECASTS WITH RETAIL STORE DEMAND FORECASTS” by Edward Kim, Pat McDaid, Mardie Noble, and Fred Narduzzi; filed on Jun. 24, 2004; and 
     Application Ser. No. 61/239,046, entitled “METHODS AND SYSTEMS FOR RANDOMIZING STARTING RETAIL STORE INVENTORY WHEN DETERMINING DISTRIBUTION CENTER AND WAREHOUSE DEMAND FORECASTS” by Edward Kim, Arash Bateni, David Chan, and Fred Narduzzi; filed on Sep. 1, 2009. 
    
    
     FIELD OF THE INVENTION 
     The present invention relates to methods and systems for forecasting product demand for distribution center or warehouse operations; and in particular to an improved method and system for determining distribution center or warehouse order forecasts from store forecasts of slow selling products. 
     BACKGROUND OF THE INVENTION 
     Today&#39;s competitive business environment demands that retailers be more efficient in managing their inventory levels to reduce costs and yet fulfill demand. To accomplish this, many retailers are developing strong partnerships with their vendors/suppliers to set and deliver common goals. One of the key business objectives both the retailer and vendor are striving to meet is customer satisfaction by having the right merchandise in the right locations at the right time. To that effect it is important that vendor production and deliveries become more efficient. The inability of retailers and suppliers to synchronize the effective distribution of goods through the distribution facilities to the stores has been a major impediment to both maximizing productivity throughout the demand chain and effectively responding to the needs of the consumer. 
     Teradata Corporation has developed a suite of analytical applications for the retail business, referred to as Teradata Demand Chain Management (DCM), which provides retailers with the tools they need for product demand forecasting, planning and replenishment. Teradata Demand Chain Management assists retailers in accurately forecasting product sales at the store/SKU (Stock Keeping Unit) level to ensure high customer service levels are met, and inventory stock at the store level is optimized and automatically replenished. The individual store product forecasts can thereafter be accumulated and used to determine the appropriate amounts of products to order from a product warehouse or distribution center to meet customer demand. The warehouse must in turn order appropriate amounts from suppliers and vendors based on its demand forecast. 
     Some currently used methods for forecasting product sales and determining suggested store order quantities (SOQs) suffer when dealing with slow moving products and may produce problematic results when used to determine warehouse or distribution center orders for low inventory, very slow selling products. Problems may include periodic spikes in order forecasts, a drop in the size of an order from week to week, and a large discrepancy between forecasted and actual orders. Described below is an improved methodology for forecasting product sales and determining suggested store order quantities and warehouse demand forecasts for slow selling products. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
         FIG. 1  provides an illustration of a product supply/demand chain from a supplier and manufacturer to a retail store and customer. 
         FIG. 2  is process flow diagram illustrating a synchronized DC/warehouse forecasting and replenishment process. 
         FIG. 3  is a high level block diagram illustration of a process for determining DC/warehouse demand from an accumulation of store suggested order quantity (SOQ) data. 
         FIG. 4  is a high level block diagram illustration of a process for determining DC/warehouse demand from a roll-up of store long range order forecasts. 
         FIG. 5A  illustrates the total demand forecast and accumulated suggested order quantity forecast for a very low selling product sold at a number of stores over a sixty-five week period. 
         FIG. 5B  illustrates the effective total inventory of the product of  FIG. 5A  over the same sixty-five week period. 
         FIG. 6  provides a simple flow diagram of a process for determining product demand forecasts and suggested order quantities for slow selling products in accordance with the resent invention. 
         FIG. 7  illustrates an accumulated suggested order quantity forecast for a very low selling product sold at a number of stores over a forty-four week period following implementation of the process illustrated in  FIG. 6 . 
         FIG. 8  illustrates the effective total inventory of the product of  FIG. 7  following implementation of the process illustrated in  FIG. 6 . 
     
    
    
     DETAILED DESCRIPTION OF THE INVENTION 
     In the following description, reference is made to the accompanying drawings that form a part hereof, and in which is shown by way of illustration specific embodiments in which the invention may be practiced. These embodiments are described in sufficient detail to enable one of ordinary skill in the art to practice the invention, and it is to be understood that other embodiments may be utilized and that structural, logical, optical, and electrical changes may be made without departing from the scope of the present invention. The following description is, therefore, not to be taken in a limited sense, and the scope of the present invention is defined by the appended claims. 
       FIG. 1  provides an illustration of a retail demand/supply chain from a customer  101  to a retail store  103 , retail distribution center/warehouse  105 , manufacturer distribution center/warehouse  107 , manufacturer  109  and supplier  111 . Arrows  115  are used to illustrate communication between the demand/supply chain entities. The Teradata Demand Chain Management system  151  includes product demand forecasting, planning and replenishment applications executed on server  153  determines store order quantities  155  and distribution center forecasts  157 , and provides for the synchronization of the warehouse/distribution center replenishment system with the replenishment ordering system from their stores. 
     A synchronized DC/warehouse forecasting and replenishment process is illustrated in the process flow diagram of  FIG. 2 . Beginning at step  205 , each retail store  201  supplied by warehouse  203  creates a store forecast and order forecast utilizing a methodology such as the methods illustrated in  FIG. 3  or  4 . In step  207 , the individual store order forecasts are accumulated to the DC/warehouse level. This rolled-up order forecast is provided to the DC/warehouse  203  for use as the DC/warehouse demand forecast, as shown in step  211 . 
     In step  213 , DC/warehouse level policies may be established for RT (Review Time from last time the replenishment system was run), LT (Lead Time from the order being cut to the delivery of product), PSD (Planned Sales Days, the amount of time the Effective Inventory should service the forecast demand), Replenishment Strategy, and Service Level. In step  215 , forecast error is calculated comparing actual store suggested order quantities (SOQs) to DC/warehouse forecast orders. Finally, in step  217 , weekly forecasts are broken down to determine daily forecasts, calculate safety stock and SOQs. Safety Stock is the statistical risk stock needed to meet a certain service level for a given order quantity. The safety stock is a function of lead times, planned sales days, service level and forecast error. 
     There are several methods that can be utilized to produce DC/warehouse demand forecasts. Two methods for generating DC/warehouse demand forecasts, illustrated in  FIGS. 3 and 4 , are described below.  FIG. 3  illustrates a process where DC/warehouse demand forecasts are determined from roll up of Suggested Order Quantities (SOQs). Suggested Order Quantity information from numerous store locations  301 - 304  is aggregated  305  and used to generate DC/warehouse profile and weekly, monthly or quarterly forecasts  307 . This method takes into account lead times, seasonality and recent trends in both store and DC/warehouse requirements. The SOQ represents true DC/warehouse demand from stores as it calculates demand for the stocking period (planned sales days), considers lost sales where they exist and subtracts the effective inventory (on hand and on order) in building the correct store orders. 
       FIG. 4  is a high level illustration of a process wherein store order forecasts determined for numerous retail stores  401 - 404  are accumulated  405  to create the DC/warehouse Synchronized Demand  407 . Store order forecasts are determined through the process described in application Ser. No. 10/737,056, referred to above and incorporated by reference herein. The DC/warehouse replenishment orders will be executed considering all stores&#39; time-phased needs net of effective inventory and applying the DC/warehouse&#39;s lead time, planned sales days, forecast error and service levels. 
     In the processes shown in  FIGS. 3 and 4  discussed above, the Suggested Order Quantity (SOQ) or store order forecast for a product is determined by subtracting the effective inventory of the product from the DCM demand forecast for the product. The effective inventory of the product includes the current or beginning inventory of the product, also referred to a beginning on-hand (BOH) stock, plus additional inventory expected to be received by the store prior to the demand forecast period, less expected sales of the product prior to the demand forecast period. 
     As stated above, some currently used methods for forecasting product sales and determining suggested store order quantities (SOQs) may produce problematic results when used to determine warehouse or distribution center orders for low inventory, very slow selling products.  FIGS. 5A and 5B  are provided to illustrate this problem. The graphs of  FIG. 5A  illustrate the total demand forecast and accumulated suggested order quantity forecast for a very low selling product sold at  1100  stores over a sixty-five week period. The graphs of  FIG. 5B  show the effective total inventory level of the product over that same sixty-five week period. In this example, the most stores have a beginning on-hand inventory of 1 unit, the same weekly average rate of sales (ARS), and decrement on-hand inventory by the same amount every week. Product forecast unit sales and inventory levels are measured against the vertical axis in  FIGS. 5A and 5B , respectively. Sales weeks are measured along the horizontal axis in both figures. 
     Graph  501  of  FIG. 5A  illustrates the DCM system generated sales forecast for a representative product with a low average rate of sales of 0.024 units/week, i.e., approximately 1 sale every 42 weeks. With a requirement that a minimum stock of 1 unit be maintained at each store, the warehouse or distribution center (DC) suggested order quantities and total store effective inventory levels generated by the DCM system are illustrated by graph  503  of  FIG. 5A  and graph  513  of  FIG. 5B , respectively. Without the requirement that a minimum stock of 1 unit be maintained at each store, the DC suggested order quantities and total store effective inventory levels generated by the DCM system are illustrated by graph  505  of  FIG. 5A  and graph  515  of  FIG. 5B , respectively. 
     As can be seen in graphs  501 ,  503 , and  513 , for the product having an ARS of 0.24, a beginning inventory of 1 at most stores, and a requirement that a minimum stock of 1 unit be maintained at each store, the DCM system will forecast a significant number of product sales near week  42  of the forecast period, followed by a drop in the effective inventory of the product, and a very large DC SOQ at week  46 . In this scenario, most of the 1100 stores will order replenishment stock during the same week, week  46 , a potentially problematic situation for the warehouse, distribution center, or product manufacturer. A higher or lower ARS for the product will vary the week in which the week in which the spike in SOQ occurs. 
     Without the requirement that a minimum stock of 1 unit be maintained at each store, graphs  501 ,  505 , and  515 , show that the DCM system will forecast a significant number of product sales near week  42  of the forecast period, followed by a drop in the effective inventory of the product, but a replenishment SOQ will not be generated until after the 65 week forecast period. The effective inventory levels are significantly lower without the requirement that a minimum stock of 1 unit be maintained at each store. Following week  46 , the effective inventory for the product drops to below 600 units, well below the inventory level needed to meet the potential demand at all locations. This may cause insufficient orders and frequent stock-outs, resulting in lost product sales. 
     Some of the problems with the currently used methods for determining store and distribution center orders are rooted in the way the way product demand forecasts are used in the order calculations. Currently, a weekly product demand forecast, or Average Rate of Sales (ARS), is a real number, which for a slow selling product is less than one and close to zero: 0≦ARS&lt;1. However, the actual weekly demand in reality is a nonnegative integer, which for a slow selling product is either zero or one: demand={0,1}. 
     The difference between the nature of actual demands and the way forecasts are defined and used creates a discrepancy between reality and the replenishment model calculations. This discrepancy is particularly substantial when dealing with slow selling products:
         Orders need to rounded up or down to be whole numbers;   The rounding error is significant when dealing with small values; and   The errors are accumulated and magnified when orders are rolled up to a distribution center or warehouse level.       

     A close inspection of demand and forecast values indicates that demand values are probabilistic, or stochastic, by nature, and the outcome of each week demand is either one or zero with probabilities that can be estimated in advance. The forecast values are in fact the estimators of expected or average weekly demand and are not the estimators of each individual outcome. 
     It is therefore proposed that within the distribution center order forecasting process, the store demand forecasts for slow selling products be converted into stochastic values which are compatible with actual demands. A stochastic process is a probabilistic method for determining the value of a random variable over time. 
       FIG. 6  provides a simple flow diagram of a process for determining product demand forecasts and suggested order quantities, which utilizes a stochastic process for determining product demand forecasts of slow selling products. Referring to  FIG. 6 , the DCM forecasting system provides a weekly store demand forecast, a beginning on-hand inventory level, an on-order inventory value, and an average rate of sale value for a product in step  601 . In step  603 , the average rate of sale value is compared to an average rate of sale (ARS) limit values to determine if the product is to be treated as a very slow selling product. In the example discussed herein, the ARS limit is 0.1 units per week. 
     If the average rate of sale value exceeds the ARS limit value, the product will not be considered a very low selling product, and in accordance with step  605  the suggested order quantity for the product is determined by subtracting the effective inventory value, i.e., the on-hand and on-order inventory values, of the product from the DCM demand forecast for the product. The DCM forecasting process continues in step  611  with the SOQ determined in step  605  for these products. 
     When the average rate of sale value for a product falls below the ARS limit value, the product will be considered a very low selling product, and a stochastic process is employed in step  607  to convert the weekly demand forecast into a stochastic forecast. Using a Bernoulli distribution, the stochastic demand forecast is determined as described below: 
     
       
         
           
             
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     where: 
     p is the expected value of the distribution, i.e., the average weekly demand; 
     k is the outcome of the distribution, i.e., the demand of a given week; 
     0≦p≦1; and 
     k={0,1}. 
     In step  609 , the suggested order quantity for the product is determined by subtracting the beginning on-hand inventory value and the on-order inventory value from the stochastic demand forecast for the product. The DCM forecasting process continues in step  611  with the SOQ determined in step  609  for the very low selling products. Store SOQs are accumulated to determine the warehouse or distribution center SOQs. 
     The use of stochastic forecasts within the process of  FIG. 6  significantly improves the stability and consistency of order forecasts for slow selling products, and more stable inventory levels at the distribution center level. The use of stochastic forecasts within the process of  FIG. 6  also improves the accuracy of order forecasts compared to actual orders, reduces the drop between the first and the second week SOQs, and generates more effective order triggers and rounding.  FIGS. 7 and 8  illustrate some of these improvements in order forecasting for slow selling products. 
       FIG. 7  provides a comparison between order forecasts for a very low selling product determined through prior DCM forecasting methods, graph  701 , and through the stochastic process described above, graph  703 . The graphs of  FIG. 7  show weekly order forecasts calculated at week  32  and rolled-up to the distribution center level, for 1970 slow selling products. These products comprise three products at 703 locations with an ARS between 0 and 0.33 units per week (0≦ARS&lt;0.33). As can be seen in graph  701 , the prior DCM forecasting method produces large variations in order quantities, particularly a large order spike at week  42 . In contrast, the order forecast provided by the stochastic method is far more stable. 
       FIG. 8  provides a comparison between on-hand inventory levels for the same product locations shown in  FIG. 7 . Graph  801  shows on-hand inventory levels resulting from the use of the prior DCM forecasting method, while graph  803  shows inventory levels resulting from the improved forecasting methodology using stochastic demand forecasts for the slow selling products. Again, the inventory levels associated with the stochastic method are far more stable those associated with the prior forecasting method. 
     CONCLUSION 
     The improved methodology for forecasting product sales and determining suggested store order quantities and warehouse demand forecasts using stochastic demand forecasts for slow selling products better represents the supply chain reality. Converting forecast values into stochastic forecast values is simple, scalable, easily implemented within the DCM forecasting system, and performed with little computational effort. Using stochastic forecasts can eliminate the need for rounding of order quantities and therefore reduces rounding error in the calculations. Use of stochastic demand forecasts for slow selling products improves the accuracy of order forecasts, reduces the drop between the first and the second week SOQs, and generates more effective order triggers and rounding. 
     Instructions of the various software routines discussed herein, such as the methods illustrated in  FIG. 6 , are stored on one or more storage modules in the system shown in  FIG. 1  and loaded for execution on corresponding control units or processors. The control units or processors include microprocessors, microcontrollers, processor modules or subsystems, or other control or computing devices. As used here, a “controller” refers to hardware, software, or a combination thereof. A “controller” can refer to a single component or to plural components, whether software or hardware. 
     Data and instructions of the various software routines are stored in respective storage modules, which are implemented as one or more machine-readable storage media. The storage media include different forms of memory including semiconductor memory devices such as dynamic or static random access memories (DRAMs or SRAMs), erasable and programmable read-only memories (EPROMs), electrically erasable and programmable read-only memories (EEPROMs) and flash memories; magnetic disks such as fixed, floppy and removable disks; other magnetic media including tape; and optical media such as compact disks (CDs) or digital video disks (DVDs). 
     The instructions of the software routines are loaded or transported to each device or system in one of many different ways. For example, code segments including instructions stored on floppy disks, CD or DVD media, a hard disk, or transported through a network interface card, modem, or other interface device are loaded into the device or system and executed as corresponding software modules or layers. 
     The foregoing description of various embodiments of the invention has been presented for purposes of illustration and description. It is not intended to be exhaustive or to limit the invention to the precise form disclosed. Many alternatives, modifications, and variations will be apparent to those skilled in the art in light of the above teaching. Accordingly, this invention is intended to embrace all alternatives, modifications, equivalents, and variations that fall within the spirit and broad scope of the attached claims.