GB2526840A - Inventory setting system - Google Patents

Abstract

Disclosed is an inventory control system comprising a predictor unit for predicting a level of safety stock that should be held. The predictor unit is arranged to determine the safety stock level as that which leaves a standard normal loss function which increases with an historic average demand level during a period corresponding to a time lag between availability of stock information for a replenishmentdecision and the end of the period for which the replenishment quantity is required, and decreases with a number of demand points within the time between availability of stock information for a replenishment decision and the end of the period for which the replenishment quantity is required, and the minimum of a standard deviation of the periodic demand for stock and a standard deviation of the historical error in forecasts for the periodic demand for stock. This differs from previous systems suited to continuous demand situations only, which would rely simply on the average demand over a replenishment cycle and the period of uncertainty, and not take into account the forecast of intermittent demands.

Description

Inventory Setting System

FIELD OF THE INVENTION

The present invention relates to an inventory setting system.

BACKGROUND ART

A typical inventory setting system aims to recommend a level of inventory that should be maintained in order to meet the demand that is likely to be experienced over a specific period. The inventory level includes two amounts; an amount intended to cover the demand for the item being stocked, and a second amount being a "safety stock" which is intended as a reserve against variability in the level of demand. A large safety stock will increase the probability that an incoming order will be met satisfactorily (the "service level"), but will increase the overall cost of the inventory held thereby increasing the investment needed. An inadequate safety stock, however, increases the risk of an order not being met thereby preventing the organisation from making a sale and/or meeting contractual obligations, and (in a competitive environment) potentially driving customers elsewhere.

There is accordingly a strong advantage in being able to predict the necessary level of safety stock, and/or correlate the level of safety stock with the service level. This will allow the safety stock level to be optimised, either to achieve a contracted or a desired service level at a minimum cost, or to maxirnise the return on investment by identifying a level of safety stock for which the service level and the stock cost are optimally balanced. An ideal inventory setting system will therefore work from historic demand data to produce a recommendation as to a level of safety stock to achieve a specific service level.

A range of inventory setting systems are therefore available. Typically, these comprise computational devices which receive information from an enterprise resource planning (ERP) system or the like as to historical demand levels and which apply computational techniques to these and to other data to produce a recommendation as to stocking levels. This recommendation can be used to guide the business, effectively by providing an interpretation of past demand levels in a more useful form.

For continuous demand patterns, it can be shown that demand will follow a normal distribution, see Brown, kG. (1962), Smoothing, Forecasting and Prediction of Discrete Time Series. Prentice Hall, Englewood Cliff, New Jersey, which discloses a calculation for the expected shortage of demand in a single replenishment cycle for normally distributed demand. This has been the basis for statistical safety stock calculations for continuous demand situations since.

For demand that is both intermittent and low volume (i.e. circa 1 unit at a time), the demand can be described using a Poisson distribution instead. For each of these two situations, basic statistical techniques allow prediction of the service level that can be achieved for a given level of safety stock. Alternatively, applying this in reverse gives the safety stock level that must be held in order to achieve a specified service level.

SUMMARY OF THE INVENTION

Neither of these approaches account for situations of intermittent high volume demand, i.e. where individual incoming orders may be for large quantities and arrive infrequently or unpredictably. The present invention seeks to provide an inventory control system that will provide reliable safety stock predictions in such conditions. In fact, the system that is described and claimed caters for high-volume demand situations whether they are intermittent or continuous.

Such situations exist within a range of contexts. Often, they can be found at or near the start of a supply chain, such as in the supply of a processed item that is used as the raw material to a production line. Often, such items are prepared and supplied in large batches in order to achieve economies of scale; an individual batch will then be used as required in the production line to which it has been supplied, and a new order for a further batch will be placed once the previous batch nears exhaustion. Generally, the raw material supplier will not have insight into the usage rate of the batch and thus may see the incoming orders as highly intermittent. Similar situations exist for suppliers who are making to order, and to suppliers to FMCG (fast-moving consumer goods) export markets.

A specific example is in the supply of branded flavoured drinks. Typically, these are made using a "syrup" which is diluted and carbonated (if appropriate) before being bottled or otherwise containerised for supply to retail outlets. To ensure quality control, consistency of flavour, and secrecy of the recipe, the syrup must be manufactured at a small number of centralised locations. However, to distribute the drink economically, the syrup must be diluted at a large number of facilities located close to the retail customers, so avoid long-distance transport of (effectively) the water into which the syrup is being diluted and the glass in which it is contained. Technical considerations mean that the syrup is best produced in large quantities, and for less popular flavours this results in them being made infrequently and intermittently.

In addition, Brown's approach assumes a single replenishment cycle and does not account for a replenishment lag that may span multiple replenishment cycles, for example due to long transit times or long planning leadtimes.

The present invention therefore provides an inventory control system comprising a predictor unit for predicting a level of safety stock that should be held, the predictor unit being arranged to determine the safety stock level as that which leaves a standard normal loss function which increases with an historic average demand level during a period corresponding to a time lag between availability of stock information for a replenishment decision and the end of the period for which the replenishment quantity is required, and decreases with a number of demand points within the time between availability of stock information for a replenishment decision and the end of the period for which the replenishment quantity is required, and the minimum of a standard deviation of the periodic demand for stock and a standard deviation of the historical error in forecasts for the periodic demand for stock. This differs from previous systems suited to continuous demand situations only, which would rely simply on the average demand over a replenishment cycle and the period of uncertainty, and not take into account the forecast of intermittent demands. By taking these additional factors into account, the predictor can cope with continuous or intermittent high demand and long replenishment lags. Usually, where a first variable "increases with" a second variable, this means that will mean that the first variable is "proportional to" the second variable, but other relationships are not ruled out.

The standard normal loss function ideally also increases with the complement of the service level to be achieved, such as by being proportional to the product of the maximum relevant demand noted above and the complement of the service level. By the "complement", we mean 1 -the service level, in situations where the service level is expressed as a value between 0 and 1. More generally, the complement could be expressed as a value between a maximum and a minimum, in which case the complement is the maximum value less the value of (service level minus the minimum), i.e. the maximum, minus the service level, plus the minimum. Including this factor allows the safety stock to be determined in accordance with the service level that the organisation wishes to achieve.

The standard normal loss function can also decrease with (or be inversely proportional to) the time between availability of stock information for a replenishment decision and the end of the period for which the replenishment quantity is required, raised to a positive power such as 1/2, to take account of order frequency.

To allow the safety stock to take account of variability in the demand, the standard normal loss function also preferably decreases with the minimum of a standard deviation of the periodic demand for stock, and a standard deviation of the historical error in forecasts for the periodic demand for stock. Taking the minimum of these two ensures that the safety stock buffers the true variability to which the business is exposed. The periodic demand for stock used in this calculation may need to be a zero-stripped periodic demand, depending on (for example) how the demand values are recorded by the organisation.

If desired, a comparison between an average historical replenishment quantity and the historic average demand level during a period corresponding to a time lag between availability of stock information for a replenishment decision and the end of the period for which the replenishment quantity is required can be made, and the higher of the two used in the above calculation. This allows the larger quantity to buffer the variability, protecting service for longer and resulting in lower safety stock.

BRIEF DESCRIPTION OF THE DRAWINGS

An embodiment of the present invention will now be described by way of example, with reference to the accompanying figures in which; Figure 1 illustrates the standard normal loss function; Figure 2 illustrates the overall system process; Figure 3 illustrates the period of uncertainty; Figure 4 illustrates the factors being input to the system and being calculated by the system; and Figure 5 shows a block diagram of the system architecture.

DETAILED DESCRIPTION OF THE EMBODIMENTS

Starting from the Brown paper ("Smoothing, Forecasting and Prediction of Discrete Time Series' above), this uses an approach called the Partial Expectation, also known as the Standard Normal Loss Integral. This is illustrated in figure 1, which shows a histogram of the relative frequency (taxis) with which a particular demand level (x-axis) is experienced. We have found that although the demand itself may be discontinuous, in that demand does not arrive at predictable intervals but is unpredictable in terms of both magnitude and frequency, a plot such as figure 1 nevertheless tends toward a normal distribution as illustrated.

Thus, the partial expectation, i.e. the unsatisfied demand, is E(k) and equates to the demand shortfall when holding a given amount of safety stock (k). E(k) is expressible as an integral: rco E(k) = j (x-k)f(x)dx k but is more usually determined via a look-up table giving corresponding values of both in normalised form, an example of which was originally compiled by Robert Brown. An extract is: k E(k) 0.00005850 3.5 0.00038220 3 0.00200000 2.5 0.00849000 2 0.02930000 1.5 0.08333110 1 0.19775360 0.5 Figure 2 illustrates the process by which an inventory control system according to the present invention would operate. The first step (100) is to import or otherwise acquire the historical demand data for the product in question, together with standard parameters S reflecting the operation of the process by which additional stock is acquired. This can include both technical factors such as the time required to manufacture or otherwise prepare further stock and organisational factors such as the lead time required for raw materials and the time required to process newly-acquired stock and make it available for delivery. The data may then (optionally) need to be reviewed for accuracy and sanitised (step 102) if any anomalies are found. This then allows the system to process the data to compute the necessary safety stock levels (step 104). The system may also calculate the predicted demand stock (i.e. the stock required to cover for the expected demand, before the safety stock is called upon), or this may be calculated by a separate system.

The calculated safety stock (and, optionally, demand stock) can then be displayed (step 106) for review by operators. If desired, this may then be subject to a "what-if' analysis, by iterating the data processing step 104 with adjustments to the data loaded at step 100 in order to detect the sensitivity of the output figure to variations in the starting points. This can highlight (for example) where the suggested safety stock level would be lowered if a change to one of the starting data points were possible, such as reducing the period of uncertainty. With the safety stock level decided in this way, the figure can be passed to a stock control system (step 108) for the necessary orders to be placed.

Looking more closely at step 104 of this process, there needs to be a suitable process for calculating the safety stock level for a given demand stock, demand history and process variables. Considering what might have been sold over a year and the service level ("CSL") that is being targeted (expressed as a figure between 0 and 1 representing a probability of being able to satisfy an incoming order from stock): Annual Shortfall Quantity = (1 -CSL) x [annual forecasted sales] Since the partial expectation approach (figure 1, above) gives the shortfall quantity S for a replenishment cycle, then: Annual Shortfall Quantity = E(k)x [Standard Deviation over a replenishment cycle] x [number of replenishments per year] Combining the equations, and solving for E(k): Ek) -(1 -CSL)x[annual forecasted sales] -[Standard Deviation oi'er a replenishment cycle] x [number of replenishments per year] Or: E -(1 -CSL)x [average demand over a replenishment cycle] (c) -[Standard Deviation over a replenishment cycle] In simple terms, the replenishment period or "period of uncertainty" ("POU") is the period of time between obtaining the stock information that a replenishment decision is to be based upon, and the end of the period for which the replenishment quantity is required to protect service levels, after which a subsequent replenishment can be made. Safety Stock is needed to cover this period because of uncertainty as to the number of stock that will be sold -it is the forecast error over this time period that is being buffered. This is illustrated in figure 3, showing a timeline over the period of uncertainty. Assuming that a stock snapshot is taken at the start of week zero, a week can typically be allowed for the planning process 110 as to what will be done during week two. During the following week (week 1), preparations can be made for this plan to be put into effect, reflecting a "frozen period" 112. During week 2, the production takes place, typically starting mid-week, and thus after a brief delay 116. There is then a short gap 114 to allow for technical processes such as Quality Assurance or maturation to take place, and another gap 118 to allow for transit time between a production facility and a storage facility. On arrival at the storage facility, the new stock will need to be checked in and recorded as being available. Beyond that point, there will also be a period 120 until the next replenishment cycle begins. The safety stock needs to buffer variability in demand across this entire period 122.

Figure 4 shows the data processing calculation steps that can be carried out in order to implement this. The inputs to the process are designated within the dotted-line box 200 and are values that are measured, acquired, estimated or pre-determined by the process in question or the people responsible for operating it. These are: The average Replenishment quantity 202, i.e. the number of stock items included in each routine replenishment, is likely to be the most efficient compromise between the cost of holding stock and the cost of making a replenishment.

The POU in periods 204, i.e. the replenishment period or "period of uncertainty" discussed above, is determined by observation of the process in action and then conversion into whatever time period is being used as the smallest unit of time in the calculations.

The Customer Service Level to Target 208 is the CSL (above), in the form of a number between 0 and 1.

The Demand by Period 210 is the historical demand recorded over a suitably long but representative time period.

Finally, the Forecast by Period 212 is a set of the historical forecasts made by a person or by a suitable external system of the (then) future demand over the same period-by-period basis as the Demand by Period 210. This could be as simple as an average (mean, media or mode) of the demand over a preset historical period, or a more complex approach looking for cyclical or other patterns in the demand history.

It should have been prepared on the same basis as will be used over the forthcoming period(s) for which the safety stock is to be calculated.

The first step is to calculate the Smoothed Forecast Error 214 for each period. This can be done by noting the difference between the average forecast 212 over the last n' periods and the average actual demand 210 over those n' periods, but returning a null character if both the forecast and the demand for a particular period were zero. Fields with a null character are (in all calculations) ignored during subsequent steps and thus do not affect averages, standard deviations etc based on the data set in question. The value of n' controls the degree of smoothing required (see later). From this, the Standard Deviation (SD) of the smoothed forecast error variability across all periods 216 can be calculated.

In parallel, the Average Demand 218 across all periods is calculated from the Demand by Period 210. Also, a Zero Stripped (ZS) Demand 220 for each period is calculated, which can be one of: ZS Demand = [Demand if Demand is nonzero] OR [null if Demand is zero] or ZS Demand = [null if Forecast and Demand are 0] OR [Zero if Demand is zero or null and Forecast > 0] ELSE equal to Demand The arithmetical mean of the ZS Demand across all periods 222 is also determined, together with the associated standard deviation 224. From these two standard deviations, i.e. the Standard Deviation (SD) of the smoothed forecast error variability across all periods 216 and the standard deviation of the 75 Demand across all periods 224, the lower of the two is selected as the Standard Deviation to Buffer 226, i.e. the standard deviation which will be used as the basis of the safety stock calculation.

Next, based on the POU length 204 and the Demand by Period 210, the number of Demand Points per POU (DPPP) 228 for each period can be calculated as: If current period = n then DPPP = Count where Demand >0 from period n to period (n+(POU-1)) We can also calculate the average DPPP per POU across all periods and the maximum DPPP across all periods 230, together with the Average Demand over POU 232 (which can be expressed as Avg Dem over POU 232 = Avg Demand per period 218 x POU in periods 204 in order to reduce the computational load, if necessary) and the Average Demand over Cycle 234 (i.e. the Average Demand per period 218 x POU Length in Periods 204.

Several further optional refinements to the above process can also be included.

First, in relation to the smoothing of forecast errors, this should be done in the context of the replenishment model of the business in question. For example, in the supply of items with short shelf lives where it is critical that the forecast is delivered in the correct period, failing which items will become obsolete, then no smoothing should be done. Where there is the flexibility to change production or delivery dates and it is not critical whether the forecast items arrive a week (or other period) early/late, then smoothing can be considered.

In relation to zero stripping, this should (ideally) not be used to remove valid data points. This choice will be a matter of user discretion based on knowledge of the manner in which the data is captured and entered into the ERP system in question.

The safety stock level can then be calculated (to complete step 104 of figure 2) in three further steps. First, an E(k) value is calculated. This is defined as the demand level that is being buffered, times (1-service level 208), divided by the standard deviation being buffered 226, divided by the square root of the demand points per POU 230. The demand level being buffered is the greatest of: -The replenishment quantity 200, and -The average demand over a PCU 232 Thus, E(k) can be represented as: E(k) -[maximum buffered demand] x (1 -service level) [std deviation to buffer] x V[Demand points per POU] That E(k) value can be converted to a k value as described above, such as by conversion using a known look-up table. The k value will be a normalised one, so to convert this into absolute values of stock simply requires multiplication back up: Units of safety stock = Ic x [std deviation to buffer] x V[Demand points per POU] Alternatively, this level of safety stock can be expressed in terms of periods of demand, if the supply system in question is set up to suit this: Units of safety stock Safety Stock in periods = -Average demand per period The average demand per period used in this equation can be either the actual average demand per period 218, or the zero-stripped demand per period 220, as discussed above.

Figure 5 shows the general architecture of the inventory control system according to the present invention, in terms of its functional relationships. A predictor unit 250 performs the numerical calculations, receiving its inputs 200 from a link 252 to the organisation's ERP system and from a memory holding values of the various quantities determined by measurement or by a user decision. After the above-described computational steps have been completed (step 104 of figure 2), the results can be displayed on a display unit 256 for review by the operator and any further iteration that is required (step 106 of figure 2).

Once approved by the operator, the predictor 250 can forward the safety stock decision to a stock control system via an output 258 (step 108 of figure 2). Usually, the predictor 250, the memory 254 and the display 256 will be embodied via or within a computing means in the form of a running process, a spreadsheet function, or the like. The inputs and outputs 252, 258 can then be embodied as networked or similar connections to other systems, or by APIS or the like to other processes running on the same computing means.

It will of course be understood that many variations may be made to the above-described embodiment without departing from the scope of the present invention.

Claims (6)

1. CLAIMS1. An inventory control system comprising a predictor unit for predicting a level of safety stock that should be held, the predictor unit being arranged to determine the safety stock level as that which leaves a standard normal loss function which S increases with: an historic average demand level during a period corresponding to a time lag between availability of stock information for a replenishment decision and the end of the period for which the replenishment quantity is required, and decreases with: a number of demand points within the time between availability of stock information for a replenishment decision and the end of the period for which the replenishment quantity is required, and the minimum of i. a standard deviation of the periodic demand for stock, and ii. a standard deviation of the historical error in forecasts for the periodic demand for stock.
2. 2. An inventory control system according to claim 1 in which the standard normal loss function also increases with the complement of the service level to be achieved.
3. 3. An inventory control system according to claim 1 or claim 2 in which the standard normal loss function increases in inverse proportion to the number of demand points within the time between availability of stock information for a replenishment decision and the end of the period for which the replenishment quantity is required, raised to the power 1⁄2.
4. 4. An inventory control system according to any one of claims 1 to 3 in which the periodic demand for stock is a zero-stripped periodic demand.
5. 5. An inventory control system according to claim 1 and 2 in which the standard normal loss function further increases with an average historical replenishment quantity where that is greater than the historic average demand level during a period corresponding to a time lag between availability of stock information for a replenishment decision and the end of the period for which the replenishment quantity is required.
6. 6. An inventory control system substantially as herein described with reference to and/or as illustrated in the accompanying figures.