WO2015185438A1

WO2015185438A1 - Inventory setting system

Info

Publication number: WO2015185438A1
Application number: PCT/EP2015/061841
Authority: WO
Inventors: Stephen Charles WALL; Sarah Elizabeth SHEPPARD; Erika BIGGADIKE; Helen RITCHIE
Original assignee: The Sequoia Partnership Limited
Priority date: 2014-06-04
Filing date: 2015-05-28
Publication date: 2015-12-10
Also published as: GB2526840A; GB201409920D0

Abstract

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. Existing approaches fail to account for situations of intermittent high volume demand, i.e. where individual incoming orders may be for large quantities and arrive infrequently or unpredictably. They also fail to account for long replenishment lags that span multiple replenishment cycles. We therefore disclose 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.

Description

I nventory Setting System

Fl ELD OF THE I NVENTI ON

The present invention relates to an inventory setting system. BACKGROUND ART

Control of inventory is often one of the major factors in production processes (and other processes involving a replenishment cycle) , but is fluid and difficult to regulate effectively. An excess of inventory is inefficient, whereas a shortage can have a serious effect on the process output. I nevitably, attention has historically been paid to the way in which a production process can be controlled so as to set the amount of inventory that is needed in a manner that maintains efficiency and output levels. Until the mid-20^th century neither the mathematics nor the hardware were available to create effective controls.

At that point, the key principles of I nventory Control Systems were pioneered by Robert Goodell Brown, evolving from his work on submarine and missile tracking systems. Brown served in the US Navy; while working with the Operations Evaluation Group (OEG) , he was a project engineer on the BOMARC missile, had a hand in creating the Stock Keeping Unit (SKU) , and was on the team at OEG (administered by MI T) that developed what became the prototype for the Air Defence System for North America. After the war he realised that the same techniques used to defend against missiles were relevant to controlling inventory levels. He developed Brown's Exponential Smoothing twice; once while at OEG developing anti-submarine warfare tactics, and again while working for Arthur D. Little in Cambridge, Mass. The publication of Brown's statistical inventory control theory in 1962 led to its interpretation and application in setting inventory levels for some production processes, although this was never extensive and the majority still relied on a system of setting Re- Order Point (ROP) levels to drive a replenishment process and trigger the necessary logistical steps. Once computers started to become more widely available during the late 1960s and early 1970s, organisations wrote their own programmes to automate an existing manual system of inventory control. At this stage there were no standardised software packages, so current ways of working were implemented, based on then-known programming languages which ran on local mainframe computers. The automation of the statistical calculations for the correct inventory levels was a technical challenge at this stage and so the parameters for "safety stock" were overwhelmingly set based on holding a blanket level of cover, such as a number of weeks' stock for each SKU.

I n the 1970s systems were expanded to incorporate the planning of parts or raw materials according to the Master Production Schedule. Materials Requirement Planning (MRP) systems offered a demand-based approach for planning the manufacture of products and ordering of inventory. However, these systems still relied on parameters being set manually for the safety stock of each SKU. These systems ran on more sophisticated mainframe computers, and standard packages started to become more widely available, implemented by the vendors, rather than being bespoke client-designed implementations. From the mid-1970s onwards, the systems evolved again to Manufacturing Resource

Planning, known as MRP-I I . These systems built on the material management capabilities of MRP systems and added capacity requirements planning capabilities to create an integrated system. For the first time MRP-I I systems made it possible to integrate both materials and production capacity requirements and constraints in the calculation of overall production capabilities. Later, the first attempts to calculate a statistical safety stock calculation were incorporated, based on Brown's approach but with distinct limitations. They did not incorporate obsolescence calculations, nor did they tackle the calculations for high volume, intermittently sold items. I n practice, the parameters for the amount of safety stock that was required were often still manual inputs to the system. During the 1980s, rapid development of software spreadsheets occurred and in 1987 the first statistical add-in for Lotus 1 -2-3 was created (known as @RI SK) . This enabled businesses to calculate safety stock parameters outside their MRP systems and then feed in the resulting parameters.

During the late 1980s and 1990s Enterprise Resource Planning ( ERP) systems appeared. These took the technical foundations of MRP & MRP-I I and extended and integrated them to include both the core manufacturing and logistics, together with nontechnical problems such as accounting, financial, human resource management, project management, service and maintenance and transportation. The power of this was to provide accessibility, visibility and consistency across the enterprise. These enterprise-wide solutions involve significant investments by businesses and enshrine the ways of working within the implementation. However, it is still the case that the inventory management elements of the ERP systems applied to many major production processes are provided with either blanket stock targets (ie not statistically based) or with calculations loosely based on Robert Brown's theory.

Thus, a typical inventory setting system faces the problem of recommending 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 reducing the efficiency of the process as a whole. An inadequate safety stock, however, increases the risk of a demand not being met, thereby preventing the process from meeting its overall aim and possibly bring ing the process to a halt.

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 maximise 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 and allow the production process to operate at an optimum efficiency. 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, R.G. ( 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 I NVENTI ON

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. I n 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.

I n 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 . I ncluding 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 ½ , 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.

I f 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. BRI EF DESCRI PTI ON OF THE DRAW I NGS

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. DETAI LED DESCRI PTI ON OF THE EMBODI MENTS

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 I ntegral. This is illustrated in figure 1 , which shows a histogram of the relative frequency (/-axis) with which a particular demand level ( -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(A) and equates to the demand shortfall when holding a given amount of safety stock (A) . E(A) is expressible as an integral:

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:

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 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. I f 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 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) :

(1 — CSL)x[annual forecasted sales]

[Standard Deviation over a replenishment cycle] x [number of replenishments per year]

Or:

(1 - CSL)x [average demand over a replenishment cycle]

[Standard Deviation over a replenishment cycle]

I n 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 1 10 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" 1 12. During week 2, the production takes place, typically starting mid-week, and thus after a brief delay 1 16. There is then a short gap 1 14 to allow for technical processes such as Quality Assurance or maturation to take place, and another gap 1 18 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. I t 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.

I n 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 ZS 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: I f 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.

I n 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 FOU 230. The demand level being buffered is the greatest of :

The replenishment quantity 200, and

The average demand over a FOU 232

Thus, E(k) can be represented as:

E(k) [^maxi-^mum buffered demand] x (1 — service level)

[std deviation to buffer] x ^[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 = k x [std deviation to buffer] x ^[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 API s or the like to other processes running on the same computing means.

I t 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

CLAI MS

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 given by a standard normal loss function value 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

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.

An inventory control system according to claim 1 in which the standard normal loss function value also increases with the complement of a service level to be achieved.

An inventory control system according to claim 1 or claim 2 in which the standard normal loss function value 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 ½ .

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.

An inventory control system according to claim 1 or claim 2 in which the standard normal loss function value 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.

An inventory control method embodied on a programmed computer, comprising a process for calculating a level of safety stock that should be held, the process including steps of :

determining 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,

determining 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,

determining a standard deviation of the periodic demand for stock determining a standard deviation of the historical error in forecasts for the periodic demand for stock,

setting a standard normal loss value according to a function whose output increases with the historic average demand level, decreases with the number of demand points, and decreases with the lesser 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, and

setting the level of safety stock based on the standard normal loss function value.

An inventory control method according to claim 6 in which the standard normal loss function value is also increased with increases in the complement of a service level to be achieved.

An inventory control method according to claim 6 or claim 7 in which the standard normal loss function value 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 ½ . An inventory control method according to any one of claims 6 to 8 in which the periodic demand for stock is a zero-stripped periodic demand.

0. An inventory control method according to claim 6 or claim 7 in which the standard normal loss function value 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.

1 . A non-transitory computer-readable medium embodied with software for inventory control, comprising a process for calculating a level of safety stock that should be held, the process including steps of :

iii. a standard deviation of the periodic demand for stock, and iv. a standard deviation of the historical error in forecasts for the periodic demand for stock, and

setting the level of safety stock based on the standard normal loss function value. A non-transitory computer-readable medium according to claim 1 1 in which the standard normal loss function value is also increased with increases in the complement of a service level to be achieved.

A non-transitory computer-readable medium according to claim 1 1 or claim 12 in which the standard normal loss function value 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 ½ .

A non-transitory computer-readable medium according to any one of claims 1 1 to 13 in which the periodic demand for stock is a zero-stripped periodic demand.

A non-transitory computer-readable medium according to claim 1 1 or claim 12 in which the standard normal loss function value 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.

16. An inventory control system substantially as herein described with reference to and/or as illustrated in the accompanying figures.