WO2000046733A1

WO2000046733A1 - Method for maintaining an inventory

Info

Publication number: WO2000046733A1
Application number: PCT/FI2000/000081
Authority: WO
Inventors: Mika Winqvist
Original assignee: Mika Winqvist
Priority date: 1999-02-05
Filing date: 2000-02-04
Publication date: 2000-08-10
Also published as: AU2550400A; FI990221A0

Abstract

The objective of the present invention is to accomplish a dynamic method of computing the order quantities simultaneously taking into account safety stocks and safety times. This is achieved by computing item by item an order quantity, a safety stock and safety time. In the beginning the method determines a plurality of deviations related to forecasts. In addition, correction factors are calculated. The deviations and correction factors can also be computed later when item specific calculations are carried out. Thereafter, the item specific calculations are started. Depending on classification of an item the order quantity is calculated using the Wagner-Whitin algorithm or using the Wilson EOQ formula. After the order quantity has been obtained, a forecast based safety stock, a quantity based safety stock, and safety time will be calculated. Values of the safety stocks are corrected with the correction factors. The effective safety stock for an item is then obtained by summing the corrected safety stocks. A fixed managerial safety stock can also be added to the effective safety stock for taking into account situations where temporary additional buffering is evident. After calculations for all items have been executed, the method gives output data which include order quantity, receipt date, the effective safety stock and safety time.

Description

METHOD FOR MAINTAINING AN INVENTORY

Field of the invention

The present invention relates generally to inventory system including a plurality of automated features such as keeping and updating records on a stock, informing on the status of a single item such as the inventory quantity, the last order point, the last order quantity, the typical demand, the safety stock level, the cost associated with the item and so on. Especially, the invention relates to a method of computing an effective safety stock including at least a forecast based safety stock .

Technical background

In the manufacturing industry there are at least four principal reasons to hold inventories: to increase operating efficiency, to provide a quick re- sponse to customers, to provide safety against normal business uncertainties, and to take advantage of unusual price opportunities or to protect against irregular business risks. Inventory management has to make several decisions every day such as how much to order, should the volume be fixed, when to order, at what point of time or at what level of stock should orders be placed and how to control the system. Further, what procedures and routines should be incorporated into the system to make these decisions easier, how should different items be controlled and how often should the inventory status be determined.

Inventory systems typically have several automated features which are arranged in modules. The recording/transaction module keeps and updates records on the stock, processes transactions and reflects the exact state of the physical system. It can tell the status of a single item: the inventory quantity, the last order point, the last order quantity, the typical demand, the safety stock level, the cost associated with the item etc. The decision rule module exists to find answers to how much to order and when to order. This module has most often a forecasting element. The order quantity decision determines the amount of the order to minimize total costs. When to order can be called the safety stock decision. Finding the lowest possible level of inventory with an acceptable risk of stock-outs is usually the problem addressed. This includes categorizing inventory items according to cost and consumption into A, B, and C items. Generally, a relatively small proportion of the total items held in inventory will account for a large proportion of total inventory value. The 80/20 rule states that typically 80 percent of a company's cost volume item usage is accounted for by 20 percent of all items. This 20 percent of the items are classified to belong to class A. The rest of the items belong to the class B or class C.

A service level, an average inventory, and a lead time are basic definitions relating to the inventory. Average inventory consists of materials, components, work-in process, and finished products typically stocked in lo- gistical facilities. Average inventories include base stock, safety stock, and transit inventory. The lead time for deliveries is the time between order placement and order receipt.

Since minimization of costs is the central issue in inventory control and the costs depends on how to answer to the previously mentioned ques- tions, the main task in the art is to find suitable methods for determining the most appropriate order quantities, safety stock, and safety time. As a consequence of this, a few inventory and order planning and optimization techniques have been developed. The most known in the art is the Basic Economic Order Quantity EOQ, also known as Wilson's formula. A less known true optimization technique is the Wagner-Whitin algorithm.

The economic order quantity, EOQ, or Wilson's formula balances the cost of holding inventory against the ordering cost for a given annual volume of need and this way tries to minimize the total cost of inventory carrying and ordering. The model is suitable for continuous inventory review systems. Those interested in the background art can find a description of EOQ in the book: Bowersox, D. J., and D. J. Closs: Logistical Management, from page 259 to page 261.

FIG. 1 visualizes the thought behind EOQ. The inventory carrying cost includes costs of capital, insurance, obsolescence, deterioration, depre- ciation in value, storage, and taxes. The ordering cost includes costs that are directly associated with ordering the components. Total material and stocking costs are obtained from the following equation (1):

2x C„ x D

E^QQ = X x p 0⁾ where EOQ = economic order quantity p = unit price

D = annual demand [units] C₀ = ordering cost C, = inventory carrying cost

It is worth to note that in the equation (1) the annual demand is considered, not a daily or weekly demand. In its basic form the EOQ is simplistic. In addition, although the assumptions underlying both the EOQ model and its known extensions appear to be restrictive, one of the most appealing aspects of the model is that it is quite robust. The extended EOQ takes also into account quantity discounts and transportation rate discounts. An especially important characteristic of the model is that the total stocking cost function, FIG. 1 , is relatively flat around the minimum point. This is important be- cause estimates of ordering and holding costs are not always accurate.

The economic order quantity model has many faults, but often it is the only appropriate way to determine order quantities. The problem with EOQ is that the derived order quantity leads to more inventory than is required per day, except for the last day, plus safety stock. The result is that working capital is tied in an unproductive place - inventory

The Wagner-Whitin algorithm uses time-series lot sizing, which means combining requirements over several periods to arrive at a procurement logic. The approach is dynamic because the order quantity is adjusted to meet current forecasts. This is different from the basic EOQ, which is static. Dynamic lot sizing techniques use varying order quantities in irregular demand situations. Those interested in the background of the Wagner-Whitin can find a description of it in the book: Silver, E. A., and R. Peterson: Decision Systems for Inventory Management and Production Planning, from page 228 to page 232. The Wagner-Whitin algorithm has an adjustment routine called look- ahead/look-back. The benefit is that it extends the planning horizon across more than one ordering point. The options for ordering requirements for periods further away from the present increase as the number of periods calculated increase. For any specific period t there are t possible options to evalu- ate. The Wagner-Whitin algorithm is used to determine order quantities for a set of requirement values. The determining of optimum order quantities is a stepwise procedure. First ordering costs of the first period are evaluated. Then the two options for ordering requirements for the first two periods are calculated and so on.

Although the Wagner-Whitin algorithm provides an optimal solution for given parameter values, it has not been widely used due to three primary drawbacks. First, the method in itself is complex and requires dynamic programming. Second, the computational effort required is considerably larger than that for most other methods. Third, the assumption is that receipts can be made only in the beginning of every period. The assumption can be over- come by splitting periods to subperiods. However, by increasing the number of periods, the computing time rapidly goes up.

Due to uncertainty in demand and supply or delivery a safety stock must to be carried. Appropriate values of safety stock and safety time are influenced by the accuracy of forecasts, the accuracy of delivered quantities, and the variability of lead times. Supply timing uncertainty can arise from variations in suppliers' lead times. Both demand and lead time can vary substantially from time to time.

Fig. 2 illustrates an inventory pattern with random demand and lead time patterns. The inventory level decreases according to the random de- mand. When a predetermined level, so called reorder point has been reached at time T.,, an order is made. Ordered items are received after a lead time at time T₂ and the inventory level goes high. During the lead time the inventory level does not reach zero. Next time at time T₃ reorder is made again. But now, due to the unexpected demand and the lead time variation, the stock becomes empty before the ordered items are received at time T₄.

The demand uncertainty is reflected in forecasting, which most often is extremely difficult. At least when lead times for components are long and thus have to be ordered long before usage and demand patterns are uncertain, forecasting usually is harder and errors get larger. Normally forecast er- rors increase more than proportionally to the forecast time period.

When planning safety stock levels historical performance data should be studied. The likelihood of stock-out and demand potential has to be determined. Also a policy decision concerning stock-out protection has to be decided on. There are two basic ways to protect oneself against uncertainty. One is to specify a quantity of safety stock. The other possibility, safety time, plans order releases earlier than indicated by the requirements plan and schedules the receipt earlier than the required due date.

If a total optimum of the inventory is the target, order quantities, safety stocks, and safety times should be optimized simultaneously. The lowest cost should be achieved when both safety stocks and safety times are used at the same time to cover different kinds of uncertainties.

None of the methods known in the art carries out the optimization task simultaneously taking into account order quantities, safety stocks, and safety times. In addition, the known methods using safety stocks are static because the safety stock level is kept totally or nearly constant during successive order periods.

Summary of the invention

The objective of the present invention is to accomplish a dynamic method of calculating the order quantities simultaneously taking into account safety stocks and safety times. A specified service level with the minimum possible cost taking into account dozens of influencing factors should be obtained.

The objective is achieved by calculating item by item an order quantity, a safety stock and safety time. In calculating the safety stock of an item into consideration are taken uncertainties in demand forecasts, quantities, and lead times. An effective safety stock is obtained by summing a forecast based safety stock which takes into account uncertainties in forecasts, and a quantity based safety stock which takes into consideration the histori- cal knowledge of the amount of the received orders that might have contained more or less units than ordered. In addition, variations in lead times are taken into account by determining a item specific safety time that has to be subtracted from the optimum order receipt date.

The invented method uses as input wide item relating input data in- eluding historical data, present day data and demand forecast, among others. Historical data contain knowledge of actual realized production or stock usage, knowledge of forecast product quantities and their lead times from order to receipt. Present day data contains different type of costs relating to the item. Forecast includes evaluation of production amount or stock usage in a given time period in the future. All data which are needed in the present invention should be retrievable from an existent ERP (Enterprise Resource Planning) system.

In the beginning the method determines a plurality of deviations related to forecasts. In addition, a first correction factor and a second correc- tion factor of a forecast based safety stock are calculated. These operations are common to all items being considered and operations are carried out only once.

It might also be possible to perform the forecast deviation calculations as item specific if historical forecasts are saved in the ERP system. Item specific calculations start by examining the type of the item being considered is examined. If the item belongs to class A, the order quantity of the item is calculated using the Wagner-Whitin algorithm. If the item does not belong to class A, the order quantity is calculated using the Wilson EOQ formula. After the order quantity has been obtained, a forecast based safety stock, a quantity based safety stock, and safety time will be calculated. Values of the safety stocks are corrected with the correction factors.

After calculations for all items have been executed, the method gives output data which include order quantity, requirement date, the effec- tive safety stock and safety time.

Brief description of the drawings

The features of the present invention will be more readily apparent from the following detailed description and drawings of illustrative embodi- ments of the invention in which:

Figure 1 visualizes the thought behind EOQ;

Figure 2 shows an inventory pattern with random demand and random lead times; Figure 3 shows the main blocks in the invented system; Figure 4 is a flow chart showing first part of steps used in the optimization process; Figure 5 illustrates consolidation; Figures 6A-C depict meaning of FETS;

Figure 7 is a flow chart showing second part of steps used in the optimiza- tion process; Figure 8 illustrates the difference between straight-line and accelerated suppression that is used when correction factor 2 is calculated;

Figure 9 illustrates behavior of an inventory when prior art method is used and when the invented method is used, and Figure 10 shows the environment to which the invention is applied, and

Detailed description of the preferred embodiment

Production industry that manufactures goods in large scale, wholesale and resale business most commonly uses some kind of information system. The systems are also called ERP (Enterprise Resource Planning) systems. A widely known and used information system is called SAP® R/3 (SAP, Systems, Applications, and Products in Data Processing) which also is the exemplary system in this description. Henceforward, it is assumed that all input data which the inventory optimization method needs is obtained from an information system like SAP R/3.

FIG. 10 shows the environment to which the invented system is applied. ERP system 100 produces wide amount of item related data which serve as input data to the invented system. Data produced by the ERP which is necessary to the invented system can be stored on floppy disk 101 which will then be inserted to separate computer 102. The computer can also be integrated into the ERP whereupon data can be retrieved directly via a bus. The method which produces effective safety stocks of items is performed on computer 102. The method will be now described in detail.

FIG. 3 depicts the main calculation blocks used in the method. All data which is necessary is obtained from the ERP system. Depending on the type of an item, order quantity of an item is calculated either within Wagner- Whitin algorithm in block 34 or with Wilson EOQ formula in block 35. Thereafter, two different item specific safety stocks are calculated, namely forecast based safety stock 31 and quantity based safety stock 32. The order quantity obtained either from block 34 or block 35 is used in safety stock calculations. In addition, a lead time based safety time 33 is calculated, calculations being based on similar equations as used in calculation of the safety stocks. The lead time based safety time can in some conditions be expressed as an item specific safety stock based on a lead time. Values of the obtained safety stocks are first corrected with correction factors in block 37 and then the corrected safety stock values are summed in block 36 to form an effective safety stock of an item.

Generally, safety stock can be established based on several factors, but the most frequently used factor is the demand service level. The demand service level, also called the fill rate, is the percentage of items that are available when demanded.

Proceeding steps of the method in accordance with the preferred embodiment of the invention will now be described in detail.

Preliminary calculations

FIG. 4 is a flow chart showing first steps used in the optimization process. If historical forecasts are not saved in the ERP system i.e. historical forecasts are not available, these steps are performed only once during the optimization procedure and they are common to all the items to be handled in the optimization process. Alternatively steps 42, 43, and 44, i.e. the forecast deviation calculations can be performed as item specific if historical forecasts are saved in the ERP system. Then computations are performed on stage A of FIG. 5. The process operating according to the method can be started anytime the user wants, once a day, once a week, for example. Starting time can be preset wherein the program itself checks the starting time. In the following explanation it is assumed that historical forecasts are not available so that forecast deviation calculations are carried out as shown in FIG. 4. In the beginning of the process all data required is collected, stage

41. Some data is stored in a storage of the optimization system. Using this data as input to external information system 410 all data required in calculations are fetched therefrom. Hence, initial inputs from the optimization system to the information system 410 are the item codes, the finished product codes, and the date ranges used in error calculations.

The item codes are component codes for which calculations are desired. The item code is used as a key to collect item specific information from the information system 410 such as the unit price, the currency of the unit price, the lead time, the safety stock level, the stock level, the forecast demand, the units that are on order, and different error distributions. Codes of the finished products are required inputs for the collection of actual production information and product forecast information. The actual production data as well as the product forecasts are used to calculate forecast errors that are required in safety stock calculations. The date range specifies the number of periods that are included in forecast, quantity, and lead time error calculations. These calculations are required in safety stock and safety time calculations.

Reference is still made to FIG. 4. In stage 42 product forecast deviations are calculated. Deviations to be calculated are mean absolute de- viation of forecast MAD_F and time based mean absolute deviation of forecast TBM_F.

Depending on the features of the used ERP system, the forecast error can be calculated as item by item calculation.

Most often demand is forecast and forecast errors can be incurred in the determination of safety stocks. The required safety stock level depends on the accuracy of the forecasting model. When forecast errors are small, less safety stock is required than when errors are considerable. A commonly used measure of forecasting accuracy is the mean absolute deviation, MAD. In this context the determined MAD_F is one factor in safety stock calculations. The MAD_F is calculated according to formula (2)

where MAD_F = mean absolute deviation in forecast, Ui = forecast or average demand in period i X; = actual demand in period i n = sample size.

In calculating MAD_F for the forecast based safety stock the sample size refers to the amount of historical data which is available and used. The value on n is >1. To ensure that safety stocks remain consistent with demand variations, time based mean absolute deviation, TBM can be used. The formula for determining TBM_F is expressed in equation (3)

where TBM_F = time based mean absolute deviation of forecast, u, = forecast or average demand in period i, x, = actual demand in period, n = sample size

By calculating deviations in stage 42 the amount of every type produced on the last day is calculated first. Then daily actual production of end products is turned to weekly production and daily forecasts are turned to weekly. This is required to be able to use either daily or weekly deviations as a basis for the forecast based safety stock calculations. When actual daily production is added to a certain week, only full weeks are included.

Safety stock calculations for items that can be received in intervals of less than a week use daily deviations. Calculations for other items use the weekly deviations. Only the latest forecasts and actual production figures are taken from information system 410 in stage 41. Older information is stored in the optimization system. The calculations are performed based on forecast and actual data for all consolidation codes on both daily and weekly level. The date range of the date to be used, i.e., the sample size can be specified by the user. The less data is used, the faster the calculations react to changes in the environment, but also the reliability of the data suffers.

Consolidation codes are needed for combining forecasts and actual usage for finished products to get appropriate data to determine MAD_F and TBM_F for a certain component. A component might be used in for instance six different end products. Thus, the forecast and actual figures of all those end products have to be included in the calculations to obtain the appropriate deviations for the component question. Consolidation has to be done if historical material demands are erased from the information system and direct historical material usage and forecast cannot be obtained.

An example of a consolidation code system needed for the calcula- tions is presented in FIG. 5. In the column left there is a list of different end products. In the upper row there is a list of consolidation codes. For instance an item having the consolidation code AX is needed in assembling end products AX1 , AX2, and AX3. Consolidation code is AX tells that the data of these product types should be included in the calculations of the consolidation code in question. Hence, the numbers in the table are multipliers. The calculations of MAD_F and TBM_F> for every consolidation code takes place only once every time the optimization program is started. The basic assumption up to here has been that the set of values used when determining safety stocks are normally distributed. That is why absolute values are used when calculating MAD_F and TBM_F. However, the approach is valid only when historical forecast approximates the mean average or trend line of actual demand. This is most often not the case and safety stock amounts being calculated as will be explained later explained need to be adjusted because of these on average too small or large forecasts. Adjustment is made with correction factor 1 and correction factor 2.

Safety stock calculations which will be described later in this application, use statistical data to formulate inventory policies. In practice, only sample estimates of these variables are available. The calculated parameters, as MAD for instance, are subject to sampling variation. Safety stock calculations assume a normally distributed set of values. It has commonly been assumed that the true mean of demand is known. However, these parameters are seldom known and are estimated. The use of sample values may lower the actual service level from the theoretical target service level. Due to this a sample size based correction factor should be used. Henceforward, the correction factor is named as correction factor 1.

Correction factor 1 can be calculated already in stage 43, FIG. 4, although it will not be needed until the safety stock value has been calcu- lated. The formula for correction factor 1 is given in following equation (4) and it applies to correct sampling variation for forecast and lead time deviations.

correction factor 1 = I+- (4)

where n = sample size

The second correction factor for correcting the safety stock values is also needed. Correction factor 2 is calculated in stage 44, FIG. 4, although it will not be needed until the safety stock value has been calculated as will be described later. Before being able to determine the value of correction factor 2, a forecast error tracking signal FETS has to be calculated.

The degree and bias of accumulated forecast error can be determined by FETS the formula of which is presented in equation (5).

where FETS = degree and bias of forecast error, u, = forecast or average demand on period i, x, = actual demand in period i, n = sample size, MAD_F = mean absolute deviation of forecast.

FETS is a close relative to the tracking signal presented in many literature sources. The basic tracking signal is cumulative and may grow without limit. The benefit with FETS is that it gives an average error that can be compared to a FETS of an other product directly even if forecast intervals and calculation periods are different. The formula considers the sign of the error, as positive and negative individual errors may cancel each other out over time and expresses the relative magnitude and bias of the error in values between -1.0 and +1.0.

The formula 5 changes slightly when time-based mean absolute deviation TBM_F is used and is expressed in equation 6.

where FETS = degree and bias of forecast error, u, = forecast or average demand in period i, x, = actual demand in period i, n = sample size,

TBM_F = time based mean absolute deviation of forecast. Meaning of FETS is shown in FIGs 6A, 6B, and 6C.

FIG. 6A shows a case where FETS is approximately zero. Average actual demand and average forecast are approximately the same.

FIG. 6B shows a case where FETS is less than zero. It portrays conservative forecasting. A negative FETS indicates that forecasts are consistently below actual demand. Here safety stock is truly needed. Forecasts should be adjusted to compensate for this bias and safety stock levels ree- valuated.

FIG. 6C shows a case where FETS is positive. A positive FETS in- dicates that forecasts are consistently greater than actual demand. Forecasts are overoptimistic and actual demand is consistently less than forecast levels. In this case a lesser level of safety stock is required.

Effect of FETS will be suppressed with correction factor 2 which is derived simply from FETS. In circumstances like in FIG. 6C, correction factor 2 is necessary to damp calculation of safety stock levels. Correction factor 2 is calculated with following equations 7:

CorrectionFactorl = 1 - FETS (FETS > 0) (7) straight - line

CorrectionFactorl = 1 - FETS (FETS > 0) accelerated

where Correction Factor 2_{staιght lιne} = straight line suppression factor, Correction Factor 2_acceι_erated = accelerated suppression factor,

Correction factor 2 is applied as an extra multiplier in safety stock calculations when FETS is greater than zero. It is a matter of personal choice which formula, straight-line or accelerated, to use. There is no right or wrong approach, it depends on how conservative one wishes to be with inventory.

The difference between straight-line and accelerated suppression is visualized in FIG. 8.

Calculating order quantity, safety stock and safety time

After the before described method steps, which are carried out only once during the optimization process and which are common to all the following steps, have been accomplished, item specific calculations will be started. It shall be stressed that the above described forecast deviation cal- culations can, depending on the abilities of the information used system, be determined as item specific.

FIG. 7 shows steps how to determine the order quantity and the safety stock for each item being considered. It should be noted that if histori- cal forecasts are available, the deviation calculations and the correction factor calculations are performed as item specific in stage A of fig. 7 and not common to all items as shown in fig. 4 However, in the following explanation it is assumed that those calculations are performed as in FIG. 4 and not on stage A of fig. 7.. After an item has been taken for processing, stage 700, the class of the item is checked, stage 701. Typically 80 percent of a company's cost volume item usage is accounted for by 20 percent of all items. This 20 percent of the items are beforehand classified to belong to class A. The rest of the items belong to the class B or class C. If the item in question belongs to class A, the order quantity is calculated with the Wagner-Whitin optimization algorithm, stage 702. If the item belongs to class B or class C, the order quantity is calculated with the EOQ formula, stage 703. An inventive feature of the present invention is to apply the rather complex but good results yielding Wagner-Whithin optimization algorithm to relatively small but costly number of the items whereas majority but less expansive number of the items are processed with the fast but less accurate results yielding EOQ formula.

When the order quantity of the item has been calculated either with the Wagner-Whithin optimization algorithm or with the EOQ formula, prelimi- nary calculations for calculating the forecast based safety stock, the quantity based safety stock, and lead time based safety time start.

In case forecast deviations are treated on the item level and therefore have not been calculated as preliminary calculations, they will be determined at this point. The equations to be used are exactly the same as equa- tions (2) and (3) presented before. Also equations for correction factor 1 (4), FETS (5) and (6), and correction factor 2 (7) are the same.

When safety stock and safety time preliminary calculations are considered there are several similarities between the calculation of forecast based, quantity based, and lead time based safety. Formulas for the devia- tion and correction factor 1 are the same for all safety calculations. Formulas for correction factor 2 are basically the same, only the sign in the formulas varies. However, for better understanding of the safety calculations they are described independently.

Firstly, calculating the forecast based safety stock is explained. The forecast based safety stock is calculated in stage 710 according to the fol- lowing equation (8).

SS , = Z_F x ₂ x TBM_F x u _{+ J} x Jm_leadnme (8)

where SS_t = safety stock for period t,

Z_F= the value corresponding to the value of E_F(Z_F), TBM_F = time based mean absolute deviation, which is calculated in stage 42, u_t+1 = forecast demand of the period to be protected, ^m _{LEAD TIME} ⁼ average lead time expressed in as a multiple of the forecast interval.

The expression u_t+1 in the equation representing the forecast period following the period t for which the safety stock is being determined, is used to ensure that the safety stock which exists at the end of each future planning period t is adequate to cover forecast of the next following period. A period that has forecast of zero, should be excluded from calculations. On the other hand, if the actual demand in some period is zero, which leads to a TBM of one, the period's TBM should be included in calculations.

Equation (8) contains a factor Z_F, which is obtained from a table of standard normal distribution probabilities. Before being able to obtain the Z_F value, the value of the service function, E_F(Z_F), has to be calculated for the desired service level. Calculation of E_F(Z_F) is carried out with following equa- tion (9).

where SL_D = demand service level required,

OQ = order quantity, which is calculated earlier in stage 702 or 703, MAD_F = mean absolute deviation in forecast, which is calculated in stage 42.

A few values of a table of standard normal distribution probabilities is presented in table 1.

Table 1. Some Z values for different values of the E(Z) function

The formula (8) used in calculation of the forecast based safety stock value does not take into consideration possible error factors caused by sample size and forecast errors. That is why the calculated safety stock value is to be corrected in stage 712. Correction is made by applying to the correction factor 1 and correction factor 2 to the result of said formula. Correction factors were previously calculated in stage 43 and stage 44, FIG. 4. In addition, a user can affect the safety stock value by setting a value for a criticality factor K.

Corrected safety stock value is obtained from following equation (10).

CorrectedSS f , = K x CorrectionFactorl x CorrectionFactorl x SS _ (10)

^F-' F, t

where K = user defined criticality factor correction factor 1 = sample size based correction factor, correction factor 2 = error tracking signal based suppression factor Next, calculating the quantity based safety stock is explained. Reference is still made to FIG. 7.

When the order quantity of the item has been calculated either with the Wagner-Whithin optimization algorithm or with the EOQ formula, preliminary calculations for calculating the quantity based safety stock start. They begin by calculating mean absolute deviation MAD_Q and time based deviation TBM_Q for an error distribution received from the company information system, stage 704 The equations are similar to those used in calculating forecast deviations. Hence, MAD_Q is obtained from the following equation (11):

∑ |»,

MAD = — — (1 1 ) Q n

where MAD_Q = mean absolute deviation of order quantity, u, = ordered quantity in period i, x, = actual number in period i, n = sample size.

TBM_Q is obtained from the following equation (12): n

Σ

TBM = (12)

where TBM_Q = time based mean absolute deviation of ordered quantity, u, =ordered quantity in period i, x, = actual number in period i, n = sample size.

After resolving MAD_Q and TBM_Q, the first correction factor of quantity based safety stock is calculated in stage 706, FIG.7. Equation is the same as equation (4) used in forecast calculation in stage 43. The first cor- rection factor is used to correct effect of the not reliable sample size. The second correction factor of the quantity based safety stock is calculated in stage 708. First, quantity error tracking signal QETS is calculated according to equation 13:

where QETS = degree and bias of error in ordered quantity, u, =ordered quantity in period i, x, = actual number in period i, n = sample size, TBM_Q = time based mean absolute deviation of ordered quantity.

After resolving QETS, the second correction factor of the quantity based safety stock can be calculated from equations 14:

CorrectionFactorl = 1 + QETS (QETS < 0) (14) straight - line

CorrectionFactorl accelerated = 1 - J V I QETS I I (QETS < 0)

where Correction Factor 2_staιght.|_ine = straight line suppression factor, Correction Factor 2_accelerated = accelerated suppression factor,

Now the value of the uncorrected quantity based safety stock SS_{Q t} can be calculated in stage 711. Equation 15 used is near the same as previous equation 8:

SS_aι = Z_Q jy₂ x TBM_Q x u_{ι + l} x m_kadlme (15)

where Z_Q= the value corresponding to the value of E_Q(Z_Q),

TBM_Q = time based mean absolute deviation, which is calculated in stage 704,

MAD_Q = mean absolute deviation, which is calculated in stage 706, u_t+1 = forecast demand of the period protected, ^m _{LEAD TIME} ⁼ average lead time expressed in as a multiple of the forecast interval.

Before applying calculated factors to equation 15, factor Z_Q must be resolved from the service function E_Q(Z_Q), which is the same as previous equation (9). Description of resolving Z_Q can therefore be omitted.

The formula (15) used in calculation of the quantity based safety stock value does not take into consideration possible error factors caused by sample size and errors in ordered quantity. That's why the calculated safety stock value is to be corrected, stage 714. Correction is made by applying to the correction factor 1 and correction factor 2 to the result of said formula. Correction factors were previously calculated in stage 706 and stage 708, FIG. 7. In addition, a user can affect the safety stock value by setting a value for a criticality factor K.

The corrected quantity based safety stock value is obtained from following equation (16).

CorrectedSS = K x CorrectionFactor l x CorrectionFactorl x SS (16)

^Q Q, t

Finally, determination of lead time based safety time will be described. Safety time is needed to cover risks resulting from bad delivery performance, i.e., late deliveries. Lead time based safety time calculations are in many ways simpler and also quite different from F and Q calculations. Mean absolute deviation MAD for lead time variation and lead time error tracking signal LETS is calculated from item specific lead time error distributions or lists of agreed and actual delivery dates. A lead time error distribution tells how many deliveries have come on time, how many have been one day late and so on.

The service function is not needed to calculate the service factor. The service factor is calculated through a normal distribution function available in known spread sheet programs. Hereafter the quantity based suppression factor and sample size based suppression factor are calculated Reference is still made to FIG. 7. When the order quantity of the item has been calculated either with the Wagner-Whithin optimization algorithm in stage 702 or with the EOQ formula in stage 703, preliminary calculations for calculating the lead time based safety time start. They begin by cal- culating mean absolute deviation MAD_L in stage 705. The equation (17) used for resolving MAD_L is as follows:

where MAD_L = mean absolute deviation for lead time variation, u, = agreed delivery date in period i x, = actual delivery date in period i n = sample size.

Then, first correction factor of lead time is calculated in stage 705. The equation used is the same as equation (4) which is used in calculating first correction factor of quantity based safety stock in stage 706.

The second correction factor of lead time is calculated in stage 707. Firstly, error tracking signal LETS is to be calculated according to equation (18):

LETS = AAJLA (18)

MAD L.

where u, =agreed in period i, x, = actual lead time in period i, n = sample size,

MAD_L = mean absolute deviation of lead time, which was calculated in stage 705.

The second correction factor for lead time based safety time can now be determined from equations (19):

CorrectwnFactor2 _t _ _{lme L} = l- LETS (LETS > 0) (19)

CorrectιonFactor2_{accekrale L} = I- -JLETS (LETS > 0)

where Correction Factor 2_staιgh,._{lιne L} = straight line suppression factor, Correction Factor 2_{acceleratecα} = accelerated suppression factor, The above mentioned calculations enable determining the required safety time SS_{L t} in stage 713. The equation (20) used is simpler as those used in stages 711 an 712:

SS_U = Z_L x J ₂ x MAD_L (20)

where Z_Q = the value corresponding to the desired probability of not stocking out, MAD_L= mean absolute deviation for lead time variation.

The corrected safety time can now obtained by using correction factor 1 and correction factor 2 as well as criticality factor K which can be set by a user, stage 717. The corrected lead time based safety time value is obtained from the following equation (21).

CorrectedSS_Ll = K x CorrectionFactorl x CorrectionFactor2 x SS_{L t} (21 )

If for example an item can be delivered only once a week and the calculated safety time is two days, the safety time would have to be rounded to a week. The rounding error is significant and therefore it is more economical to convert the safety time to safety stock in units, stage 718. This is performed by adding the demanded quantities for the two days that have to be protected. This lead time based safety stock then replaces the safety time.

Item specific processing explained before ends by summing the two safety stocks, namely the corrected forecast based safety stock and the corrected quantity based safety stock, stage 715. If the safety time has been converted to lead time based safety stock, it is also added to the effective safety stock. If the user wants to add a fixed managerial safety stock, the user enables it in the same stage. Managerial fixed safety stock refers to situations where sudden changes or anticipated changes in the operation environment, like war, strikes, or natural disasters, can influence the availability and the need of temporary additional buffering is evident. In the following the next item will be examined and the process returns back to stage 701. After all the items have been gone over, the optimization process will be terminated.

The result of the invented method is a file containing items, their order quantities, safety stocks, safety times and order or receipt dates. The file additionally contains a multitude of item specific data that enables the decision maker to track the trend of forecast accuracy and performance of suppliers. Decision makers of a company can now utilize the results as such or the file can be input to the existent information system as shown in FIG.3. FIG. 9 shows how the inventory of a tested item behaved during three and a half months and how the inventory would have behaved if the optimization system would have been used. All data used in testing is real and was obtained from information system SAP R/3. The upper narrow line curve depicts changes of the inventory level when the prior art ordering method was used. Sudden increase of the inventory level means reception of ordered items. Safety stock has been set manually to level 90. The lower thick line curve depicts changes of the inventory level when the invented method was used. Safety stock decreased radically because of the use of safety time. As seen in FIG. 9, level of the safety stock is very low. An im- portant feature is that the level is not static as it is in the prior art system but it varies dynamically in course of time.

The method steps described before are selected only for better understanding of the invention. Its clear for those skilled in the art that the method can be realized in various ways. Safety stock and safety time calcu- lations are based on dynamic principles. The system dynamically determines optimum or economic order quantities, order receipt dates, safety stocks, and safety times This means that safety stocks are flexible when demand levels or the operating environment change. One possibility is to use a spreadsheet program, such as MS Excel ®, for example. The optimization system can be coded as an MS Excel macro. By using a spreadsheet program the optimization system can be built around the idea of a main information sheet and several calculation subsheets.

Claims

1. A method to be performed on a computer for automatically optimizing an inventory consisting of a plurality of items, c h a ra cte rized by steps of: reading into a memory of the computer a) historical data comprising knowledge of actual realized item demand or production, b) historical forecast of item demand or product quantities, c) present day data comprising different type of costs relating to the items, d) lead times of the items from order to receipt, and e) demand forecast comprising evaluation of item demand or production amount in a given time period in the future; computing or reading from the memory an order quantity of an item; computing deviation between demand forecast and actual number; computing a forecast deviation based safety stock of the item based at least on the order quantity of the item, forecast demand of the item, lead time of the item, and the deviation in forecast; computing an effective safety stock comprising at least the forecast based safety stock; and displaying the effective safety stock.

2. A method as in claim 1, further comprising steps of: computing lead time deviation between agreed delivery dates and actual delivery dates; computing a lead time based safety time for the item based on deviation of agreed delivery dates from actual delivery dates so taking into account variations in lead times of the item; outputting the lead time based safety time.

3. A method as in claim 2, wherein the lead time based safety time is converted to a lead time based safety stock and the lead time based safety stock is added to the effective safety stock.

4. A method as in claim 1 or 2, further comprising steps of: computing deviation in quantity between ordered quantity and ac- tual number; computing a quantity based safety stock of the item based at least on the order quantity of the item, forecast demand of the item, average lead time of the item and the deviations in quantity; and adding the quantity based safety stock to the effective safety stock.

5. A method as in claim 1 , wherein the order quantity of at least a part of the items is calculated using the Basic Economic Order Quantity formula known as such.

6. A method as in claims 1 or 5, wherein the order quantity of at least a part of the items is calculated using the dynamic Wagner-Whitin algo- rithm known as such.

7. A method as in claim 1 , wherein the deviation in forecast is mean absolute deviation and is calculated according to the following formula:

where MAD_F = mean absolute deviation in forecast, Xj = actual demand in period i n = sample size, u, = forecast demand in period i

8. A method as in claim 1 , wherein the deviation in forecast is time based mean absolute deviation and is calculated according to the following formula: n Σ

TBM F- =

where TBM_F = time based mean absolute deviation in forecast,

Uj = forecast or average demand in period i,

Xι = actual demand in period i, n = sample size

9. A method as in claim 2, wherein the deviation in lead time is mean absolute deviation and is calculated according to the following formula:

where MAD_L = mean absolute deviation in lead time, x, = actual delivery date in period i, n = sample size, u, = agreed delivery date in period i.

10. A method as in claim 4, wherein the deviation in quantity is mean absolute deviation and is calculated according to the following formula:

∑k - ^χ

MAD„ = — f n

where MAD_Q = mean absolute deviation in quantity, x, = actual number in period i, n = sample size, u, = ordered quantity in period i.

11. A method as in claim 4, wherein the deviation in quantity is time based mean absolute deviation and is calculated according to the following formula: n Σ

!=1

TBM_Q =

where TBM_Q = time based mean absolute deviation in quantity, u, = ordered quantity in period i, x, = actual number in period i, n = sample size

12. A method as in claim 1 , wherein value of the forecast based safety stock is corrected by multiplying with criticality factor K which can be set by a user.

13. A method as in claim 2, wherein value of the lead time based safety time is corrected by multiplying with criticality factor K which can be set by a user.

14. A method as in claim 4, wherein value of the quantity based safety stock is corrected by multiplying with criticality factor K which can be set by a user.

15. A method as in claim 1 , wherein value of the forecast based safety stock is corrected by multiplying with correction factor 1 , which corrects errors caused by sampling variation.

16. A method as in claim 4, wherein value of the quantity based safety stock is corrected by multiplying with correction factor 1 , which corrects errors caused by sampling variation.

17. A method as in claim 2, wherein value of the lead time based safety stock are corrected by multiplying with correction factor 1 , which corrects errors caused by sampling variation.

18. A method as in any one of the preceding claims 15-17, wherein correction factor 1 is calculated according to the formula:

correction factor 1 = .U ⁺ — n

where n = sample size.

19. A method as in claim 1 , wherein value of the forecast based safety stock is corrected by multiplying with correction factor 2, which corrects errors caused by too small or large forecasts on the average.

20. A method as in claim 19, wherein correction factor 2 for the forecast based safety stock is calculated according to the formulae:

CorrectionFactorl = 1 - FETS (FETS > 0) straight - line

CorrectionFactorl = 1 - FETS (FETS > 0) accelerated

where Correction Factor 2_{staιght lιne} = straight line suppression factor, Correction Factor 2_acce(erated = accelerated suppression factor,

where FETS = degree and bias of forecast error, U| = forecast or average demand in period i, x, = actual demand in period i, n = sample size, TBM_F = time based mean absolute deviation of forecast.

21. A method as in claim 2, wherein value of the lead time based safety stock is corrected by multiplying with correction factor 2, which corrects errors caused by too small or large lead times on the average.

22. A method as in claim 21 , wherein correction factor 2 for the lead time based safety stock is calculated according to the formulae:

CorrectionFactor2 = I - LETS (LETS > 0) CorrectionFactorl straight - l ,ine L = 1- LETS ( 'LETS > 0)

where Correction Factor 2_staιght.„_{ne L} = straight line suppression factor,

Correction Factor 2 _{accelerated,!.} ⁼ accelerated suppression factor,

n I U, - X, and LETS = - ι=ι n MAD,

MAD_L = mean absolute deviation of lead time.

23. A method as in claim 4, wherein value of the quantity based safety stock is corrected by multiplying with correction factor 2, which corrects errors caused by too small or large quantities on the average.

24. A method as in claim 23, wherein correction factor 2 for the quantity based safety stock is calculated according to the formulae:

CorrectionF actor 1 1 + QETS (QETS < 0) straight - line

CorrectionFactorl accelerated = 1 - J V I Q ^&ETS I I (Q^ETS < 0)

where Correction Factor 2 staig t-line = straight line suppression factor, Correction Factor 2_accelerated = accelerated suppression factor,

where QETS = degree and bias of error in ordered quantity, U_| =ordered quantity in period i, X| = actual number in period i, n = sample size,

TBM_Q = time based mean absolute deviation of ordered quantity.

25. A method as in claim 2, wherein the lead time based safety time is calculated according to the following formula:.

SS, = Z J^π x MAD _r

where SS_{L t} = lead time based safety time

Z_L = the value corresponding to the desired probability of not stocking out, MAD_L= mean absolute deviation for lead time variation.

26. A method as in claim 1 , wherein the forecast based safety stock is calculated according to the following formula:

^SSF = ^Z _F ^X /2 ^{X TBM}F ^{X U}, ₊ J' lead time

where SS_F = forecast based safety stock for period t,

Z_F = obtained from a table of standard normal distribution probabili- ties,

TBM_F = time based mean absolute deviation of forecast, u_t+1 = forecast demand of the period to be protected, ^m _{EAD TIME} ⁼ average lead time expressed in as a multiple of the forecast interval.

27. A method as in claim 4, wherein the quantity based safety stock is calculated according to the following formula: SS_r = Z x

Q A x TBM x u {•^■

where SS_Q = forecast based of quantity based safety stock for period t,

Z_Q = obtained from a table of standard normal distribution probabilities, TBM_Q = time based mean absolute deviation of forecast or quantity u_t+1 = forecast demand of the period to be protected, ΠD_{LEAD TIME} ⁼ average lead time expressed in as a multiple of the forecast interval.

28. A method as in claims 26 or 27, wherein the factor Z_F and Z_Q corresponds the value of the service function, E_{F Q}(Z_{F Q}), which is calculated according to the following equation

(l - SL_d) x OQ

E (Z ) = -— - ^d ^F'^{Q F}-^Q x MAD

V / F

where SL_D = demand service level required, OQ = order quantity MAD_F= mean absolute deviation in forecast

29. A method as in claims 1 , wherein, due to the lack of historical forecasts, product quantities have been read from the memory and the order quantity of an item has been computed each item is provided with a consolidation code; the forecast and actual figures of all products included in the same code are included in the deviation calculations.

30. A method as in claiml , wherein a fixed managerial safety stock is added to the effective safety stock for taking into account situations where temporary additional buffering is evident.