Easy-to-use inventory management systems for small companies

Easy-to-use inventory small companies

management systems for

W. BRUGGEMAN S. P.S.O.,

State

University

of Ghent,

Belgium

P. VANDENDAELE SOCOMA,

Belgium

Received Revised

June 1982 August 1982

Many small companies. are running their businesses with strongly unbalanced inventories. Since micro-computers have become cheaper these companies now have the opportunity to manage their inventories more efficiently. This paper discusses the various functions of easy-to-use inventory management software for micro-computers. From our experience in implementing these systems in wholesale companies, retail companies and spare-part warehouses we will report on - the link between the inventory management system and the accounting system; - how operations research and inventory models can be applied; - when statistical forecasting is useful and when it is not useful; - the behaviour and the reaction of the software user. We also describe a simple approach to assess the potential ordering, stockholding and stockout cost savings and the service improvement due to scientific inventory control.

1. Introduction: cro-computers

New perspectives in using mi-

Although micro-computers are a product of the recent technological progress in the field of informatics, they penetrate very quickly into the business environment. In more companies they are integrated into the existing MIS and support management decison making. Especially small companies (with less than 50 people and an annual turnover up to 4 million dollar) have identified the potential benefits of micro-computer systems for their decision making. They are easy to use and to handle, they can be used interactively, they are user friendly and modNorth-Holland European Journal 0377-2217/83/$3.00

of Operational

Research

0 1983, Elsevier

14 (1983)

Science

52-58

Publishers

ular, they are easily connectable to larger systems to exchange data, and require a low capital investment. But micro-computers are only micro with regard to their dimension and their price. Their internal architecture, their power and their storage capacity (Winchester hard disc up to 64 Mb) gives them strong capacities and often they can be used as stand alone computers. Most small companies in Belgium starting to use these systems are implementing an accounting system. We can state that up to now micro-computers only have been used for information processing and administration purposes. When inventory control is concerned, existing software systems only take care of the inventory accounting and the inventory administration and not really assist in Inventory Management Decision Making. In this paper we will describe how existing inventory accounting software was linked with a computerized inventory management package. The purpose is also to show how Operations Research models can be used easily on micro-computers,

2. Interactive inventory accounting Before one can think of implementing an inventory management system one has to desgin an inventory accounting system to update physical inventory and the,inventory on order and to keep a statistics history of all items. Using the inventory accounting software on micro-computers, the user can easily transact all inflows and outflows of goods. When a usage or a sales order is processed, an invoice is printed and the outgoing quantities of all items are immediately subtracted from the inventory. The monthly and annual sales (or usage) statistics are updated and the gross margin is calculated on the basis of the actual selling price and the mean buying price. Automatically the accounts receivable and the Value Added Tax accounts are adjusted. When a replenishment order is received from a supplier, the invoice is reg-

B.V. (North-Holland)

W. Bruggeman, Table 1 Description

P. Vandendaele

of an item form

Codification of the item Description Quantity in inventory Minimum stock level Maximum stock level Quantity on order Quantity reserved by the customer In transit quantity Package size (units per package) Minimum order quantity Buying price Mean purchase price Gross margin Monthly sales Yearly sales Supplier codifications Information typical to the Belgian

legislation

istered, the accounts payable account and the inventory accounts (both in units and in monetary value) are updated. These transactions can be done interactively with a response time of less than 3 seconds. At the time of the monthly closing of the accounts the monthly sales totals are transferred to a history-file (which also contains the Lead Times, Ordering Cost, Inventory Holding Cost, Stockout Cost and the Desired Service Level for each item), which can be accessed by the inventory management system (see Section 3) to determine the replenishment policy of the items. At every moment the inventory manager can get a display of - the complete stock-list (in units and in monetary value), - the items on order, with specification of the quantity on order, the quantity reserved by the customers, the quantity on order with the suppliers, the quantities in transit. - the estimate of the total worth of buying. Table 1 shows the information items contained in the item file of the systems. This information can also be displayed in the format of an item form.

3. The inventory management system

/ Easy-to-use

inventory

53

mum stock level for each item. In traditional inventory software packages for micro-computers these parameters have to be determined by the inventory manager and are a manual input to the system. The problem is that many inventory managers of small companies have difficulties to determine these parameters, such that, even after the introduction of the computer, the inventories are still unbalanced, still too much capital is invested in inventory and too many stockouts occur. To facilitate the determination of minimum and maximum inventory levels we have linked the inventory accounting system with an inventory management system (see also Fig. 1). The package is called DIAPRO and computes optimal reorder points and reorder quantities for all items in the inventory information system. The system is executed yearly using the updated sales history files and the actual information of the item file. 3.1. The relevance of reorder point systems It must be stressed that reorder point systems are only valid for single stage inventory management problems when - the usage or demand process is a stochastic process and the demand is not to a large extent known in advance (or is on order), - the lead time cannot be managed by the inventory manager and may also be a stochastic process. These two assumptions mean that reorder point inventory management can be applied to spare parts, service and maintenance products and to independent retail and whole sale warehouses. Reorder points systems should not be used in production environments and in distribution warehouses. In a production environment demand for end products is planned, on order or following a master production schedule, and the requirements for subassemblies, components and raw materials are dependent on the production plan for the end products. Moreover in these systems the lead times can be managed internally. These planning problems should be handled by using a Materials Requirements Planning approach (see

Pll). The inventory item file of the inventory accounting system shows a minimum and a maxi-

Also in distribution chains the demands of different levels of distribution are dependent on each

W. Bruggeman,

SUPPLIEIL FILE

P. Vandendaele

/ Easy -to-use

inventory

.

I

I PumlAslm

I

-r

CUSTOMEI

IHFOUATIOII PIOCSSSIIIG

ACCWllTlllG SYSTEM

Fig.

1. Modules

of the integrated

inventory

management

system

other. Distribution Requirements Planning should be applied here. Although reorder point systems can be easily implemented, our experience in Belgium is that the number of unbalanced spare parts and maintenance inventories is very high and that many small retail and wholesale companies still experience severe inventory control problems. 3.2. The relevant OR models The DIAPRO package is based on four continous review inventory models developed by Hadley and Whitin [9]: (1) inventory model with Poisson demand and backorder possibility, Table

(2) inventory model with Poisson demand and lost sales, (3) inventory model with normally distributed demand and backorder possibility, (4) inventory model with normally distributed demand and lost sales. In these models the reorder point and the reorder quantity are determined by iterative simultaneous optimization. When the inventory is reviewed periodically the models are used heuristically by adding a review period to the lead time. The history files and the item files are merged into a DIAPRO input file containing the following input data for each inventory item: - the item code plus description, - sales history,

2 Optimal policy

Reorder point Order quantity Max. inventory level Exp. number of orders Exp. total cost Service level

per year

9 10 19 2.10 949 1 76

replenishment

Evaluation of the current replenishment policy I 2 9 10.5 33854 49

W. Bruggemun.

P. Vandendaele

- lead time, - actual minimum inventory level (reorder point), - actual maximum inventory level, - purchasing price, - stockoutcost or desired service level, - inventory holding cost percentage, - ordering cost, - packaging quantity, - minimum order quantity, - lost sales/backorder possibility. On the basis of the characteristics of the demand process (Poisson/normal) and the lost sales/backorder situation the program chooses the adequate inventory model and for each item it computes the following output results (see example in Table 2). So, after the reorder point and the order quantity is optimized and evaluated by substituting it into the Hadley-Whitin total cost model, the reorder point and the reorder quantity currently in use is also evaluated by the same cost model and the results are compared. The cost consequences of the optimal policy and the current policy are summed over all items, and the global evaluation of Table 3 is printed out. By its capability to compare optimal and current total costs DIAPRO has been used frequently as a tool for diagnostic analysis of the potential savings of scientific inventory management. Many companies already use some kind of minimum stock level in the warehouse and from the order books one can derive what quantities were ordered on the average. In these cases one can evaluate the replenishment policy existing before the introduction of a scientific inventory control system and compare it with the results of the optimized policy generated by the package. Table 3 shows such an example computed on the basis of a small item sample. This table shows that the current replenishment policy in use for this sample keeps the inventory holding cost too low, leads to an inefficient ordering system (too Table 3 Global cost analysis

Expected Expected Expected Expected Expected

(example

sheet

total ordering cost inventory holding cost total stockout cost number of order per year total cost

for a sample

/ Easy-to-use

55

inoentov

many orders and too high an ordering cost) and too many stockouts. 3.3. The relevance of statistical demand Jbrecclstirlg for inventory control During the last 20 years a wealth of statistical demand forecasting techniques have been published. Brown [5] and Winters [22] have introduced a class of exponential smoothing methods. These methods try to distinguish between the systematic (predictable) pattern and the random fluctuations (unpredictable variation) in time series data by smoothing the observations. Some of the already widely used methods are simple exponential smoothing (for time series with a constant mean), double exponential smoothing (for time series with a linear trend) and the seasonal trend models of Brown [4] and Winters [22] (for time series with trend and/or seasonal effects). In using one of thes forecasting techniques one has to determine the optimal value of the smoothing constant(s). This can be done ‘ex ante’ (before the forecasting process starts) or ‘ex post’ (during the forecasting process). In the ex ante optimization procedure various values of the smoothing constant(s) are tried out by means of simulation on the data-history. The value of the smoothing constant(s) which results in the minimum mean square error is then used for making forecasts. Using the ex post optimization procedure the initial forecast is computed with a smoothing constant equal to 0.1 or 0.2, because these values have been found to provide accurate forecasts in practice. Afterwards the forecast is compared with the real observation and if necessary a monitoring procedure is started to adjust the parameters and improve the response rate of the forecasting system. Monitoring procedures have been proposed by Brown [4,5], Van Dobben De Bruyn [ 181, Chow

of items) Optimal

Current

4823 12852 1952 4 19627

15819 3507 143848 15 163174

56

W. Bruggeman,

P. Vandendaele

[7], Trigg and Leach [ 161, Roberts and Reed [ 141, Montgomery [lo] and Whybark [19]. Applied researchers have expended considerable effort in comparing the forecasting accuracy of different smoothing systems (see Torfin and Hoffman [ 171, Adam, Berthot and Riley [2], Adam [ 11, Whybark [20], Muller Bruggeman et al. [ 121). It is felt that an overall best forecasting strategy does not exist, and that the differences in forecasting accuracy depend upon the demand pattern and the measure of forecasting accuracy used. Since the work of Box and Jenkins [3], the question “which smoothing system is most accurate?” has seemed to be no longer relevant. It is thought that each observed time series is a member of the general class of autoregressive integrated moving average processes (or ARIMA processes) for which a parsimonious model can be identified and estimated such that the mean squared forecasting error is a minimum and the series of forecasting errors is free of autocorrelation. Moreover it can be shown that the exponential smoothing models are equivalent to specific ARIMA-models, such that theoretically exponential smoothing is optimal only for a limited class of stochastic processes, while the Box-Jenkins approach is more powerful and provides accurate forecasts for a wide spectrum of time series. However, in many practical cases the demand time series turn out to be white noise processes: when the autocorrelation function of the demand process is computed no significant autocorrelation coefficients can be shown. When significantly predictable patterns are present, Groff [8] found that in many practical applications the forecasting accuracy of the BoxJenkins method was lower than the accuracy of exponential smoothing methods. These empirical results contradict the existing theoretical evidence, but can be explained as follows. When the Box-Jenkins method is used one assumes implicitly that the observed time series has a consistent auto-correlation structure, or, in other words, is generated by an ARIMA-model with constant parameters. This assumption is only valid when the observed stochastic process is generated by a large number of independent forces. When for example a demand process is generated by a very large number of customers in an atomistic market, one can expect a consistent buying behav-

/ Easy -to - use inventory

ior. Many companies do not operate in an atomistic environment. If only a limited number of forces determines the time series pattern (for example in forecasting problems in an oligopolistic environment) the assumption of consistent autocorrelation structure can hardly be made. In such an environment sophisticated forecasting systems usually fail. It should be noted that until now most researchers have only evaluated forecasting systems on the basis of the accuracy of forecasts (measured by the mean square error). However, when forecasting is used in decision making, forecasting accuracy frequently is not of much interest to the decision maker. For example, in forecasting demand for inventory control the inventory manager is only interested in the cost-effectiveness of the reorder policy, computed on the basis of the demand forecasts. Bruggeman [6] compared the total ordering, inventory holding, and stock-out cost of BoxJenkins forecasting and exponential smoothing in case of demand time series with a consistent autocorrelation structure. Although Box-Jenkins forecasting yielded the lowest mean square error, it led to higher total costs than exponential smoothing models when the demand showed negative serial autocorrelation. In cases with positively autocorrelated demand the Box-Jenkins method had significantly lower total costs. For low value items with low stockout costs the expected cost of the Box-Jenkins method was not significantly different from the cost of exponential smoothing. 3.4. The forecasting

module

in DIAPRO

For many inventory problems in practice where reorder-point systems can be applied no sophisticated demand forecasting techniques should be used. Yearly adjustment of the reorder point and the reorder quantity on the basis of an updated average demand level works well in most cases. We feel that, especially in the field of spare parts and maintenance inventory management, sometimes, too much effort is spent in designing too sophisticated auto-adaptive forecasting systems, making the inventory control system very unstable and less transparent for the system user. For these problems DIAPRO bases its reordering policy on a simple average demand and a standard deviation

W. Bruggeman,

P. Vandendaele

computed by using the demand observations of the last year. Only in retail and whole-sale environments some predictable patterns show up. Most of them are autoregressive in nature or reflect some kind of seasonality. For these situations the forecasting system in DIAPRO can provide the necessary ARIMA-forecasts.

4. Limitations problems

of the system and implementation

Knowing that the information necessary for the inventory management are quite numerous (see Table l), at the beginning, we have been limited by the capacity of the magnetic supports (500 Kb, lMb), but now, with the Winchester hard disk technology, we no longer experience capacity limitations. Nevertheless, our experience has shown that the constraints come from the people who use the system. A good executive can hardly handle more than 5000 items, because of the numerous data available to manage. When the number of items gets larger, the number of people in charge has to be increased, or the number of items managed by the system has to be limited (regarding price, degree of importance,. . . ). We can say that a typical system for a small company manages about: - 1500 customers, - 800 suppliers, - 6000 invoices a year, - 3000 to 4000 items in inventory. The cost of such an installation, hardware and software, ranges from 6000 and 10000 dollar depending on the capacity of the magnetic support. Although in most cases DIAPRO can easily be used and implemented (in most cases it only has to be executed once a yea), many executives have difficulties to define the ordering cost, inventory holding cost, the stockout costs and the service levels. In our experience the consultant has a crucial role to play during the cost estimating process. For example he has to make sure that the estimate of the ordering cost really is a fixed cost per individual order. It is clear that unrealistic cost estimates will produce unrealistic replenishment policies, and will prevent successful implementation.

/ Easy -to - use inventory

51

5. Conclusion We believe that Operations Research has contributed successfully in solving practical single stage inventory management problems. With the break-through of the micro-computer, existing inventory theory is really getting to be successfully applied even in small companies. We feel that the assumptions usually made in developing inventory models (for example: stationarity of the demand distribution) do not restrict too much the practical use of these models in practice and that in many instances too sophisticated a forecasting system is dangerous. Most of the time single stage inventory systems do not show highly and consistently predictable patterns in the demand series. In designing inventory management systems for small companies the main task is to link an inventory accounting system with an inventory reordering package based on the reorderpoint inventory models (see Hadley and Whitin [9]). Only little effort should be spent on the forecasting task. In implementing these systems the analyst should work closely together with the user to determine the ordering cost, the inventory holding cost and the stockout cost correctly. It should be made clear that these costs are real, even if they are not directly visible in the company books. However, statistical inventory control should only be applied on single stage problems. Here, it can contribute a lot to a better balancing of maintenance, spare parts, retail and wholesale inventories. It should not be used in controlling raw materials and components in a multistage production-inventory environment. References [I] [2]

[3] [4] [5] [6]

E. Adam, Individual item forecasting model evaluation, Decision Sci. 4 (1973) 458-469. E.E. Adam, J.M. Berthot and H.E. Riley, Individual item forecasting models: A comparative evaluation based on demand for supplies in a medical complex, Proc. 14th International Conference of the American Productron Inventory Control Society (197 I) 82-90. G.P. Box and G.M. Jenkins, Times Series Analysis Forecasting and Control (Holden-Day, San Francisco, 1970). R.G. Brown, Statistrcal Forecasting for Inventory Control (McGraw-Hill, New York, 1959). R.G. Brown, Smoothing, Forecasting and PredictIon (Prentice-Hall, Englewood Cliffs, NJ, 1962). W. Bruggeman, Cost-effectiveness of Box-Jenkins forecasting for inventory control, in: J.P. Brans, Ed., Opera-

W. Bruggeman,

58

(ions

Research

81

(North-Holland,

Amstedam,

P. Vandendaele 1981)

791-808. [7]

[8]

[9] [lo]

[ 1 lj [ 121

[13]

W.M. Chow, Adaptive control of the exponential smoothing constant, J. Industrial Engrg. 16 (1965) 314-317. G.K. Groff, Empirical comparison of models for shortrange forecasting, Management Sci. 20 (1) (1973) 29-31. G. Hadley and T.M. Whitin, Analaysis of Inoentoty Systems (Prentice-Hall, Englewood Cliffs, NJ, 1963). D.C. Montgomery, Adaptive control of exponential smoothing parameters by evolutionary operation, AIIE Trans. 2 (1970) 268-269. D.C. Montgomery and L.A. Johnson, ForecastIng and Time Series Analysis (McGraw-Hill, New York, 1976). H. Muller, W. Bruggeman, S. De Samblanckx, G. Bruyneel and R. Van De Vloed, Comparison of forecasting techniques by means of simulation methods, Proc. Internatronal S.vmposium and Course Simulation 1975, Zurich, June 23-26 (1975) 415-479. H. Muller, W. Bruggeman and S. De Samblanckx, Forecasting accuracy, cost minimization and investment optimization in inventory management, Seminar “Modeling in Business”, Amsterdam, Jan. 12- 13 (1978) 94- 105.

/ Easy -to

we inventory

[14] SD. Roberts and R. Reed, The development of a selfadaptive forecasting technique, AIZE Trans. I (4) (1969) 314-322. [ 151 D.W. Trigg, Monitoring a forecasting system, Operational Res. Quart. 15 (3) (1964) 271-274. [ 161 D.W. Trigg and A.G. Leach, Exponential smoothing with an adaptive response rate, Operational Rex Quart. 18 (1) (1967) 53-59. [ 171 G. Torfin and T. Hoffmann, Simulation tests of some forecasting techniques. Production and Inventory Management 2nd Qtr. (1968) 71-78. [ 181 C.S. Van Dobben De Bruyn, Prediction by progressive correction, J. Royal Statist. Sot. Ser. B 26 (1) (1964) 113-122. [ 191 C. Whybark, Testing and adaptive inventory control model, Working paper, School of Business Administration, Harvard University, Boston, MA, No. 72-73. [20] C. Whybark, A comparison of adaptive forecasting techniques, Logistics Transportation Rev. 8 (3) 13-26. [21] O.W. Wight, Production and Inventory Management in The Computer Age (CBI, Boston, 1974). [22] P.R. Winters, Forecasting sales by exponentially weighted moving averages, Management Sci. 6 (3) (1960) 324-342.