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  1. 1. Towards the development of an intelligent inventorymanagement system Khairy A.H. Kobbacy University of Salford, Salford, UK Yansong Liang University of Salford, Salford, UKKeywords obviously, he may not be able to solve theInventory control, Expert systems, Introduction problem effectively. It is clear that when aKnowledge-based systems Inventory management is a complex problem manager is faced with an inventory problemAbstract area owing to the diversity of real life and he has an expert available for choosingThis paper is concerned with the situations. Successful inventory manage- the right model then he can be confident thatdevelopment of an intelligent the effort put into analysis will be successful.inventory management system ment requires sophisticated methods to cope The emergence of expert systems has pro-which aims at bridging the sub- with the continuously changing environ-stantial gap between the theory vided a useful approach to solve this problem. ment. Literature is rich with papers aboutand the practice of inventory The current applications of expert systemsmanagement. The proposed sys- independent demand inventory modelling have demonstrated quite successful results intem attempts to achieve this by (Fleming, 1992). These provide a theoretical terms of better decision making (Bramer,providing automatic demand and foundation for the field of inventory man- 1988; Land and Hickman, 1993; Buchanan,lead time pattern identificationand model selection facilities. The agement and makes it one of the most 1986). In order to reap the benefits of thisprocess of demand pattern identi- developed fields of OR. However, the practi- technology some inventory expert systemsfication together with the statisti- cal implementation of inventory models lags have been developed since 1988, to helpcal tests used is discussed. Themodels incorporated cover deter- behind the development of inventory model- manage large-scale inventories (Sinha et al.,ministic demand models including: ling (Silver, 1981). 1989; Parlar, 1989; Hosseini et al., 1988; Luxhojconstant, quasi-constant, trended et al., 1993). These efforts have engendered The discrepancy between theory and prac-and seasonal demand as well as tice of inventory is partly caused by the widespread hopes of effective computer solu-stochastic demand models. Thispaper includes an empirical eva- different goals of academics and practi- tions to inventory problems. However, thereluation of the system on real data tioners (Zanakis et al., 1980). Much of the is still a lot of theoretical and practical workfrom the manufacturing and airline research is aimed at rigorous analysis of necessary in order to achieve this which shows that this underlying equations representing the First, the knowledge bases of these systemssystem can lead to significantsavings in inventory cost. inventory problems and developing mathe- were not fully or properly structured. There matically elegant decision models. This type were no inventory models included in Sinha of theoretical work is most highly valued by et al.s (1989) conceptual system and Parlars the academic community. Therefore, there is (1989) system. Sinha et al. (1989) presented a often less attention given to providing work- conceptual design of an inventory expert able solutions to real problems. On the other system but did not build an actual model hand, inventory managers may not be aware base. The knowledge base in Parlars (1989) of the mechanics and applicability of the system is only a collection of inventory theoretical models. This hinders the practical bibliography to help users to find inventory application of inventory models because an models in papers and books. The inventory understanding of the fundamental structure models built in both of the systems of of complex models is the first step necessary Hosseini et al. (1988) and Luxhoj et al. (1993) to provide a workable solution of the problem were limited to models for constant or being considered. Moreover, the mathemati- stochastic demand. The functions for the cal techniques and other methods are only knowledge-based systems are mainly depen- aids to management decision making. They dent on what knowledge has been built in the cannot replace the judgement of human knowledge base. Therefore, an improper experts. A manager may have several inven- knowledge base will result in poor knowl- tory models available to him, but if he is not edge-based systems (KBS).Integrated Manufacturing sure which is the best one for the situation, Second, all of these published systemsSystems seem to lack the ability to automatically10/6 [1999] 354±366 select suitable inventory models, for exam- The current issue and full text archive of this journal is available at# MCB University Press ple, by analysing historical data. Thus these[ISSN 0957-6061] systems can only make a decision after[ 354 ]
  2. 2. Khairy A.H. Kobbacy and the user has provided all the parametersYansong Liang necessary for selecting models. This makes Outline structure of the proposedTowards the development of inventory expert systeman intelligent inventory the system just like a classification of in-management system ventory models by using computers, or at In general, an expert system is designed toIntegrated Manufacturing best, like the commercial inventory manage- use knowledge and inference procedures toSystems solve problems that are difficult enough to10/6 [1999] 354±366 ment packages. Obviously, if such systems cannot select require significant human expertise for their the appropriate inventory model automati- solutions. It is distinguished from other types cally, then they are also unable to switch to a of computer-based information systems by new model for an item when its demand employing knowledge of the techniques, pattern has changed. This will have severe information, heuristics, models, and pro- drawbacks when managing inventories with blem-solving processes that human experts several thousand items, which is typical in use to solve such problems. There are three both manufacturing and service industries. main phases in developing an expert system: Third, the problem of interfacing such knowledge acquisition, knowledge represen- inventory expert systems with existing tation, and knowledge implementation. The inventory information systems has been methodology of the research presented in largely neglected despite the fact that 90 per this paper is the practical development of the cent of companies (Fleming, 1992) use com- software called knowledge-based inventory puters for inventory management purposes. management system, and its evaluation Finally, these published systems seem to be using real data (Liang, 1997). academic exercises. There are no examples The integration approach, particularly given by any of the authors to show the adapting and incorporating a pattern identi- correctness and efficiency of their systems on fying component and rule base component real data. into a unified system to integrate the data To overcome the drawbacks of the pub- collection, parameter estimation, model se- lished systems and in order to achieve an lection and order decision functions is the efficient knowledge-based inventory system central idea behind the system developed in one should answer the following fundamen- this project. This makes the system more tal questions. applicable because it greatly reduces its First, does the system require responses reliance on the user. Building such an from the user to questions in order to select a efficient knowledge-based inventory system suitable model? Second, how are the para- requires a coherent strategy of combining the meters used to choose suitable models esti- computer technology with quantitative mated? Third, which inventory models methods. should be included in the knowledge base? The structure of the system is outlined in Finally, how should the system communicate Figure 1. The user interface of the system with the user and access other management developed in this study includes a top-level information systems? The responses to these menu (Figure 2), the dialogue boxes, alert questions cannot be made unless a detailed text, confirmation text, and help information study is made of inventory modelling, quan- facilities. The appearance of the user inter- titative forecasting, existing knowledge- face of this system is highly graphical and the based inventory systems, and the tools menus, commands, and dialogue boxes are available to develop a KBS. visually the same as other Windows applica- The main objective of this research is to tions. The data manager manipulates the histor- develop such a system which has an appro- ical demand data and other useful informa- priate knowledge scope and focuses on the tion. The operations of the data manager are interrogation of the historical data rather classified into two categories. The first cate- than on asking the user to describe the gory of commands performs the general system under analysis. In addition, the tools operations on data files such as creating a used to develop the system must be compa- data file, deleting a data file, and renaming a tible with the most popular software to allow data file. The second category of commands the proposed system to communicate with manipulates the records of the data files by other information systems. carrying out the following actions: This study has attempted to address the 1 adding a new item; above questions in order to develop a system 2 modifying an existing item; which can offer a new approach to solving 3 deleting an existing item; and the inventory management problem. 4 displaying an item. [ 355 ]
  3. 3. Khairy A.H. Kobbacy and Figure 1Yansong Liang The outline structure of the proposed systemTowards the development ofan intelligent inventorymanagement systemIntegrated ManufacturingSystems10/6 [1999] 354±366 The data manager is also responsible for points and the foreign exchange rate, can be updating the demand data when new usage highly changeable or difficult to predict data become available. using mathematical methods, but they can be The pattern identifier then analyses the readily known to the inventory managers. historical data to identify the demand pat- Other parameters such as demand and lead terns of inventory items. The output of the time patterns are usually difficult to identify pattern identifier is stored as facts for model without carrying out statistical analysis of selection. The monitor is used to check the historical data. inventory status and generate replenishing The nature of the demand of an independent reports. The inventory monitor can provide demand inventory item can range from being the current status of the inventory of any stable to highly variable. In general, such item and list all items that require replen- demand is influenced by market forces, in the ishment. The model selector chooses a case of final products, or failure patterns, in suitable inventory model based on the user the spare parts case. Many published papers responses and the facts produced by the deal with the classification of inventory pattern identifier. Then the interpreter models rather than demand patterns. Based reports the order decision computed by the on the study of the nature of the demand of calculator. inventory items, a proposed classification of The system includes an extensive help demand patterns of inventory items is given facility and also provides integrated access to in Figure 3. packages such as Excel and Word. The centre Muir (1980) proposed that all inventory part of the system is the pattern identifier items with independent demand can be and the model base which are described in divided into statistically predictable and the following section. unpredictable patterns. We propose the addition of a third category, i.e. the low demand pattern of slow moving items. Pattern identifier and inventory The statistically predictable demand pat- model base terns have relatively smooth and repetitive fluctuations and can be analysed using Pattern identifier statistical forecasting methods. These pat- The selection of policy and hence a model terns of demand may change with time, and that will be employed to achieve successful hence they are further divided into time intelligent inventory management is based dependent and time independent demand on the current values of parameters which patterns. In the former, the type of replen- define the state of the inventory item. Some ishment quantity is dependent on the time of the parameters, such as the discount break when the replenishment decision is made,[ 356 ]
  4. 4. Khairy A.H. Kobbacy and Figure 2Yansong Liang Top-level menu of the user interfaceTowards the development ofan intelligent inventorymanagement systemIntegrated ManufacturingSystems10/6 [1999] 354±366 while it is not the case in the latter. Under seasonal, and seasonal with superimposed the condition of time independent demand, trend. uncertainty may exist. If the demand is The statistically unpredictable demand reasonably stable and can be accurately patterns have sudden fluctuations caused by forecast, then it can be assumed to be lumpy demand. They can be classified into constant. The constant demand is further approximative and non-approximative pat- divided into absolutely constant demand terns. The demand of an item with non- (variation is near to zero) and quasi-constant approximative pattern has severe, but regu- demand (variation is less than a selected lar highs and lows of demand which do not value). In other cases, if there is significant recur at the same time each year but at uncertainty which can be specified by a predictable intervals. The demand of an item theoretical or empirical distribution, the with approximative pattern has severe and demand is referred to as stochastic demand. random highs and lows of demand which do The probability distributions that the system not recur predictably. Conventional fore- can identify are the Poisson and Normal casting techniques, including statistical distributions. Time dependency of demand techniques, are not suitable for dealing with may be caused by seasonal variations, trend these demand patterns. However, they may or both. If a product is at its growth or be approximated by a statistically predict- saturation stage of its life-cycle, then its able pattern within a tolerable range of error. demand will tend to increase or decrease, An inventory item which has low demand, respectively. Therefore, time dependent i.e. a slow-moving item, usually has very few demand is classified into demand with trend, transactions occurring over a reasonable [ 357 ]
  5. 5. Khairy A.H. Kobbacy and Figure 3Yansong Liang Classification of demand patternsTowards the development ofan intelligent inventorymanagement systemIntegrated ManufacturingSystems10/6 [1999] 354±366 historical period. The definition of a slow- If H b 12 …L À 1†, where L is the number of moving item is arbitrary. For example, in seasons, the demand is seasonal; otherwise, this study, if an items annual demand is six the demand has no significant seasonality or less (or less than a given constant) and the (where 12 …L À 1† is Chi-square distribution a demand at each time is one or zero, it is with L±1 degrees of freedom). classified as a slow-moving item. Forecasting demand for a slow-moving item is not an easy Trend test matter. A purely objective estimate of a The non-parametric test for trend can be demand rate is usually not feasible. Instead, constructed using Spearmans rank-order one should take advantage of the subjective correlation coefficient rs. It is defined as knowledge of inventory managers. Pearsons product moment correlation coef- Test process ficient r between the ranks of two variables ti To identify the demand patterns described in and yi, i.e. to replace a sample of pairs of the previous section, the system should have measurements (t1,y1), (t2,y2), ... ... (tn,yn) with the ability to separate seasonal movements their respective pairs of ranks (R(ti ), R(9i)) from the basic demand, if there is any, and (Lewise, 1970). The test statistics are then identify the basic demand pattern. For explained as follows: the non-seasonal demand, the system should Small sample (n 30) be able to identify the stationary, linear or If there are no ties (two or more observations probabilistic demand patterns. A self-expla- exactly equal to each other): natory flow chart for the demand pattern € n analysis process is shown in Figure 4. 6 …R…ti À R…yi ††2 iˆ1 rs ˆ 1 À Seasonal movements test n…n2 À 1† The Kruskal-Wallis Test (Farnum and Stan- Otherwise, if there are ties, then the exact ton, 1989) is adopted for detecting seasonal relation is (Press et al., 1986): movements, which is based on testing the 2 3 € n € m € k rank of the specific seasonal …YiH …t††. The test 1 À n36 Àn …R…ti † À R…yi ††2 ‡ 1 2 …fj3 À fj † ‡ 1 2 3 …gj À gj † iˆ1 jˆ1 jˆ1 statistic is: rs ˆ € m € k ˆ R2 ! …fj3 Àfj † 3 …gj Àgj † 12 i …1 À jˆ1 †…1 À jˆ1 † Hˆ À 3…n ‡ 1† n3 Àn n3 Àn n…n ‡ 1† ni where where fi = the number of ties in the ith group of ni = number of observations in ith season; ties among the R…ti †s; n = total number of specific seasons ( = gi = the number of ties in the ith group of Æni); ties among the R…yi †s; YtH = specific seasonal for time t; m = the number of groups of ties among Ri = ÆRank( Yt H ) ith season. the R…ti †s;[ 358 ]
  6. 6. Khairy A.H. Kobbacy and Figure 4Yansong Liang The flowchart of demand pattern identificationTowards the development ofan intelligent inventorymanagement systemIntegrated ManufacturingSystems10/6 [1999] 354±366 k= the number of groups of ties among the R…yi †s. r U À u Zˆ Y u ˆ 2…n À 2† Y u ˆ 16n À 29 Large sample (n 30) u 3 90 rs À rs 1 Zˆ Y where rs ˆ 0Y and rs ˆ p X If jZj b Za2 , the demand is not random, rs nÀ1 otherwise, the demand is random. For small samples, if jrs j b ra2 the demand has a trend; otherwise, and for large samples Identification of probability distribution Under stochastic condition, we need to iden- if jZj b Za2 , the demand has no trend. If demand is found to be increasing (or tify a suitable probability distribution for decreasing), then the parameters of the linear demand. As mentioned above, two distribu- statistical model are estimated using the tions can be identified by the system, i.e. standard least squares method (Lingren, the normal distribution and Poisson 1976). distribution. To test the appropriateness of using the Poisson distribution to describe the demand Test for randomness pattern for large samples, the modified The turning points test (Farnum and Stanton Pearsons Chi-square (Lingren, 1976) statistic 1989) is used to check whether the demand is used, i.e. pattern is random or not. The turning point ˆ ‰fi À n%i …†Š2 m ” in a time series is a point where the series 12 ˆ ” n%i …† iˆ1 changes direction. Each turning point repre- sents either a local peak or local trough. This and the statistic method is based on the premises that a 1 ˆ fj m 2 trended or positively autocorrelated series 12 ˆ À nX ” n jˆ1 %j …† should have fewer turning points than a random one and a negatively autocorrelated is used for the cases of small samples (n 30). series should have more. If the series is Where stands for the probability distri- actually a random series, the sampling dis- ” bution parameter to be tested, is an tribution of the number of turning points U is estimate of obtained from the sample, %i() approximately normal for even moderate is the probability of category i if the as- numbers of observations (n ! 10), i.e. ” sumption that = is true and m is the [ 359 ]
  7. 7. Khairy A.H. Kobbacy and number of categories of sample which is used. Otherwise, the Kolmogorov-SmirnovYansong Liang obtained using a rule of thumb, say, the statistic is used to test the goodness of fit ofTowards the development of sample size n is four or five times m. the data to the normal distribution, and thean intelligent inventorymanagement system If 12 1a2 , then reject the suggested modified Pearsons Chi-square statistic to testIntegrated Manufacturing distribution; otherwise accept the suggested the goodness of fit to the Poisson distribution.Systems distribution. If both tests were negative, then an empirical10/6 [1999] 354±366 To test the appropriateness of using the distribution can be used. normal distribution to describe the demand The subjective method used to estimate the pattern the Kolmogorov-Smirnov statistic Dn lead time is based on Bayes theorem. Basi- (Lewise, 1970) is used: cally, if we use a number of experts to give Dn ˆ sup jFn …x† À F…x†j their opinions about the number of the lead all x times that fall within a given interval, then using the property of the Dirichlet distribu- where F(x) is the suggested distribution tion (Kendall and Stuart, 1977) the frequency function and Fn(x) is the sample cumulative of the lead time in the ith interval can be frequency. If Dn K (reject limit) reject the obtained (Liang, 1997). suggested distribution; otherwise, accept the suggested distribution. In selecting the methods for the statistical tests discussed above, the following consid- Inventory model base erations have been taken into account. First, From the practical point of view, a good nonparametric methods are most preferred inventory model should feature: because we cannot assume the kind of . the analysis process of obtaining the demand that an item has before the testing is model is straightforward and easy to carried out. Second, the methods with fewer understand; assumptions are selected because more re- . the ``how many and when to order strictions tend to limit the applicability of the decisions made by the model do not methods. Finally, the selected methods must include complicated algorithms; be suitable for programming because they . the model has few restrictions and can will be incorporated into a computerised cope with a wide range of inventory system. problems; and The mean and variance of an items . the application of the model will lead to demand, that are used in the above tests, efficient inventory management and sig- were estimated from the past n demand nificant cost savings. In what follows, the values, where n is decided by the user. The models included in the systems knowl- period of time over which these observations edge base are discussed. are made is obviously dependent on the frequency of saving the demand data. When Models for constant demand new data become available, old values are The constant inventory problems are char- discarded, e.g. as in moving average calcula- acterised by the features that both the tions. The frequency of updating demand demand and lead time patterns are known pattern identification and the impact of with certainty and stay constant in the changing the significance levels of the above future, and the ordering cost and holding cost statistical tests are discussed later. are constant. Figure 5 illustrates the possible Identifying lead time pattern types of the constant demand inventory Most inventory items have a lead time models. In this Figure, ``Q1-Q12 refers to a between placing and receiving an order. The variety of the economic order quantity mod- method used in this system depends on the els which are detailed in Liang (1997). The availability of data. If data are available, then factors which affect model selection for items a statistical method can be used. But if data with constant demand include: whether are not available, as is the case in many shortage is allowed, presence and types of practical situations, then a subjective unit price discount, and supply rate. In the method is used. case of back ordering, there is a cost of The statistical methods used here are shortage which is proportional to the quan- similar to, but simpler than, the methods used tity and the time of delivery. with demand identification. The lead time pattern is classified into constant and sto- Models for probabilistic demand chastic. Thus the process of pattern identifi- The probabilistic inventory problems include cation starts with run test to decide whether the cases of constant demand with probabil- the lead time is constant or stochastic. If the istic lead time, probabilistic demand with lead time is constant, then its average value is constant lead time, and probabilistic demand[ 360 ]
  8. 8. Khairy A.H. Kobbacy and Figure 5Yansong Liang Model tree of constant demand inventoriesTowards the development ofan intelligent inventorymanagement systemIntegrated ManufacturingSystems10/6 [1999] 354±366 with probabilistic lead time. There are sev- Models for seasonal demand eral inventory policies for items with prob- For the cases of seasonal variation based on abilistic demand that are well documented in constant basic demand, the seasonal demand the literature (Peterson and Silver, 1979). can be described as a time-independent con- Among the continuous review policies which stant rate plus a time-dependent seasonal suit the computerised inventory systems, the movement. If a year is divided into equal (s, S) is our policy of choice which is intervals according to the length of season, frequently used in practice (Archibald and then the demand over each interval equals Silver, 1978) (whenever inventory reaches s the sum of the constant demand and seasonal or lower, inventory is topped up to level S). movement over the interval. This converts The computational details of implementing the problem into deterministic time-varying this model in the expert system can be found demand inventory problems which can be in Liang (1997). solved using Silver and Meals (1973) heur- istic. This heuristic can also cope with the future fluctuation of demand in each period Models for items with linear demand within the planning horizon (in fact, this Mitras method (Mitra et al., 1984) for items heuristic does need an ending point). In with linear demand has been selected in this addition, the use of Silver and Meals heur- study. It has several advantages, including its istic can result in a low average cost penalty straightforward procedure and the feature of around 0.4 per cent compared with the that replenishments are made at equal inter- optimal algorithm (Tuite and Anderson, 1968). vals makes the model much easier to admin- For the cases of seasonal variation based ister. on a linear trend demand, the demand This method is equally applicable to the consists of a basic linear trend and seasonal negative trend where analytical methods are movement. Thus the replenishment decision not presently available and can be smoothly transferred from linear demand to steady is made following two stages. First, to decide demand to deal with the cases where the the replenishment interval T of the basic demand may become steady after a period of component as the basis of reorder interval; increase (or decrease). Moreover this model then add the seasonal movement for this can be used to estimate the exact amount to interval. Thus the problem can be solved by cover the demand over a period to deal with deciding the replenishment quantity for each the items with negative trends in demand demand component, i.e. the basic component which will not be stored after a certain with linear trend and the seasonal movement period. component during the interval. The first The procedure presented by Mitra et al. component can be determined by Mitra et (1984) modifies the EOQ model to accommo- al.s (1984) model. The seasonal movement date the special cases of increasing and (Qs) within replenishment quantity can be decreasing linear demand patterns. Details of decided in terms of the length of replenish- model implementation in the expert system ment interval T and the length of season l. If can found in Liang (1997). T/l is an integer, the seasonal movement is [ 361 ]
  9. 9. Khairy A.H. Kobbacy and T ˆ l programming was completed (Liang, 1997). InYansong Liang Qs ˆ si X what follows, we discuss sample results fromTowards the development of iˆ1 the system using spare parts inventory dataan intelligent inventorymanagement system supplied by a high-tech manufacturer of If Tal is not an integer, then it is divided into optical fibres and an airline. The dataIntegrated ManufacturingSystems an integer n and a fraction , supplied by the manufacturing company10/6 [1999] 354±366 Tal ˆ n ‡ contained up to three years data of over 2,000 spare part items and the airline data con- and the seasonal movement is decided by tained 24 months data for around 16,000 ˆn items. Qs ˆ si ‡ Á si‡1 X iˆ1 Demand analysis The demand data file is updated by adding Models for low demand items new demand data into the file and shifting For the low demand items, the (s, s + 1) policy the oldest demand data out of the file, so that is adopted, which is a special case of (s, S) the analysis results can reflect the recent policy with S = s + 1 or Q = 1. Therefore, the demand situation. If the analysis results only decision parameter which needs to be show that an items current demand pattern estimated is the reorder point (s) which is has changed, then a different inventory calculated in a similar way to items with model will be automatically selected by the stochastic demand patterns (Liang, 1997). rule base to deal with the new situation. The It has been claimed that in theory the (s,S) impact of the length of history data on policy provides the best management of low pattern identification is discussed later. and intermittent demand items. However, The Appendix shows demand data of five Sani and Kingsman (1997) have shown, based inventory items used as spare parts in the on practical study, that a company may use manufacturing company. Table I shows the any of the inventory models, as none has analysis process of these demand data. At proved to be more successful than the others. each stage of the testing process, both the statistic and critical values for different statistical methods are given by the system. Results This would explain to the user why the test hypothesis was rejected or accepted and how The system was developed by using Visual the analysis results were achieved. The last Basic which is a complete event-driven row of each column contains the final programming language that supports the analysis result of each item. structured programming constructs found in The system can carry out the demand most other modern programming languages. analysis of a large file in a short time period, The Visual Basic programming system which allows the user to repeat the analysis allows users to create applications that fully or experiment. For example, a data file of exploit the graphical user interface (GUI) and 10,000 items can be analysed in less than nine the key features of Microsoft Windows, minutes on a 66MHz 486 PC with 16MB RAM. Using simulation to evaluate the impact of including multiple-document interface the systems ordering decisions on inventory (MDI), object linking and embedding (OLE), cost, Liang (1997) has shown that for a sample dynamic data exchange (DDE), graphics, etc. of 24 items, the cost savings are significant Visual Basic can also be extended by adding (around 23 per cent). Obviously, such savings custom controls and by calling procedures in will depend on the type of inventory and the dynamic-link libraries (DLL). The system management policies employed, but none- development started with the production of theless this figure points at the potential the proposed design, shown in Figure 1, and saving that can be achieved as a result of the design of the application form or main employing the proposed system. menu (Figure 2) which controls the execution of the data manager, pattern identifier, order Sensitivity analysis of pattern decision, and help facilities. The system was identification process developed as several self-contained executa- Table II shows the percentage of items with ble modules. each demand pattern identified for two large The system verification, which ensures inventory data files provided by an airline. that the software correctly implements a The analysis has shown that for the shorter specific function, was carried out using unit period file, about one-third of the items are testing while the system was developed and classified as having unpredictable demand integration testing after the system and hence cannot be modelled. On the other[ 362 ]
  10. 10. Khairy A.H. Kobbacy and hand, more than half the items in the longer also lead to higher inventory costs. DecidingYansong Liang period file were classified as low demand on the frequency of running the patternTowards the development ofan intelligent inventory items. It is obvious that the length of history identifier is an important research areamanagement system data used in the analysis will affect the which is currently being studied. But theIntegrated Manufacturing results and the selected patterns system provides some tools, including theSystems partition of data into different sizes and the10/6 [1999] 354±366 To assess the effect of the length of period of the used history data on pattern identifi- calculation of the number of items which fall cation, a sample of 10,000 items was studied. in each category, which can help the user to The results were compared for using 15 and experiment with different history data 18 months of data with two sets of tests lengths. critical values. Another important factor in running this Table III shows that when the length of system efficiently, is the selection of the history is increased from 15 to 18 months, the significant levels associated with the statis- most significant change is an increase in the tical tests used in pattern identification. number of low demand and quasi-constant Table IV shows the impact of changing the demand items and a drop in the number of significance level for these tests. For exam- constant demand items. This change may be ple, comparing cases one and two indicates specific to this particular data set and it can that a change of the significant level of the be rather difficult to draw general conclu- trend test from 0.05 to 0.1 increases the sions from this behaviour. number of items identified in this category Of direct relevance here is the frequency by 42 per cent. Comparing cases two and of running the demand pattern identification three indicates that reducing the upper limit module. Obviously, if we repeat this pattern of low demand from six to five per year has identification too frequently, there may be no significant influence on the number of frequent changes in the models used in items identified in this category. In general, ordering which may lead to inconsistency within the reasonable range of significant in decisions leading to higher inventory levels variations shown in Table IV, there costs. On the other hand, if the frequency is only minor variation in the number of of updating the patterns was low, then items identified as having a low demand or wrong models may be identified, which can unpredictable demand pattern.Table IProcess of demand analysis (based on the data shown in the Appendix) ItemTest A B C D ESeasonal C = 7.81 C = 7.81 C = 19.68 C = 19.68 C = 19.68 T = 2.83 T = 0.71 T = 11.0 T = 10.19 T = 10.62 R: Reject R: Reject R: Reject R: Reject R: RejectTrend C = 1.34 C = 2.23 C = 1.32 C = 1.32 C = 1.32 T = 1.06 T = 0.73 T = ±0.15 T = 0.71 T = 0.69 R: Reject R: Reject R: Reject R: Reject R: RejectRandomness C = 1.28 C = 1.28 C = 1.28 C = 1.28 C = 1.28 T = 0.39 T = 2.27 T = 0.67 T = 4.87 T = 2.35 R: Accept R: Reject R: Accept R: Reject R: RejectNormal distribution C = 0.29 C = 0.25 T = 46.94 T = 1.91 R: Reject R: RejectPoisson distribution C = 11.07 C = 16.92 T=I T = 4.02 R: Reject R: AcceptEmpirical distribution R: AcceptStrictly constant C = 0.5 C = 0.5 C = 0.5 T = 0.28 T = 1.61 T = 17.94 R: Accept R: Reject R: RejectQuasi-constant C = 1.9 C = 1.9 T = 1.61 T = 17.94 R: Accept R: RejectUnpredictable pattern R: AcceptNotes: C = the critical value; T = the value of the statistic; R = the result of the statistical test [ 363 ]
  11. 11. Khairy A.H. Kobbacy and Table IIYansong Liang Classification of items demand patterns for two large data files (percentages)Towards the development ofan intelligent inventory Patternmanagement system Data file Low demand Seasonal Trend Probabilistic Constant UnpredictableIntegrated ManufacturingSystems File 110/6 [1999] 354±366 24 months 15,731 items 52 0.0 14 8.4 22 3.6 File 2 12 months 5,000 items 24.3 0.0 0.002 12.1 32.2 31.4 Table III The impact of the sample size on the results of pattern identification Low Strictly Quasi- Unpred- Patterns demand Seasonal cons. cons. Trend Normal Poisson Empirical ictable Sample size Critical value a7 0.05 1.0 1.5 0.05 0.05 0.05 0.05 15 months No. of items 3,881 0 3,337 767 592 0 724 432 267 18 months No. of items 4,391 0 2,511 922 690 0 723 485 278 Change 490 0 826 55 98 0 1 53 11 Critical value a7 0.1 1.0 0.5 0.1 0.1 0.1 0.1 15 months No. of items 3,881 0 3,244 619 1,324 0 534 383 277 18 months Critical value 4,391 0 2,247 831 1,340 0 457 382 351 Change 510 0 997 212 16 0 74 1 74 Notes: a = annual demand; = standard deviation Table IV The impact of different significance levels (or critical values) on the results of pattern identification Low Strictly Quasi- Unpred- Patterns demand Seasonal cons. cons. Trend Normal Poisson Empirical ictable Case 1 Critical value a7 0.05 1.0 0.5 0.05 0.05 0.05 0.05 No. of items 5,229 0 1,004 1,101 1,385 0 487 362 441 Case 2 Critical value a7 0.1 1.0 0.5 0.1 0.1 0.1 0.1 No. of items 5,229 0 808 966 1,968 0 300 301 428 Case 3 Critical value a6 0.1 0.1 1.5 0.05 0.05 0.05 0.5 No. of items 5,176 0 0 2,350 1,392 0 483 362 441 Case 4 Critical value a6 0.05 0.1 1.0 0.05 0.05 0.05 0.05 No. of items 5,176 0 0 2,146 1,392 0 483 362 237 Case 5 Critical value a6 0.05 0.5 1.0 0.1 0.1 0.1 0.1 No. of items 5,176 0 844 966 1,984 0 301 301 428 Case 6 Critical value a6 0.1 0.1 1.0 0.1 0.1 0.1 0.1 No. of items 5,176 0 0 1,810 1,984 0 301 301 428 Notes: a = annual demand; = standard deviation or too complex for formal mathematical Conclusions modelling (Kastner, 1984). The complex nat- Generally, practitioners in OR have used ure of the problems encountered today in classical mathematical approaches for mod- business and industry, and the competitive elling and decision making. These provide a environment in which they exist, requires firm theoretical foundation and often lead to the processing of increasing volumes of data optimal solutions. However, real-world pro- in increasingly complex, innovative and blems are often too vague, too ill-structured, efficient ways (Muhanna and Pick, 1994).[ 364 ]
  12. 12. Khairy A.H. Kobbacy and Recent advances in MS/OR and ES techni- Lewise, C.D. (1970), Scientific Inventory Control.Yansong Liang ques provide tools enabling this need to be Butterworth-Heineman, Oxford.Towards the development of Liang, Y. (1997), ``The development of a knowl-an intelligent inventory addressed. Consequently there has been amanagement system marked advance in the use of KBS to support edge-based inventory management system,Integrated Manufacturing management decision making in different PhD thesis, University of Salford.Systems Lingren, B.W. (1976) Statistical Theory, Macmil-10/6 [1999] 354±366 areas of business and industry. This paper lan, Basingstoke. has described a knowledge-based inventory Luxhoj, J.T., Agnihotri, D., Kazunas, S. and management system which is able to obtain Nambiar, S. 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  13. 13. Khairy A.H. Kobbacy andYansong Liang AppendixTowards the development ofan intelligent inventorymanagement system Table AIIntegrated Manufacturing Demand data for spare partsSystems10/6 [1999] 354±366 Item Period A B C D E 1 59 80 6 12 50 2 80 80 11 5 25 3 79 80 4 5 70 4 80 79 10 5 80 5 20 80 8 5 25 6 77 80 7 5 25 7 77 80 3 5 45 8 80 80 4 5 25 9 80 80 7 5 25 10 80 80 7 5 25 11 80 80 8 5 25 12 80 80 7 5 25 13 80 8 5 25 14 51 2 5 35 15 80 7 3 25 16 80 9 5 25 17 80 7 5 25 18 79 4 5 25 19 7 5 25 20 7 5 50 21 5 7 15 22 8 7 25 23 8 7 35 24 5 4 80 25 3 7 21 26 4 11 20 27 3 10 20 28 5 6 40 29 5 6 40 30 2 5 20 31 8 32 2[ 366 ]