1. Towards the development of an intelligent inventory
management system
Khairy A.H. Kobbacy
University of Salford, Salford, UK
Yansong Liang
University of Salford, Salford, UK
Keywords obviously, he may not be able to solve the
Inventory control, Expert systems, Introduction problem effectively. It is clear that when a
Knowledge-based systems
Inventory management is a complex problem manager is faced with an inventory problem
Abstract area owing to the diversity of real life and he has an expert available for choosing
This paper is concerned with the
situations. Successful inventory manage- the right model then he can be confident that
development 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 about
and the practice of inventory The current applications of expert systems
management. The proposed sys- independent demand inventory modelling have demonstrated quite successful results in
tem 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 identification
and model selection facilities. The agement and makes it one of the most 1986). In order to reap the benefits of this
process of demand pattern identi- developed fields of OR. However, the practi- technology some inventory expert systems
fication together with the statisti-
cal implementation of inventory models lags have been developed since 1988, to help
cal tests used is discussed. The
models 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; Luxhoj
constant, 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. This
paper includes an empirical eva- different goals of academics and practi- tions to inventory problems. However, there
luation of the system on real data tioners (Zanakis et al., 1980). Much of the is still a lot of theoretical and practical work
from the manufacturing and airline
research is aimed at rigorous analysis of necessary in order to achieve this goal.
industries which shows that this
underlying equations representing the First, the knowledge bases of these systems
system can lead to significant
savings 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 Parlar's
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 Parlar's (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 systems
Systems seem to lack the ability to automatically
10/6 [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] http://www.emerald-library.com
systems can only make a decision after
[ 354 ]

2. Khairy A.H. Kobbacy and the user has provided all the parameters
Yansong Liang necessary for selecting models. This makes
Outline structure of the proposed
Towards the development of inventory expert system
an 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 to
Integrated Manufacturing best, like the commercial inventory manage- use knowledge and inference procedures to
Systems solve problems that are difficult enough to
10/6 [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. Khairy A.H. Kobbacy and Figure 1
Yansong Liang The outline structure of the proposed system
Towards the development of
an intelligent inventory
management system
Integrated Manufacturing
Systems
10/6 [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. Khairy A.H. Kobbacy and Figure 2
Yansong Liang Top-level menu of the user interface
Towards the development of
an intelligent inventory
management system
Integrated Manufacturing
Systems
10/6 [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. Khairy A.H. Kobbacy and Figure 3
Yansong Liang Classification of demand patterns
Towards the development of
an intelligent inventory
management system
Integrated Manufacturing
Systems
10/6 [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 item's 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 Spearman's rank-order
one should take advantage of the subjective
correlation coefficient rs. It is defined as
knowledge of inventory managers.
Pearson's 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. Khairy A.H. Kobbacy and Figure 4
Yansong Liang The flowchart of demand pattern identification
Towards the development of
an intelligent inventory
management system
Integrated Manufacturing
Systems
10/6 [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 Pearson's 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. Khairy A.H. Kobbacy and number of categories of sample which is used. Otherwise, the Kolmogorov-Smirnov
Yansong Liang obtained using a rule of thumb, say, the statistic is used to test the goodness of fit of
Towards the development of sample size n is four or five times m. the data to the normal distribution, and the
an intelligent inventory
management system If 12 1a2 , then reject the suggested modified Pearson's Chi-square statistic to test
Integrated Manufacturing distribution; otherwise accept the suggested the goodness of fit to the Poisson distribution.
Systems distribution. If both tests were negative, then an empirical
10/6 [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 item's . 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 system's 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. Khairy A.H. Kobbacy and Figure 5
Yansong Liang Model tree of constant demand inventories
Towards the development of
an intelligent inventory
management system
Integrated Manufacturing
Systems
10/6 [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 Meal's (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
Mitra's 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 Meal's 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. Khairy A.H. Kobbacy and
T
ˆ
l
programming was completed (Liang, 1997). In
Yansong Liang Qs ˆ si X what follows, we discuss sample results from
Towards the development of iˆ1 the system using spare parts inventory data
an intelligent inventory
management 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 data
Integrated Manufacturing
Systems an integer n and a fraction , supplied by the manufacturing company
10/6 [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 item's 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 system's 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. Khairy A.H. Kobbacy and hand, more than half the items in the longer also lead to higher inventory costs. Deciding
Yansong Liang period file were classified as low demand on the frequency of running the pattern
Towards the development of
an intelligent inventory items. It is obvious that the length of history identifier is an important research area
management system data used in the analysis will affect the which is currently being studied. But the
Integrated Manufacturing results and the selected patterns system provides some tools, including the
Systems partition of data into different sizes and the
10/6 [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 I
Process of demand analysis (based on the data shown in the Appendix)
Item
Test A B C D E
Seasonal 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: Reject
Trend 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: Reject
Randomness 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: Reject
Normal distribution C = 0.29 C = 0.25
T = 46.94 T = 1.91
R: Reject R: Reject
Poisson distribution C = 11.07 C = 16.92
T=I T = 4.02
R: Reject R: Accept
Empirical distribution R: Accept
Strictly constant C = 0.5 C = 0.5 C = 0.5
T = 0.28 T = 1.61 T = 17.94
R: Accept R: Reject R: Reject
Quasi-constant C = 1.9 C = 1.9
T = 1.61 T = 17.94
R: Accept R: Reject
Unpredictable pattern R: Accept
Notes: C = the critical value; T = the value of the statistic; R = the result of the statistical test
[ 363 ]

11. Khairy A.H. Kobbacy and Table II
Yansong Liang Classification of items' demand patterns for two large data files (percentages)
Towards the development of
an intelligent inventory Pattern
management system
Data file Low demand Seasonal Trend Probabilistic Constant Unpredictable
Integrated Manufacturing
Systems File 1
10/6 [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. 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 a
management 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. (1993), ``A proposed knowledge
history data from existing inventory data- based system (KBS) for selection of inventory
bases, identify demand patterns based on control policies'', International Journal of
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practical situation in hand. It is hoped that Muhanna, W.A. and Pick, R.A. (1994), Meta-
the system would promote the applications of modelling concepts and tools for model man-
agement: a system approach'', Management
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Science, Vol. 40 No. 9, pp. 1093-123.
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Muir, J.W. (1980), ``Forecasting items with irre-
tive performance of inventory management.
gular demand'', American Production and
The development of a prototype KBS
Inventory Society Conference Proceedings, 23rd
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Annual International Conference, pp. 143-5.
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[ 365 ]

13. Khairy A.H. Kobbacy and
Yansong Liang
Appendix
Towards the development of
an intelligent inventory
management system Table AI
Integrated Manufacturing Demand data for spare parts
Systems
10/6 [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 ]