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Expert systems for inventory control management
Computers ind. Engng Vol. 17, Nos 1-4, pp. 425-429, 1989
0360-8352/89 $3.00+0.00 Copyright © 1989 Pergamon Press plc
Printed in Great Britain. All rights reserved
IJBWERTORY EXPERT
SYSTEMS
Diptendu
FOR
Sinha,
INVENTORY
Nasir
CONTROL
Ghiaseddin,
MANAGEMENT
Khalil
Matta
Management Department U n i v e r s i t y of N o t r e D a m e
ABSTRACT An e x p e r t s y s t e m for i n v e n t o r y m a n a g e m e n t is p r e s e n t e d in this paper. The focus is on the d e v e l o p m e n t of a s i m p l e , u s e r f r i e n d l y tool that can be used by m a n a g e r s to i n c r e a s e the e f f e c t i v e n e s s of t h e i r i n v e n t o r y c o n t r o l systems. The e x p e r t s y s t e m is c a p a b l e of d e r i v i n g i n p u t p a r a m e t e r s by p e r f o r m i n g n e c e s s a r y a n a l y s i s on d a t a b a s e s , i m p l e m e n t i n g a set of r u l e s for the s e l e c t i o n of i n v e n t o r y m o d e l s , and p r e s e n t the o u t p u t t h r o u g h tables, plots, or g r a p h s . The s c o p e of this p a p e r is l i m i t e d to the s i n g l e item, s i n g l e location problem.
INTRODUCTION Most organizations i n v o l v e d in the m a n a g e m e n t of i n v e n t o r i e s are f a c e d w i t h m a k i n g d e c i s i o n s for t h o u s a n d s of items. T h e s e items d i f f e r in s e v e r a l key a t t r i b u t e s s u c h as cost, d e m a n d p a t t e r n , s u p p l i e r l e a d times, n u m b e r of s t o c k i n g p o i n t s w i t h i n the o r g a n i z a t i o n a n d i m p a c t of its i n v e n t o r y p o l i c i e s on o t h e r items. These factors influence inventory operating policies significantly. E s t a b l i s h m e n t of o p t i m u m p o l i c i e s r e q u i r e s that they are a n a l y z e d and set f o r t h in p r e c i s e m a t h e m a t i c a l f o r m u l a s . Such modeling k n o w l e d g e g e n e r a l l y lie in the d o m a i n of e x p e r t s in the field, such as, o p e r a t i o n r e s e a r c h a n a l y s t s who are c o n c e r n e d w i t h m a t h e m a t i c a l a s p e c t s of the i n v e n t o r y t h e o r y . P r a c t i c i n g m a n a g e r s on the o t h e r h a n d are only c o n c e r n e d w i t h the o p e r a t i o n a l a s p e c t s of the p r o b l e m . Namely: i.
E n s u r e that available.
2.
Identify
3.
Provide
4.
Expend
sufficient
excess accurate,
least
fast
quantity
and
concise
amount
of
of g o o d s
slow-moving and
timely
resources
and material
are
always
items. report
to
the
in a c c o m p l i s h i n g
top m a n a g e m e n t . the
above
goals.
S i n c e the a v e r a g e i n v e n t o r y c o n t r o l d e c i s i o n m a k e r u s u a l l y l a c k s the level of sophistication in t h e o r y to come up w i t h the o p t i m u m s o l u t i o n , s i m p l i s t i c m o d e l s are u s u a l l y s u b s t i t u t e d for the a c t u a l m o d e l s . This p r a c t i c e n o r m a l l y p r o d u c e s a s u b o p t i m a l s o l u t i o n w h i c h in t u r n r e s u l t s in a c o s t l y i n v e n t o r y o p e r a t i o n and l i m i t s the p r o f i t of the o r g a n i z a t i o n .
EXPERT
SYSTEM
OBJECTIVES
AND
METHODOLOGY
It is the o b j e c t i v e of this r e s e a r c h p r o j e c t to n a r r o w the gap b e t w e e n the t h e o r y a n d p r a c t i c e of i n v e n t o r y c o n t r o l o p e r a t i o n . To a c h i e v e this goal, we i n t e n d to d e s i g n a n d i m p l e m e n t the c o n c e p t u a l f o u n d a t i o n of an a r t i f i c i a l l y i n t e l l i g e n t e x p e r t s y s t e m for i n v e n t o r y c o n t r o l . T h i s e x p e r t s y s t e m can be u s e d by any i n v e n t o r y c o n t r o l m a n a g e r w h o w a n t s to m a k e i n t e l l i g e n t d e c i s i o n s w i t h o u t b e i n g b u r d e n e d b y the c o m p l e x i t y and d e t a i l s of i n v e n t o r y c o n t r o l theory. The u s e r can s i m p l y c o n s u l t w i t h the e x p e r t s y s t e m for an a d v i c e
425
426
Proceedings of the l lth Annual Conference on Computers & Industrial Engineering
w h e n e v e r a d e c i s i o n n e e d s to be made. The a d v i c e g i v e n by the s y s t e m w i l l be b a s e d on the o p t i m a l s o l u t i o n of the p r o b l e m a n d u n n e c e s s a r y compromises will not be made. Our e x p e r t s y s t e m w i l l i n c l u d e all the e x p e r t i s e of an o p e r a t i o n r e s e a r c h a n a l y s t as w e l l as the h e u r i s t i c u s e d by s u c c e s s f u l inventory control managers. In o t h e r w o r d s the k n o w l e d g e b a s e of our e x p e r t system will include a model base containing the v a r i o u s m o d e l s u s e d in i n v e n t o r y c o n t r o l as w e l l as r u l e s g o v e r n i n g the J u s t i f i c a t i o n for u s i n g those m o d e l s . The e x p e r t s y s t e m w o u l d n o t o n l y i n c l u d e the k n o w l e d g e of mathematical m o d e l i n g , b u t it w o u l d a l s o i n c l u d e the r e a s o n i n g knowledge for s e l e c t i n g the m o s t a p p r o p r i a t e m o d e l for a g i v e n p r o b l e m s i t u a t i o n . The c o n c e p t u a l d e s i g n of our e x p e r t s y s t e m w i l l be b a s e d on p r e d i c a t e calculus and resolution principle [1,2]. The use of p r e d i c a t e calculus in this c o n t e x t o f f e r s a n u m b e r of b e n e f i t s . Among them conciseness, unambiguity, conformity to o t h e r e x i s t i n g a r t i f i c i a l intelligence t o o l s are of g r e a t i m p o r t a n c e to us. The r e s o l u t i o n principle [3] is a t e c h n i q u e for inference within predicate calculus, and a l l o w s a u t o m a t i c deduction of n e w facts f r o m an e x i s t i n g k n o w l e g e - b a s e .
FEATURES The
key
OF
THE
EXPERT
features
of
the
SYSTEM
FOR
expert
INVENTORY
system
can
be
defined
The s y s t e m s h o u l d be u s e r - o r i e n t e d and in a h i g h - l e v e l english-like language. The s y s t e m s h o u l d f i r s t a t t e m p t m o d e l s f r o m s o u r c e s s u c h as the data.
as:
capable
to p r o v i d e d a t a base,
of
accepting
the i n p u t d a t a to the b e f o r e a s k i n g the u s e r
The s y s t e m s h o u l d be c a p a b l e of a n a l y z i n g an i n v e n t o r y determining the a p p r o p r i a t e mathematical model. The s y s t e m m u s t models provided
be in
able to c o n s t r u c t the m o d e l base.
new
queries
models
from
problem
more
for
and
primitive
The s y s t e m m u s t f i r s t a t t e m p t to o p t i m i z e one or m o r e of the r e q u i r e d performance measures, or e l s e f i n d a p p r o x i m a t e o p t i m a l s o l u t i o n or pseudo optimal solutions if the m a t h e m a t i c a l m o d e l s c a n not be solved. 6.
The o u t p u t f r o m the s y s t e m s h o u l d be p r o v i d e d w i t h the u s e r in mind. T h a t is, it s h o u l d be e a s i l y u n d e r s t o o d by the user. T a b l e s and g r a p h s s h o u l d be u s e d to e n h a n c e the u n d e r s t a n d i n g of the r e s u l t s .
DESCRIPTION
OF
THE
EXPERT
SYSTEM
The f o l l o w i n g three functions have been identified a n d are c r i t i c a l to successful implementation of an e x p e r t s y s t e m for i n v e n t o r y m a n a g e m e n t : I.
The
ability
to
2.
The a b i l i t y to d e r i v e an i n v e n t o r y m o d e l .
3.
The a b i l i t y identified.
to
select
an
appropriate
the
provide
inventory
parameters/variables
a solution
to
the
the
model. required
inventory
model
in
selecting
once
one
is
In o r d e r to p e r f o r m the f i r s t f u n c t i o n , an i n v e n t o r y m o d e l c l a s s i f i c a t i o n s c h e m a is u t i l i z e d . T h i s s c h e m a is b a s e d in p a r t on the one p r o p o s e d by S i l v e r [4]. For the sake of s i m p l i c i t y , h o w e v e r , we f o c u s our a t t e n t i o n on the s i n g l e item, s i n g l e l o c a t i o n i n v e n t o r y p r o b l e m . Those models consider each item in i s o l a t i o n of o t h e r items. T h e r e are six s p e c i f i c f a c t o r s that i n f l u e n c e the s e l e c t i o n of i t e m s for this c a t e g o r y of m o d e l s : A.
TvDe
of
Demand:
i.
Deterministic
The
following
with
a known
demand demand
categories mean.
are
considered:
Sinha et al.: Expert systems for inventory management
2.
B.
1 .
C.
D.
E.
F.
Probabilistic with a known probability distribution (i.e., n o r m a l or g a m m a ) or an u n k n o w n d i s t r i b u t i o n of d e m a n d .
Nature
2.
427
of
the
Supply
Process:
We
consider:
All material o r d e r e d is r e c e i v e d a f t e r All material o r d e r e d is r e c e i v e d a f t e r a s s u m i n g m e a n a n d v a r i a n c e are k n o w n .
Shortages:
We
consider
two
treatments
i.
' Unfilled
demand
is b a c k o r d e r e d .
2.
Unfilled
demand
is
Review
Period:
We
of
a k n o w n l e a d time. a r a n d o m l e a d time,
shortages:
lost.
consider
i.
Continuous review is r e v i e w e d a f t e r
2.
Periodic review models and ordering decisions
the
following:
m o d e l s w h e r e the i n v e n t o r y each transaction.
position
w h e r e the i n v e n t o r y p o s i t i o n is are m a d e at p e r i o d i c intervals.
Costs: The f o u r t y p e s of c o s t s f r e q u e n t l y i n c l u d e d in m o d e l s are the r e p l a c e m e n t or o r d e r i n g c o s t s , c a r r y i n g shortages cost. The u n i t c o s t s are e i t h e r t r e a t e d as: I.
Constant
(i.e.,
the
2.
Quantity
discounts
same) are
Control procedure: We s h a l l procedures to d e t e r m i n e w h e n
of
for
all
offered
on
units all
or
reviewed
inventory c o s t s and
marginal
units. used
i.
(s,Q) s y s t e m : A fixed quantity inventory l e v e l r e a c h e s s.
2.
(s,S) s y s t e m : The o r d e r is p l a c e d or b e l o w s. The size of the o r d e r i n v e n t o r y l e v e l to p o s i t i o n S.
3.
(t,S) s y s t e m : A n o r d e r is p l a c e d e v e r y t time u n i t s . is e q u a l to the d i f f e r e n c e b e t w e e n S a n d the i n v e n t o r y at the e n d of t.
is
item
ordered.
consider three frequently a n d h o w m u c h to order: Q
an
ordered
as
soon
as
control
the
whe'n i n v e n t o r y p o s i t i o n is is c h o s e n to i n c r e a s e the
at
The o r d e r position
In F i g u r e i, we p r e s e n t a d e c i s i o n tree for s e l e c t i n g the i n v e n t o r y m o d e l s i n g l e i t e m g i v i n g the f a c t o r s m e n t i o n e d p r e v i o u s l y . N o t e that r u l e s pertaining to the p r o b a b i l i s t i c l e a d time c a s e are n o t shown. Each node the tree r e p r e s e n t s a decision. E a c h b r a n c h on the tree r e p r e s e n t s the c r i t e r i a or f a c t o r that is a p p l i e d or is c o n s i d e r e d .
for on
The d e c i s i o n tree in f i g u r e i e s t a b l i s h e s the f o u n d a t i o n for the m o d e l selection. However, it is a s s u m e d that the u s e r h a s i n f o r m a t i o n regarding all the p a r a m e t e r s r e q u i r e d for the e x p e r t s y s t e m to s e l e c t the m a t h e m a t i c a l model. A l i s t of t h o s e p a r a m e t e r s and variables is p r e s e n t e d in T a b l e I. Note that w h i l e s o m e of t h e m are e a s y to d e t e r m i n e s u c h as the u n i t cost, o t h e r s r e q u i r e t h a t the m o d e l be s o l v e d s u c h as the o r d e r q u a n t i t y and reorder point. It is t h e r e f o r e c r i t i c a l that the e x p e r t s y s t e m has the capability to a n a l y z e the p a r a m e t e r s r e q u i r e d to m a k e a m o d e l s e l e c t i o n . In o r d e r to i l l u s t r a t e w h a t we mean, let us take the d e m a n d as an e x a m p l e . The d e m a n d c a n e i t h e r be d e t e r m i n i s t i c or p r o b a b i l i s t i c . If the u s e r can not d e c i d e the e x p e r t s y s t e m s h o u l d be a b l e to r e t r i e v e that i n f o r m a t i o n by analyzing database containing historical d e m a n d data. A calculation of the m e a n and the s t a n d a r d d e v i a t i o n is a r e l a t i v e l y e a s y task. T h o s e c a n be u s e d to c a l c u l a t e the c o e f f i c i e n t of v a r i a t i o n w h i c h if s m a l l (< .2) i n d i c a t e s that the d e m a n d is d e t e r m i n i s t i c . If the d e m a n d is p r o b a b i l i s t l c / a Chis q u a r e d test ( g o o d n e s s of fit test) c o u l d be p e r f o r m e d to d e t e r m i n e if the N o r m a l , G a m m a or P o i s s o n d i s t r i b u t i o n s approximate the d e m a n d p a t t e r n . This is i m p o r t a n t s i n c e it c a n i m p a c t the s o l u t i o n p r o c e d u r e . If the d e m a n d is deterministic, the u s e r c o u l d be p r e s e n t e d w i t h h i s t o r i c a l g r a p h s to determine if t h e r e are c y c l i c a l p a t t e r n s or time v a r y i n g d e m a n d s .
428
Proceedings of the 1lth Annual Conference on Computers & Industrial Engineering
Once an i n v e n t o r y m o d e l is i d e n t i f i e d , the e x p e r t s y s t e m m u s t be able to find a s o l u t i o n b a s e d on m a x i m l z i n g / m i n i m i z l n g one or m o r e of the o p e r a t i n g characteristics s h o w n in T a b l e 2. It is i m p o r t a n t to n o t e that w h i l e e x a c t s o l u t i o n s c a n e x i s t for the d e t e r m i n i s t i c c a s e s for e x a m p l e , it c a n be extremely difficult to s o l v e some m o d e l s s u c h as the q u a n t i t y d i s c o u n t m o d e l s for the p r o b a b i l l s t i c cases. The
strategy
implemented
I.
Find
an
2
Develop a mathematical characteristic(s) and optimum; if n o t
3.
Use
exact
in
the
solution;
a simulation
expert
system
is
as
follows:
if not formulation, if p o s s i b l e , for the o p e r a t i n g use a s e a r c h t e c h n i q u e to l o c a t e a l o c a l
routine
to
find
an
approximate
optimum
solution.
A general simulation m o d e l is p r o v i d e d w h i c h c a n be a c c e s s e d by the e x p e r t s y s t e m to s o l v e the m o r e c o m p l e x i n v e n t o r y s y s t e m s . T h i s is p a r t i c u l a r l y useful when performing sensitivity a n a l y s i s s u c h as the i m p a c t of a d d i n g constraints. T h r e e t y p e s of c o n s t r a i n t s are c o n s i d e r e d : i.
Supplier constraints cycle, m i n i m u m o r d e r
2.
Marketing level.
3.
Internal
constraints
constraints
such lead such
such
as m i n i m u m time, etc. as
as
minimum
storage
order
size,
tolerable
space,
fixed
replenishment
consumer
budget,
service
etc...
CONCLUSION The c o m p l e x i t i e s of m u c h of i n v e n t o r y c o n t r o l t h e o r y h a s p r e v e n t e d its application in m a n y o r g a n i z a t i o n s . The e x p e r t s y s t e m p r e s e n t e d in this p a p e r is an a t t e m p t to b r i d g e this gap b e t w e e n the t h e o r e t i c i a n s a n d the practitioners. Facilities are p r o v i d e d in the e x p e r t s y s t e m to not o n l y aid the p r a c t i t i o n e r in s e l e c t i n g the a p p r o p r i a t e m o d e l b u t a l s o in o b t a i n i n g and calculating the p a r a m e t e r s r e q u i r e d for s o l v i n g s u c h p r o b l e m s . The e x o e r t s y s t e m is i n t e r f a c e d w i t h b o t h a d a t a b a s e ( u s e d to e x t r a c t i n p u t p a r a m e t e r s ) and a s i m u l a t i o n m o d e l ( u s e d to m o d e l the m o s t c o m p l e x s y s t e m s ) . Future r e s e a r c h in this a r e a s h o u l d f o c u s on e x p a n d i n g the s c o p e of the e x p e r t s y s t e m to i n c l u d e a n a l y s i s of m u l t i - i t e m , multi-locatlon inventory problems.
REFERENCES
[i]
Nilsson, N. , P r i n c i p l e s of A r t i f i c i a l Co., P a l o A l t o , C a l i f o r n i a , 1980.
[2]
B o n c z e k , H.B. , C.W. H o l s a p p l e , a n d A.B. W h i n s t o n , "A G e n e r a l i z e d Decision Support System Using Predicate Calculus and Network Data Base," Operations R e s e a r c h , Vol. 29, No. 2, M a r c h - A p r l l 1981.
[3]
Robinson, J . A . , "A M a c h i n e O r i e n t e d L o g i c Principle. J o u r n a l of ACM, M a r c h 1965.
[4]
S i l v e r , E. Review and
A. , " O p e r a t i o n s Critique," Vol.
Intelli~ence,
Based
on
Tioga
Publishing
Resolution
Research in I n v e n t o r y M a n a g e m e n t : 29, No. 4., J u l y - A u g u s t , 1981.
A
Sinha et al.: Expert systems for inventory management
TABLE
1
TABLE
PARAMETERS/VARIABLES:
i 2 3 4 5 6 7 8 9 i0 II 12 13
429
2
OPERATING CHARACTERISTICS (PERFORMANCE MEASURES)
O r d e r Q u a n t i t y (Q) O r d e r - u p t o L e v e l (S) O r d e r P o i n t (s) U n i t C o s t (C) Fraction Carrying Cost H o l d i n g C o s t (H) B a c k O r d e r C o s t (B) M e a n L e a d T i m e (L) M e a n D e m a n d (D) S.D. of D e m a n d (SD) S.D. of L e a d T i m e (SL) R e v i e w I n t e r v a l (T) Set Up C o s t (K)
FI~
No. of C y c l e s ( O r d e r s ) No. of S t o c k - o u t s A v e r a g e No. of B a c k O r d e r s Average Inventory Average Inventory Value I n v e n t o r y C a r r y i n g Cost Shortage Cost Ordering Cost Total Cost
(F)
1.
Inwntory
ALL UNITS
~
~
t
D e c l s l o n Tree
(~J~olmt)
OTY-DI~. 1 FIXED
FIXED LEAIEIM~
I
FINITE
lOq 1 ] ~ )
~ISI~miT
Is,Q)
SF_JtR~ 12 s t e p )
COV < I
OTY.-DISC,
Io ~
smo~
I
~
~ ss
DE~)
FOR~YLATIONI
OTHER
cov< .2
~
ANALYTICAL SEARCH
OTHER
C0V > .2
APRN3XIMATION
SIMULATE
SIMULATE
DIST.
Dm~A~D MUDEL NO
DISCiPERIODIC I
IS'S)
I COV > I SDfJLATE ~OV < 1 P C ~ R APPROXD~TION
it,s)
I
PROBABILISTIC D~AND
REVIE~ ]
I LOST SALES SIMEW.JkTE LARGE PROBABILISTIC LEAD T D ~
~ ~ PROCESS
SOLVEFOR S
AEPE)F,3~IATE SOLVEFOR S t-not
t
~l~L-d
SALES U ~ ~
SMALL
t-fLied
SC~O
NO
~mPROXIMATION
SDqJ~TE
0360-8352/89 $3.00+0.00 Copyright © 1989 Pergamon Press plc
Printed in Great Britain. All rights reserved
IJBWERTORY EXPERT
SYSTEMS
Diptendu
FOR
Sinha,
INVENTORY
Nasir
CONTROL
Ghiaseddin,
MANAGEMENT
Khalil
Matta
Management Department U n i v e r s i t y of N o t r e D a m e
ABSTRACT An e x p e r t s y s t e m for i n v e n t o r y m a n a g e m e n t is p r e s e n t e d in this paper. The focus is on the d e v e l o p m e n t of a s i m p l e , u s e r f r i e n d l y tool that can be used by m a n a g e r s to i n c r e a s e the e f f e c t i v e n e s s of t h e i r i n v e n t o r y c o n t r o l systems. The e x p e r t s y s t e m is c a p a b l e of d e r i v i n g i n p u t p a r a m e t e r s by p e r f o r m i n g n e c e s s a r y a n a l y s i s on d a t a b a s e s , i m p l e m e n t i n g a set of r u l e s for the s e l e c t i o n of i n v e n t o r y m o d e l s , and p r e s e n t the o u t p u t t h r o u g h tables, plots, or g r a p h s . The s c o p e of this p a p e r is l i m i t e d to the s i n g l e item, s i n g l e location problem.
INTRODUCTION Most organizations i n v o l v e d in the m a n a g e m e n t of i n v e n t o r i e s are f a c e d w i t h m a k i n g d e c i s i o n s for t h o u s a n d s of items. T h e s e items d i f f e r in s e v e r a l key a t t r i b u t e s s u c h as cost, d e m a n d p a t t e r n , s u p p l i e r l e a d times, n u m b e r of s t o c k i n g p o i n t s w i t h i n the o r g a n i z a t i o n a n d i m p a c t of its i n v e n t o r y p o l i c i e s on o t h e r items. These factors influence inventory operating policies significantly. E s t a b l i s h m e n t of o p t i m u m p o l i c i e s r e q u i r e s that they are a n a l y z e d and set f o r t h in p r e c i s e m a t h e m a t i c a l f o r m u l a s . Such modeling k n o w l e d g e g e n e r a l l y lie in the d o m a i n of e x p e r t s in the field, such as, o p e r a t i o n r e s e a r c h a n a l y s t s who are c o n c e r n e d w i t h m a t h e m a t i c a l a s p e c t s of the i n v e n t o r y t h e o r y . P r a c t i c i n g m a n a g e r s on the o t h e r h a n d are only c o n c e r n e d w i t h the o p e r a t i o n a l a s p e c t s of the p r o b l e m . Namely: i.
E n s u r e that available.
2.
Identify
3.
Provide
4.
Expend
sufficient
excess accurate,
least
fast
quantity
and
concise
amount
of
of g o o d s
slow-moving and
timely
resources
and material
are
always
items. report
to
the
in a c c o m p l i s h i n g
top m a n a g e m e n t . the
above
goals.
S i n c e the a v e r a g e i n v e n t o r y c o n t r o l d e c i s i o n m a k e r u s u a l l y l a c k s the level of sophistication in t h e o r y to come up w i t h the o p t i m u m s o l u t i o n , s i m p l i s t i c m o d e l s are u s u a l l y s u b s t i t u t e d for the a c t u a l m o d e l s . This p r a c t i c e n o r m a l l y p r o d u c e s a s u b o p t i m a l s o l u t i o n w h i c h in t u r n r e s u l t s in a c o s t l y i n v e n t o r y o p e r a t i o n and l i m i t s the p r o f i t of the o r g a n i z a t i o n .
EXPERT
SYSTEM
OBJECTIVES
AND
METHODOLOGY
It is the o b j e c t i v e of this r e s e a r c h p r o j e c t to n a r r o w the gap b e t w e e n the t h e o r y a n d p r a c t i c e of i n v e n t o r y c o n t r o l o p e r a t i o n . To a c h i e v e this goal, we i n t e n d to d e s i g n a n d i m p l e m e n t the c o n c e p t u a l f o u n d a t i o n of an a r t i f i c i a l l y i n t e l l i g e n t e x p e r t s y s t e m for i n v e n t o r y c o n t r o l . T h i s e x p e r t s y s t e m can be u s e d by any i n v e n t o r y c o n t r o l m a n a g e r w h o w a n t s to m a k e i n t e l l i g e n t d e c i s i o n s w i t h o u t b e i n g b u r d e n e d b y the c o m p l e x i t y and d e t a i l s of i n v e n t o r y c o n t r o l theory. The u s e r can s i m p l y c o n s u l t w i t h the e x p e r t s y s t e m for an a d v i c e
425
426
Proceedings of the l lth Annual Conference on Computers & Industrial Engineering
w h e n e v e r a d e c i s i o n n e e d s to be made. The a d v i c e g i v e n by the s y s t e m w i l l be b a s e d on the o p t i m a l s o l u t i o n of the p r o b l e m a n d u n n e c e s s a r y compromises will not be made. Our e x p e r t s y s t e m w i l l i n c l u d e all the e x p e r t i s e of an o p e r a t i o n r e s e a r c h a n a l y s t as w e l l as the h e u r i s t i c u s e d by s u c c e s s f u l inventory control managers. In o t h e r w o r d s the k n o w l e d g e b a s e of our e x p e r t system will include a model base containing the v a r i o u s m o d e l s u s e d in i n v e n t o r y c o n t r o l as w e l l as r u l e s g o v e r n i n g the J u s t i f i c a t i o n for u s i n g those m o d e l s . The e x p e r t s y s t e m w o u l d n o t o n l y i n c l u d e the k n o w l e d g e of mathematical m o d e l i n g , b u t it w o u l d a l s o i n c l u d e the r e a s o n i n g knowledge for s e l e c t i n g the m o s t a p p r o p r i a t e m o d e l for a g i v e n p r o b l e m s i t u a t i o n . The c o n c e p t u a l d e s i g n of our e x p e r t s y s t e m w i l l be b a s e d on p r e d i c a t e calculus and resolution principle [1,2]. The use of p r e d i c a t e calculus in this c o n t e x t o f f e r s a n u m b e r of b e n e f i t s . Among them conciseness, unambiguity, conformity to o t h e r e x i s t i n g a r t i f i c i a l intelligence t o o l s are of g r e a t i m p o r t a n c e to us. The r e s o l u t i o n principle [3] is a t e c h n i q u e for inference within predicate calculus, and a l l o w s a u t o m a t i c deduction of n e w facts f r o m an e x i s t i n g k n o w l e g e - b a s e .
FEATURES The
key
OF
THE
EXPERT
features
of
the
SYSTEM
FOR
expert
INVENTORY
system
can
be
defined
The s y s t e m s h o u l d be u s e r - o r i e n t e d and in a h i g h - l e v e l english-like language. The s y s t e m s h o u l d f i r s t a t t e m p t m o d e l s f r o m s o u r c e s s u c h as the data.
as:
capable
to p r o v i d e d a t a base,
of
accepting
the i n p u t d a t a to the b e f o r e a s k i n g the u s e r
The s y s t e m s h o u l d be c a p a b l e of a n a l y z i n g an i n v e n t o r y determining the a p p r o p r i a t e mathematical model. The s y s t e m m u s t models provided
be in
able to c o n s t r u c t the m o d e l base.
new
queries
models
from
problem
more
for
and
primitive
The s y s t e m m u s t f i r s t a t t e m p t to o p t i m i z e one or m o r e of the r e q u i r e d performance measures, or e l s e f i n d a p p r o x i m a t e o p t i m a l s o l u t i o n or pseudo optimal solutions if the m a t h e m a t i c a l m o d e l s c a n not be solved. 6.
The o u t p u t f r o m the s y s t e m s h o u l d be p r o v i d e d w i t h the u s e r in mind. T h a t is, it s h o u l d be e a s i l y u n d e r s t o o d by the user. T a b l e s and g r a p h s s h o u l d be u s e d to e n h a n c e the u n d e r s t a n d i n g of the r e s u l t s .
DESCRIPTION
OF
THE
EXPERT
SYSTEM
The f o l l o w i n g three functions have been identified a n d are c r i t i c a l to successful implementation of an e x p e r t s y s t e m for i n v e n t o r y m a n a g e m e n t : I.
The
ability
to
2.
The a b i l i t y to d e r i v e an i n v e n t o r y m o d e l .
3.
The a b i l i t y identified.
to
select
an
appropriate
the
provide
inventory
parameters/variables
a solution
to
the
the
model. required
inventory
model
in
selecting
once
one
is
In o r d e r to p e r f o r m the f i r s t f u n c t i o n , an i n v e n t o r y m o d e l c l a s s i f i c a t i o n s c h e m a is u t i l i z e d . T h i s s c h e m a is b a s e d in p a r t on the one p r o p o s e d by S i l v e r [4]. For the sake of s i m p l i c i t y , h o w e v e r , we f o c u s our a t t e n t i o n on the s i n g l e item, s i n g l e l o c a t i o n i n v e n t o r y p r o b l e m . Those models consider each item in i s o l a t i o n of o t h e r items. T h e r e are six s p e c i f i c f a c t o r s that i n f l u e n c e the s e l e c t i o n of i t e m s for this c a t e g o r y of m o d e l s : A.
TvDe
of
Demand:
i.
Deterministic
The
following
with
a known
demand demand
categories mean.
are
considered:
Sinha et al.: Expert systems for inventory management
2.
B.
1 .
C.
D.
E.
F.
Probabilistic with a known probability distribution (i.e., n o r m a l or g a m m a ) or an u n k n o w n d i s t r i b u t i o n of d e m a n d .
Nature
2.
427
of
the
Supply
Process:
We
consider:
All material o r d e r e d is r e c e i v e d a f t e r All material o r d e r e d is r e c e i v e d a f t e r a s s u m i n g m e a n a n d v a r i a n c e are k n o w n .
Shortages:
We
consider
two
treatments
i.
' Unfilled
demand
is b a c k o r d e r e d .
2.
Unfilled
demand
is
Review
Period:
We
of
a k n o w n l e a d time. a r a n d o m l e a d time,
shortages:
lost.
consider
i.
Continuous review is r e v i e w e d a f t e r
2.
Periodic review models and ordering decisions
the
following:
m o d e l s w h e r e the i n v e n t o r y each transaction.
position
w h e r e the i n v e n t o r y p o s i t i o n is are m a d e at p e r i o d i c intervals.
Costs: The f o u r t y p e s of c o s t s f r e q u e n t l y i n c l u d e d in m o d e l s are the r e p l a c e m e n t or o r d e r i n g c o s t s , c a r r y i n g shortages cost. The u n i t c o s t s are e i t h e r t r e a t e d as: I.
Constant
(i.e.,
the
2.
Quantity
discounts
same) are
Control procedure: We s h a l l procedures to d e t e r m i n e w h e n
of
for
all
offered
on
units all
or
reviewed
inventory c o s t s and
marginal
units. used
i.
(s,Q) s y s t e m : A fixed quantity inventory l e v e l r e a c h e s s.
2.
(s,S) s y s t e m : The o r d e r is p l a c e d or b e l o w s. The size of the o r d e r i n v e n t o r y l e v e l to p o s i t i o n S.
3.
(t,S) s y s t e m : A n o r d e r is p l a c e d e v e r y t time u n i t s . is e q u a l to the d i f f e r e n c e b e t w e e n S a n d the i n v e n t o r y at the e n d of t.
is
item
ordered.
consider three frequently a n d h o w m u c h to order: Q
an
ordered
as
soon
as
control
the
whe'n i n v e n t o r y p o s i t i o n is is c h o s e n to i n c r e a s e the
at
The o r d e r position
In F i g u r e i, we p r e s e n t a d e c i s i o n tree for s e l e c t i n g the i n v e n t o r y m o d e l s i n g l e i t e m g i v i n g the f a c t o r s m e n t i o n e d p r e v i o u s l y . N o t e that r u l e s pertaining to the p r o b a b i l i s t i c l e a d time c a s e are n o t shown. Each node the tree r e p r e s e n t s a decision. E a c h b r a n c h on the tree r e p r e s e n t s the c r i t e r i a or f a c t o r that is a p p l i e d or is c o n s i d e r e d .
for on
The d e c i s i o n tree in f i g u r e i e s t a b l i s h e s the f o u n d a t i o n for the m o d e l selection. However, it is a s s u m e d that the u s e r h a s i n f o r m a t i o n regarding all the p a r a m e t e r s r e q u i r e d for the e x p e r t s y s t e m to s e l e c t the m a t h e m a t i c a l model. A l i s t of t h o s e p a r a m e t e r s and variables is p r e s e n t e d in T a b l e I. Note that w h i l e s o m e of t h e m are e a s y to d e t e r m i n e s u c h as the u n i t cost, o t h e r s r e q u i r e t h a t the m o d e l be s o l v e d s u c h as the o r d e r q u a n t i t y and reorder point. It is t h e r e f o r e c r i t i c a l that the e x p e r t s y s t e m has the capability to a n a l y z e the p a r a m e t e r s r e q u i r e d to m a k e a m o d e l s e l e c t i o n . In o r d e r to i l l u s t r a t e w h a t we mean, let us take the d e m a n d as an e x a m p l e . The d e m a n d c a n e i t h e r be d e t e r m i n i s t i c or p r o b a b i l i s t i c . If the u s e r can not d e c i d e the e x p e r t s y s t e m s h o u l d be a b l e to r e t r i e v e that i n f o r m a t i o n by analyzing database containing historical d e m a n d data. A calculation of the m e a n and the s t a n d a r d d e v i a t i o n is a r e l a t i v e l y e a s y task. T h o s e c a n be u s e d to c a l c u l a t e the c o e f f i c i e n t of v a r i a t i o n w h i c h if s m a l l (< .2) i n d i c a t e s that the d e m a n d is d e t e r m i n i s t i c . If the d e m a n d is p r o b a b i l i s t l c / a Chis q u a r e d test ( g o o d n e s s of fit test) c o u l d be p e r f o r m e d to d e t e r m i n e if the N o r m a l , G a m m a or P o i s s o n d i s t r i b u t i o n s approximate the d e m a n d p a t t e r n . This is i m p o r t a n t s i n c e it c a n i m p a c t the s o l u t i o n p r o c e d u r e . If the d e m a n d is deterministic, the u s e r c o u l d be p r e s e n t e d w i t h h i s t o r i c a l g r a p h s to determine if t h e r e are c y c l i c a l p a t t e r n s or time v a r y i n g d e m a n d s .
428
Proceedings of the 1lth Annual Conference on Computers & Industrial Engineering
Once an i n v e n t o r y m o d e l is i d e n t i f i e d , the e x p e r t s y s t e m m u s t be able to find a s o l u t i o n b a s e d on m a x i m l z i n g / m i n i m i z l n g one or m o r e of the o p e r a t i n g characteristics s h o w n in T a b l e 2. It is i m p o r t a n t to n o t e that w h i l e e x a c t s o l u t i o n s c a n e x i s t for the d e t e r m i n i s t i c c a s e s for e x a m p l e , it c a n be extremely difficult to s o l v e some m o d e l s s u c h as the q u a n t i t y d i s c o u n t m o d e l s for the p r o b a b i l l s t i c cases. The
strategy
implemented
I.
Find
an
2
Develop a mathematical characteristic(s) and optimum; if n o t
3.
Use
exact
in
the
solution;
a simulation
expert
system
is
as
follows:
if not formulation, if p o s s i b l e , for the o p e r a t i n g use a s e a r c h t e c h n i q u e to l o c a t e a l o c a l
routine
to
find
an
approximate
optimum
solution.
A general simulation m o d e l is p r o v i d e d w h i c h c a n be a c c e s s e d by the e x p e r t s y s t e m to s o l v e the m o r e c o m p l e x i n v e n t o r y s y s t e m s . T h i s is p a r t i c u l a r l y useful when performing sensitivity a n a l y s i s s u c h as the i m p a c t of a d d i n g constraints. T h r e e t y p e s of c o n s t r a i n t s are c o n s i d e r e d : i.
Supplier constraints cycle, m i n i m u m o r d e r
2.
Marketing level.
3.
Internal
constraints
constraints
such lead such
such
as m i n i m u m time, etc. as
as
minimum
storage
order
size,
tolerable
space,
fixed
replenishment
consumer
budget,
service
etc...
CONCLUSION The c o m p l e x i t i e s of m u c h of i n v e n t o r y c o n t r o l t h e o r y h a s p r e v e n t e d its application in m a n y o r g a n i z a t i o n s . The e x p e r t s y s t e m p r e s e n t e d in this p a p e r is an a t t e m p t to b r i d g e this gap b e t w e e n the t h e o r e t i c i a n s a n d the practitioners. Facilities are p r o v i d e d in the e x p e r t s y s t e m to not o n l y aid the p r a c t i t i o n e r in s e l e c t i n g the a p p r o p r i a t e m o d e l b u t a l s o in o b t a i n i n g and calculating the p a r a m e t e r s r e q u i r e d for s o l v i n g s u c h p r o b l e m s . The e x o e r t s y s t e m is i n t e r f a c e d w i t h b o t h a d a t a b a s e ( u s e d to e x t r a c t i n p u t p a r a m e t e r s ) and a s i m u l a t i o n m o d e l ( u s e d to m o d e l the m o s t c o m p l e x s y s t e m s ) . Future r e s e a r c h in this a r e a s h o u l d f o c u s on e x p a n d i n g the s c o p e of the e x p e r t s y s t e m to i n c l u d e a n a l y s i s of m u l t i - i t e m , multi-locatlon inventory problems.
REFERENCES
[i]
Nilsson, N. , P r i n c i p l e s of A r t i f i c i a l Co., P a l o A l t o , C a l i f o r n i a , 1980.
[2]
B o n c z e k , H.B. , C.W. H o l s a p p l e , a n d A.B. W h i n s t o n , "A G e n e r a l i z e d Decision Support System Using Predicate Calculus and Network Data Base," Operations R e s e a r c h , Vol. 29, No. 2, M a r c h - A p r l l 1981.
[3]
Robinson, J . A . , "A M a c h i n e O r i e n t e d L o g i c Principle. J o u r n a l of ACM, M a r c h 1965.
[4]
S i l v e r , E. Review and
A. , " O p e r a t i o n s Critique," Vol.
Intelli~ence,
Based
on
Tioga
Publishing
Resolution
Research in I n v e n t o r y M a n a g e m e n t : 29, No. 4., J u l y - A u g u s t , 1981.
A
Sinha et al.: Expert systems for inventory management
TABLE
1
TABLE
PARAMETERS/VARIABLES:
i 2 3 4 5 6 7 8 9 i0 II 12 13
429
2
OPERATING CHARACTERISTICS (PERFORMANCE MEASURES)
O r d e r Q u a n t i t y (Q) O r d e r - u p t o L e v e l (S) O r d e r P o i n t (s) U n i t C o s t (C) Fraction Carrying Cost H o l d i n g C o s t (H) B a c k O r d e r C o s t (B) M e a n L e a d T i m e (L) M e a n D e m a n d (D) S.D. of D e m a n d (SD) S.D. of L e a d T i m e (SL) R e v i e w I n t e r v a l (T) Set Up C o s t (K)
FI~
No. of C y c l e s ( O r d e r s ) No. of S t o c k - o u t s A v e r a g e No. of B a c k O r d e r s Average Inventory Average Inventory Value I n v e n t o r y C a r r y i n g Cost Shortage Cost Ordering Cost Total Cost
(F)
1.
Inwntory
ALL UNITS
~
~
t
D e c l s l o n Tree
(~J~olmt)
OTY-DI~. 1 FIXED
FIXED LEAIEIM~
I
FINITE
lOq 1 ] ~ )
~ISI~miT
Is,Q)
SF_JtR~ 12 s t e p )
COV < I
OTY.-DISC,
Io ~
smo~
I
~
~ ss
DE~)
FOR~YLATIONI
OTHER
cov< .2
~
ANALYTICAL SEARCH
OTHER
C0V > .2
APRN3XIMATION
SIMULATE
SIMULATE
DIST.
Dm~A~D MUDEL NO
DISCiPERIODIC I
IS'S)
I COV > I SDfJLATE ~OV < 1 P C ~ R APPROXD~TION
it,s)
I
PROBABILISTIC D~AND
REVIE~ ]
I LOST SALES SIMEW.JkTE LARGE PROBABILISTIC LEAD T D ~
~ ~ PROCESS
SOLVEFOR S
AEPE)F,3~IATE SOLVEFOR S t-not
t
~l~L-d
SALES U ~ ~
SMALL
t-fLied
SC~O
NO
~mPROXIMATION
SDqJ~TE