a sensitivity analysis of stochaux, inventory systems
TRANSCRIPT
"A SENSITIVITY ANALYSIS OF STOCHAUX,INVENTORY SYSTEMS"
by
Yu-Sheng ZHENG*and
Xavier DE GROOTE**
N° 92/16/TM
* Department of Decision Sciences, The Wharton School, University of Pennsylvania,Philadelphia, PA 19104, U.S.A..
** Assistant Professor of Operations Management, INSEAD, Boulevard de Constance,Fontainebleau 77305 Cedex, France.
Printed at INSEAD,Fontainebleau, France
A SENSITIVITY ANALYSIS
OF STOCHASTIC INVENTORY
SYSTEMS
Yu-Sheng Zheng *
Xavier de Groote **
October 1991
Revised, January 1992
Department of Decision SciencesThe Wharton SchoolUniversity of PennsylvaniaPhiladelphia, PA 19104-6366USA
** Technology Management AreaINSEADBoulevard de Constance77305 Fontainebleau CedexFRANCE
Abstract
This paper derives sensitivity properties of the single item inventory model with stochastic
demand and positive setup costs. The anaivaissumbssiSsetheeffect of changes in the variability
of the leadtime demand. For the order-quantity/reorder-point systems, we prove that when the
variability of the leadtime demand increases: (i) the optimal order quantity increases, but,
somewhat contrary to the conventional wisdom, the optimal reorder point does not necessarilyincrease; (ü) the minimum cost of the inventory system increases, and it increases at a slower rate
than and converges to the cost of the optimal base-stock policy; and (iii) the cost performance
becomes more robust to the choice of order quantity. In addition, we also show that both the
optimal reorder point and the optimal order-up-to level decrease (increase) as the inventory
holding (shortage penalty) cost increases.
1. Introduction
It is common sense that, for the management of inventories, the variability of the leadtime demand
has a negative impact on the precision of control and on costs. An effective way of reducing
the variability of the leadtime demand is to shorten the leadtime itself. This reduction requises
effort and extra cost. With the current emphasis on "just-in-time" inventory management, and on
"time-based" competition, there are increasing needs for a more precise analysis of the effect of
the variability of the leadtime demand ou the control and performance of inventory systems. This
paper addresses this problem for one of the widely used stochastic inventory systems, the order
quantity/reorder point system.
The order quantity/reorder point system is also referred to as the (Q,r) system, where an order
of Q units is placed as soon as the inventory position (i.e., the inventory on hand plus on order minus
backorders) drops to the critical level r. This inventory control system is the simplest model that
simultaneously addresses economies of scale in order quantities, and a random (leadtime) demand.
The cost function of the (Q,r) system has been well known for about three decades, ever since the
publication of the popular textbook by Hadley and Whitin (1963). However, it had been perceived
to be too complex to analyse, and, until very recently, our knowledge of the optimal control of
titis system had been limited. We refer readers to Lee and Nahmias(1989) and Federgruen and
Zheng(1988) for recent reviews of the related literature.
From a modeling point of view, two simple inventory models, the EOQ model and the base stock
model, are special cases of the (Q,r) model. The EOQ model crystallizes the tradeoff between the
1
inventory holding costs and the fixed ordering costs by assuming a deterministic demand. h is clear
that a positive (deterministic) leadtimc does not affect the EOQ model in any essential way because
of the predictable leadtime demand. The base stock model, on the other hand, stresses the balance
between the inventory holding costs and the shortage penalty costs by assuming away the fixed
ordering costs. In a base stock model, an order is placed to restore the inventory position to a fixed
"base stock" (or "order-up-to") level whenever a demand occurs. The optimal order-up-to level
can be determined by minimizing the expected inventory holding costs and shortage penalty costs,
which is essentially the newsboy problem -where the demand for newspaper is interpreted-as the
leadtime demand. The optimal order-up-to point, which is often referred to as the newsboy point,
enjoys a closed form solution. In that case, the effect of the variability of the leadtime demand is
relatively simple to analyze.
With little theoretical support, it has often been argued that in a (Q,r) system, the order
quantity should be determined by the EOQ formula in order to exploit the economies of scale, while
the reorder point should be set to the expected leadtime demand plus some safety stock reflecting
the variance of the leadtime demand and the service level (or the costs associated with shortage).
While this argument is intuitive and therefore has played an important role in popularizing the
model, it essentially dismisses the (Q,r) model by the rough functional segregation of the two control
parameters.
Our analysis is based on recent results of Zheng(1989), who proves for the first tinie that the
(Q,r) model can be viewed as an aggregation of a. variant of the EOQ model and the base stock
model. In his analysis, alter the reorder point is chosen optimally for any given order quantity, the
(Q,r) model reduces to a problem of finding the best tradeoff between the average ordering cost
and the average holding and penalty cost. The average cost of the model is shown to be the sum of
two components: the cost oi the optimal base stock policy and a cost function that is very similar
but smaller than that of the EOQ model (with backorder allowed). The analysis of these two
cost components has led to the establishment of 2 number of properties of the stochastic inventory
systems. In particular, it is shown in Zheng (1989) that the optimal order quantity of the (Q,r)
model is larger than the corresponding EOQ, that the EOQ is a good heuristic when economies
of scale prevail, that the cost of the (Q,r) model is bounded below by the maximum of the cost
of the EOQ model and the cost of the base stock model, and bounded above by the sum of these
costs, and that the expected total cost of the (Q,r) system is more robust to the choice of order
quantity than the corresponding EOQ system. By comparing a system with stochastic leadtime
demand with the corresponding deterministic EOQ system, these results provide first cut answers
2
to the analysis of the effect of the variability of the leadtime demand.
The results presented in this paper augment the above results by further showing how changes
in the variability of the leadtime demand affect.the o ptimal control parameters and the system cost
performance. Specifically, we show that when the variability of the leadtime demand is increased:
(i) the optimal order quantity increases, but, somewhat contrary to the conventional wisdom, the
optimal reorder point does not necessarily increase; (ii) the minimum cost of the inventory system
increases, and it increases at a slower rate than and converges to the cost of the optimal base-stock
policy; and (iii) the cost performance becomes more robust to the choice of order quantity. We also
show that both the optimal reorder point and order-up-to level decrease (increase) as the inventory
holding (shortage penalty) cost rate increises, which complement the results on the effects of the
fixed order cost of Zheng(1989): namely, that the optimal order quantity increases and the optimal
reorder point decreases as the fixed ordering cost increases.
Two recent papers are relevant. Gerchack(1990) derives comparative statics for the (Q,r) model
for both backiogging and lost sale models. For bac.klogging models, some of his results are sim-
ilar to ours, but they appear with some qualifications which are not needed in our case. These
qualifications are apparently due to the use of an approximate cost function, which systematically
undercharges holding costs. Gerchack and Mossman(1988) investigate the effect of the leadtime de-
mand variability, and conclude that the relationship between the variance of the leadtime demand
and both the optimal reorder point and the optimal order quantity is not definit!ve. Again, this
discrepancy appears to be due to the use of the approximate cost function.
The paper is organized as follows. Section 2 describes the model and notation. The effect of
changes in the cost parameters is discussed in Section 3. Section 4 is devoted to the analysis of
changes in the variability of the leadtime demand. In section 5, we discuss the sensitivity of the
system performance to changes of the various problem parameters and the potential application of
the cost insensitivity to the choice of order quantity. Section 6 is a brief conclusion.
2. Model and notation
We consider a single-item continuous-review inventory system that faces a stationary stochastic
demand. Unless otherwise specified, the notation and assumptions are the sanie as in Zheng(1989).
The arrivai rate is denoted by Replenishment orders are delivered after a positive leadtime L.
All stockouts are backordered. The relevant costs are a fixed replenishment cost K for each order
3
placed and proportional inventory holding (penalty) costs accumulating at constant rate h (p) per
unit stock (backorder) per unit time. The criterion is the (long run) average total cost per unit
time.
We assume the demand process and the leadtime are such that, under a (Q,r) policy, the
following three conditions are satisfied: (a) both the inventory position and inventory level processes
have a limiting distribution; (b) the fundamental equation IL = IP - D holds and IP and D are
independent, where IL and IP dente the steady state inventory level and inventory position
respectively, D the leadtime demand; (c) IP is uniform between r and r Q. It is. well known
that these conditions are satisfied if the demand process is a Poisson or a renewal process and the
leadtime is constant. These conditions can also be shown to hold when the leadtime is stochastic,
under certain assumptions (see Zipkin 1986), and when the demand process is a Markov-Chain-
Driven process (see Zipkin 1991). These conditions are required for the cost function (2) below to
hold. [Since the entire analysis of Zheng(1989) is based on (2), the assumption of constant leadtime
in Zheng(1989) can be replaced by the above three more general conditions.)
Let G(y) be the rate (per unit time) at which the conditional expected inventory (holding
and penalty) costs accumulate when the inventory position equals y. Let FO be the distribution
function (cdf) of the leadtime demand D. By condition (b) we have
G(y) = E[h(y - p(D - y)+] = (h p) jv F(x)dx - p(y - ED) (1)
where E denotes the expectation over the leadtime demand. It is well known that G(•) is a convex
function. By (c), the average cost function of a (Q,r) system can be written as:
c(Q, r) = AK r+Q G(y ) dy (2)
Equation (2) is exact when the cumulative demand can be modeled as a nondecreasing stochastic
process with stationary increments and continuous sample paths (see Browne and Zipkin 1991). It
is an adequate approximation when the demand is a counting process (and Q is not too small). We
treat both the reorder point and the order quantity as continuous decision variables.
Let y° be the minimum point of GO. It is well known that y° = F-1(.11-p). (Throughout
this paper, we assume, for notational convenience, that F(•) is continuous and strictly increasing.)
When K = 0, the base stock policies are optimal. In that case, y° is the optimal order-up-to level
and G(y°) is the optimal average cost. In the sequel, we refer to y° and G(y°) as the newsboy point
and the newsboy cost, respectively.
4
Let r- and Q" denote the optimal reorder point and the optimal order quantity. The following
lemma is established in Zheng(1989).
Lemma 1 Q = Q" and r = if and oney G(r)= G(r + Q). r• < y° < r` + Q*.
The optimality equations in the above lemma are simply the first order condition of the cost
function. The lut part of the lemma follows from G(e) = G(r* + QI and the convexity of
function G.
3. Changes in the cost parameters
It has been shown (Zheng 1989) that the optimal order quantity increases and the optimal reorder
point decreases as the fixed ordering cost K increases. In order to obtain further comparative
statics results, we need to differentiate varions components of the model with respect to h and
p. For clarity, we will write expressions such as 8G(y)18h without explicitly incorporating the
dependency of G(y) on h in the notation. We also denote dG(y)/dy by G'(y).
Let the optimal order-up-to level be denoted by = r" + Q"). We first show that both
the optimal reorder point and order-up-to level decrease (increase) as the holding (penalty) cost
rate increases. Define a(y) = ERy — D)+ ]. Note that a(-) is a convex increasing function.
Proposition 1 Or* 18h < 0, 8r"18p > 0, OS" 18h < 0, 8S'/8p > O.
Proof: By totally differentiating the optimality condition G(r) = G(r + Q) = c(r,Q) with respect
to h at r = re , Q = Q*, we get
0G(r) , Or OG(r + Q) Or 8Q Oc+ G (r) ah
= ah + G (1. Q)( 7971 + = (3)Ohwhere the lut term has been simplified by recognizing that °c/& = 0 and &IN = 0 at r = r-,
Q = Q . From (1), we have G'(y) = (h + p)F(y) — p and Oc(y)/ah = a(y). From (2), aclah =
(g.+Q. a(y)dy)/Q". Solving for Or* 10h in (3), we get
ar•(f,.r.+Q. a( y ) dY)1(2" — a(**)Oh (h + p)F(r*) — p
Since a(y) is increasing, the numerator is positive. It follows from Lemma 1, F(r") < p/(h + p),
which implies that the denominator is negative. Thus, 8r"10h > O. The proof is similar for the
other three cases.
5
4. Changes in the leadtime demand
In this section. we study how the variability of the leadtime demand affects the optimal order
quantity, the cost performance, and its sensitivity to the choice of order quantity. Throughout theanalysis, we compare systems with different mean and variance of leadtime demand, while assumingthat ail the other parameters (i.e., K, h, p and À) remain unchanged. Note that the cost function(2) depends on the leadtime demand only through the expected inventory cost function G.
We start by briefiy reviewing some useful results from Zheng (1989). To focus -on -the-role oforder quantity, we assume that the reorder point is chosen optimally for any given order quantity.Let r(Q) be the optimal reorder point for a given Q. The reorder-point is characterized by thefollowing lemme:
Lemme 2 For any Q > 0, r = r(Q) if and only if G(r) = G(r Q), and r(Q) < y° < r(Q) 1- Q.
Let C(Q) de min,.min,.c(Q,r). Let H(Q) G(r(Q)),Q > 0, with //(0) G(y°). Sincefrre))+Q G(y) dy = fo H(y)dy, the optimal order quantity solves
C(Q) = „ie.+ I QH(y)dy)IQ. (4)
H(Q) can be interpreted as the marginal (expected) inventory cost for the Q-th unit in a batch.
Since C(Q) is convex, the first order condition of (4) gives
C(Q. ) = H(Q"), (5)
which is simply one of the optimality equations in Lemma 1.
Let A(Q) QH(Q) — g H(y)dy. Condition (5) is then equivalent to the following lemma.
Lemma 3 Q = Q • if and only if A(Q) = ÀK.
Furthermore, we have
Lemme 4 H(•) and A() are increasing convez fonction. H(Q) > eQ, // 1(0) = 0 and H'(Q)
e as Q Do.
6
Lemmas 3 and 4 are illustrated in Figure 1. The following lemma is geometrically obvious, therefore
its proof is omitted.
Lemma 5 For a > 1(< 1) and ci et;e001k4>W1H(Q).
[Figure 1 approximately here]
Before proceeding with the formai aaalysis, it is helpful to conjecture about our results on
the basis of the geometrical intuition given in Figure 1. The asymptotic line of H(Q), Hd(Q) =
hpQ/(h p), can be interpreted as the marginal inventory cost function of the system with de-
terministic leadtime demand. It is geometrically clear that the introduction of variability of the
leadtime demand increases the expected marginal inventory cost. It is also economically intuitive
that a more variable leadtime demand should yield a higher H-curve. With the asymptotic line
remaining the same, we expect a higher H-curve to be flatter. For fixed Q, A(Q) is the shaded
area between the H-curve and the horizontal line z H(Q). At the optimal order quantity Qe,
this area equals AK (Lemma 3). Therefore, a flatter H-curve, which makes the shaded area smaller
for fixed Q, requires a luger Q. Consequently, our first conjecture is that Q* increases with the
variability of the leadtime demand.
Furthermore, since Q" depends only on the shape but not on the absolute height of the H-
curve, it is conceptually helpful to decompose HO in two parts:
H(Q) = G(e) + 1-1.(Q)•
Let C* be the optimal average cost of the (Q,r) system, i.e., C" = minQ>o C(Q). Then, (4) can be
rewritten as
C'=G(y°)+ Cô
dewith C: = minc».0C.(Q) =) (AI( j Ho(y)dy)IQ. H.( . ) can be interpreted as the part of the
marginal inventory cost that can be used to trade off the ordering cost through the choice of order
quantity, and therefore is referred to as the controllable inventory cost. Note that H. is a
vertical shift of H. Therefore, a more variable leadtime demand would be associated with a flatter
H.-curve. Since H.(0) = 0, a flatter Hecurve means 11.(Q) is smaller. Hence, for any Q > 0 fixed,
110(Q) should decrease as the variability of the leadtime demand increases. This leads us to more
conjectures. First, as variability of the leadtime demand increases, the controllable inventory cost
110(Q) is diminishing, so is C. Therefore, the optimal average cost of the system, which is the
7
sum of the newsboy cost and C:, should grow more slowly than the newsboy cost when variability
of the leadtim, demand increases, and it should be close to the newsboy cost when the variability
is high. Second, for more variable leadtime denund, the total average cost should be less sensitive
to the choice of order quantity because Co(Q) is smatier and it is the only part of the total cost
that is affected by Q. We proceed to prove these conjectures analytically.
To proceed with the analysis, we need a dear definition of the variability of the leadtime demand.
We assume in the sequel that the leadtime demand distribution takes the form of F(z)=
where p and a are its mean and standard deviation respectively, and 4i is strictly increasing. Then,the variability of the leadtime demand can be unambiguously represented by We will show howthe optimal control parameters and the optimal colts change as o changes. The above assumption is
certainly satisfied when the leadtime demand is Normal, which is often an adequate approximationwhen the (mean) leadtime demand is not too small. The above construction is also a special case
of the general notion of convex-ordering; see Rothschild and Stiglitz (1970) for a discussion.
We note that the variance of the leadtime demand is determined by both the demand process and
the leadtime. When the demand process is given exogenously, the variance of the leadtime demandis affected only by the leadtime. For deterministic leadtimes, a longer leadtime typically leads toa larger variance of the leadtime demand. When a Normal distribution is used to approximatethe leadtime demand, o is often assumed to be linear to f.t. When the leadtime is stochastic,the variance of the leadtime demand is determined by the variability of the demand process and
by the mean and the variance of the leadtime. More specifically, o can be computed by _using
the conditional variance formula (interested readers are referred to Zipkin 1991 for a detaileddiscussion).
The G-function can now be written as
G(y) = (h + p) 41(z-
)dz - p(y --00 o
= a[(h p) 4,(z)dz ---00
We observe that a change of p in (6) would only cause a horizontal shift of the G(•)-function, whichdoes not affect the newsboy cost nor the H(•)-function. The reexamination of equation (4) yieldsthe following proposition.
Proposition 2 For a given demand process, the optimal order quantity and the minimum cost of
the (Q,r) system are independent of the mean of the leadtime demand.
(6)
8
Therefore, in the sequel, we set = 0 in (6) for notational simplicity. Moreover, we add the
subscript a to all the notation to indicate its dependency upon the leadtime demand variance
(subscript d instead of 0 is used to indicate zero variance of the leadtime demand, which can be
true either when the demand process dateininittic or the leadtime is zero).
It follows from (6) that
G.(0= aG1(Y10) (7)
where G t (y) = (h + p) poe 4(y)dy— py is the (shifted) expected inventory cost function when the
variance of the leadtime demand is 1.
Let e be the minimum point of Ga ( .). The following result is immediate.
Proposition 3 The newsboy cost grows linearly in a, Ge( g ) = crGi(e)•
Proof: By (7), e = agi.
The following lemma is crucial:
Lemma 6 110(Q) = all1(Q1e)
Proof: By definition of H, we need to show
Ga(ro(Q)) = eGi(ri(Q1cr))•
(8)
Since by (7) GrGi(ri(Q/a)) = Ga(ar i (Q1a)), (8) is equivalent to Ga(r„(Q)) = Gcr(ar1(Q1a)).Thus, it suffices to show ra (Q)= ar i (Q1a), which follows from the following equations
G«,(ar1 (Q1a)) = aGi( rt(Q la )) = GrGi( rt(Q/a)+ Q/a)
= G 5( 49r1(Q/a)+ Q)
where the first and the third equations are due to (7), and the second is by Lemma I.
Now, we are able to show
Corollary 1 For any flzed Q > 0, Hc,(Q) is increasing in o.
9
Proof: It suffices to prove 11„(Q)> H1 (Q) for any o > 1. By Lemma 5, 111 (Q/al> Hi (Q)la for> 1. By Lemma 6, II„(Q)= a I 1 i (Q1a). Therefore. //e(Q) > HI(Q). q
Corollary 2 For any fixed Q > 0, 11,;(Q) and are deLrèosing in a; Hf, (Q) j 0 as a 1‘ oo.
Proof: Differentiating the equation in Lemma 6, we have II,,(Q)= I4(Q la). Fix Q > O. The factthat II:,(Q) is decreasing in a follows from the convexity of H1 . 110,e(Q) is decreasing in a because
H:,,,„(Q)(= 14(Q)) is decreasing and 1/,,,„(0) = O. The rest of the corollary is due to 14(0) = O.
Corollary 3 For fized Q > 0, A„(Q) is decreasing in a; A,,(Q) j 0 as cr j oo.
Proof: It follows from Corollary 2 and A,(Q) = Q11,1,(Q) that AgQ) j 0 as a j oo. The corollary
then follows from A,,(0) = 0 and A(Q) = g A'(y) dy. q
The effect of variability of the leadtime demand on the optimal order quantity is now clear.
The following proposition is a direct implication of Lemma 4 and Corollary 3.
Proposition 4 The optimal order quantity Q; increases in cr. Moreover Qa" j oo as a I oo.
We note for contrast that the reorder point is not necessarily mcreasing in o. , particularly whenp is not very large relative to h. Zheng(1989) provides counter examples which show that the
reorder point of a stochastic (Q,r) system can be lower than that of the corresponding EOQ system= 0).
Although the optimal order quantity grows with a, the following proposition shows that it growsat a rate slower than o..
Proposition 5 is decreasing in a, and I 0 as a j oo.
Proof:
ak = A0(C2;) = Q;14(Q;) — .10 He(Y)(1Y
= (72 [ 4-2-10 Hi(Q; /a ) — tnia Hi(Y)cild
= a2A1(Q;/a)•
10
The proposition follows from the fact that A 1 is increasing and A i (0) = O. q
Then the following result is also immediate.
Proposition 6 (a )The optimal conteellable cost C",;„„ is decreasing in cr, and C;0 1, 0 as o j oo;
(b) The optimal mienne cost C; is increasing in a, but the increase is slower than the newsboy
cost, and C; crG i (yî) as a j oo.
Proof: (a) Since 110,,,(y) is decreasing in o, so is the controllable cost function Co(Q) and itsminimum By Lemma 8 in Zheng(1989), we have Co,,Q; < 2À/C, thus 1 0 as ex î oobecause Q; j oo as cr j oo.
(b) The cost function (4) and Corollary 1 imply that C; is increasing in o. C; ti aGi(e) becauseC; = Go (g) Co,,,, 0 as a j oo and Proposition 4. q
Fin*, we show that the total cost is more robust to the choice of order quantity when thedemand variance is larger. More specifically, we show that ea(a) c"ca•77) decreases as o in-
creases. This result augments the inequality ea (a)< ed(a) (where ea(a) = 1(a + 1/a)) establishedin Zheng(1989).
Proposition 7 For a > 0, ea(a) is decreasing in a, and eo (a) j 1 as o j oo.
Proof:
Co(aQ;) )tk + Ha(y)dy fe: ii,(y)dyeo(a)= —
C; aQ;C;
rce; Ha(Y)dY;" Q;Hu(Q7,)1 fia Ha(13Q;)d,C1
)-(1 +a Ho(Q;)1 r HHi0Q;,a)
+ J1 (zicy) di3)
where the third equation is due to (5) and the fifth Lemma 6. In view of Proposition 5, it sufficesto show that
clef Hi(AQ)H1(Q)
11
is increasing in Q for > 1 and decreasing for d < 1. We show the former, the latter is similar.
For fi > 1,
;11(Q) = HuQ)[0e1(PQ)111(Q)—
where the inequality follows from
egh(RQ)] >
HI(PC2) Ht(AQ)14(Q) Ait(Q)
where the first inequality is due to the convexity of H1 and the second follows from Lemma
5. Sensitivity of the System Cost
In this section, we briefly discuss how the problem parameters affect the cost performance of a
(Q,r) system. It is well known that, due to the square root formula, the cost of the EOQ model
is robust to change in all its parameters (K, h, p, A). It would be interesting to know whether this
robustness carries over to the cost of the (Q,r) system.
First, since the ordering cost K affects only the cost function C., which is smaller than that
of the EOQ and diminishing as o increases, the system cost is robust, and it is more robust when
the leadtime demand is more variable. This can be verified formally as follows. Differentiating
(AI( fe; He (y)dy)IQ; with respect to K yields dC;IdK = XIQ;. Since Q; increases in o,dC;IdK decreases in o.
The effect of change in the holding cost h or the penalty cost p is more involved because the
change affects both the newsboy cost and Since the newsboy model does not enjoy the sanie
degree of insensitivity as the EOQ model, we do not expect that the average cost of the (Q,r)
system to be as robust to change in h or p, unless the effect of economies of scale dominates.
We can dso quantify, at least approximately, the effect of a change in the leadtime on the cost
performance of the (Q,r) system. A change in the leadtime affects both the mean and standard
deviation of the leadtime demand. Since the mean does not have any impact on the optimal average
cost, the system's cost would be affected only through the change of o. Assuming that the leadtime
demand is constant and o is linear in ft-, we conclude, by Proposition 6, that the change in the
system cost is sublinear in ././, and approximately linear in -IL when L (and hence o) is large.
When the leadtime is stochastic, not only its mean, but also its standard deviation would have an
impact on o. The reader is referred to Zipkin(1991) for a discussion.
12
If a change in À does not cause a change in the leadtime demand, thon its effect on the system
performance is identical to that of K because À and K are symmetric in the cost function Ciee (2)).
This assumption, however, is very ite t practice. Typically, a change in the demand rate
induces a change in o. In this caue,thei0bal effect is more complex. Assuming that the leadtime
L is constant and the demand process is Poisson (but approximately Normal), we have o=
Therefore, the Newsboy cost changes linearly in f (Proposition 3); Cc, ,̀,, is affected by change of
both A and o. The effect of A on CZ, is sublinear in N/X. Since the effect of a on CZ„ is in the
opposite direction as indicated by Proposition 6(a), the total average cost C:„." must be sublimer to
VI In other words, the average cost of the (Q,r) system is more robust to change in the demand
rate than that of the EOQ model.
Finally, we comment on Proposition 7, which states that a larger variance in the leadtime de-
mand makes the average cost more robust to the choice of order quantity assuming the monter point
is always chosen optimally. Care is needed in interpreting this insensitivity result. In particular,
we cannot condude from this proposition that the average cost is insensitive to inaccurate data.
The reason is that when a suboptimal order quantity is chosen because of the inaccuracy ofsome
pazameter estimates, the reorder point is unlikely to be set optimally (with respect to the chosen
order quantity).
This proposition, and Theorem 4 in Zheng(1989), are motivated by their potentiel nsefulness
for analyzing multi-stage stochastic systems. For multi-stage systems with constant demand, such
an insensitivity property of the EOQ model has led to remarkable worst case performance bounds
for the power-of-two heuristic policies (Roundy 1985, 1986). Here, we briefly discuss how-there
insensitivity results for the (Q,r) model could be useful for similar analysis on some plausible policies
for multi-stage stochastic inventory systems. For multi-stage inventory systems where demands are
stochastic and where there are fixed costs for inventory replenishment at each stage, a plausible
control policy is to use an order-quantity/reorder-point policy at each stage. Since upstream stages
are the suppliers for their downstream stages, the order quantities of different stages should be
coordinated. For example, it is plausible to use the "integer ratio policy," under which the order
quantity of an upstream stage is restricted to an integer multiple of that of a downstream stage
(if the downstream stage is the only customer of the upstream stage); see e.g. De Bodt and
Graves(1985). Such a quantity coordination across different stages imposes a constraint on the
choice of order quantities, but not on the reorder points; that is, while the order quantity at a stage
may be required, for the global coordination, to deviate from its own "optimal" value the reorder
point remains "local", and can be chosen optimally for the choice of order quantity. Our insensitivity
13
results indicate that such a quantity coordination would not cause a significant cost increase from
each stage's minimum cost. For systems with deterministic demands, Roundy(1986) showed by his
lower bounding theorem that the sum of the singiereage minimum cost of all the stages (with some
additional minor constraints on the order quantities i ni a. sumer vound on the system-wide average
cost, which in turn leads a very tight worst case performance of the power-of-two policies (whichare a subset of the integer ratio policies). For stochastic systems, a parallel lower bounding theorem
seems significantly more difficult to formulate. However, even in the absence of such a theorem, theheuristic policies that require quantity coordination across different stages are much encouraged byourInsensitivity results for the single-item (Q,r) system. For a serial system with Poisson demandat the lowest stage, an accurate cost evaluation procedure has been devised (Chen and Zheng 1991
a) for echelon stock order-quantity/reorder point policies. Numerical studies(Chen and Zheng 1991
b) show that for a fairly wide range of data these policies are indeed close to optimal. Research onworst case analysis of heuristic policies for multi-stage systems is in progress.
6. Conclusion
Combining the results of this paper with those of Zheng(1989), we now have a more completeunderstanding of the behavior of (Q,r) systems. By assuming that the leadtime demand is (ap-prcximately) Normal, a (Q,r) system can be fully characterized by the cost parameters K,h, p and
the demand parameters o. It is shown in Zheng(1989) that when K is large relative to cr, the
(Q,r) model behaves like the EOQ model in every respect, and that the optimal control parameters
and the optimal average cost of the EOQ model (with backorder allowed) are very good approxi-
mations of those of the (Q,r) model. The results of this paper show that when a is large relative
to K, on the other hand, the expected marginal inventory cost function Ha is relatively flat. In
that case. we can use a large order quantity to offset the ordering cost without incurring much
increase in the average inventory cost; consequently, the total average cost of the system is close to
the newsboy cost.
Strictly speaking, the (Q,r) model only applies to continuous review inventory systems with
unit demand. When the inventory system is reviewed periodically, or when the demand size is
random, the reorder point can be "overshot," in which case the control policy must be revised. A
well known inventory system that accommodates the overshot is the (s,S) system, where an order
is placed to increase the inventory position to S as soon as the inventory position drops to or below
s. Here s denotes the reorder point and S the order-up-to level. The order quantity is no longer
(S-s), the difference between the order-up-to level and reorder point, but that plus the overshot,
which varies from order to order. Another variation that can accommodate overshot is the so
called (nQ, r) system, where an order is placed whenever the inventory position drops to or below
the reorder point r. The order quantity is chop te be an integer (n) multiple of Q such that the
inventory position is raised to between r+1 and r+Q. For recent analyses on these systems, see
Zheng(1990), Zheng and Federgruen(1991) and Zheng and Chen(1990). Although the (Q,r) model
appears as a special case of the more general (s,S) and (nQ,r) modela, the qualitative properties
derived for the former shed light on these general stochastic inventory systems. It should especially
be emphasized that when the overshot is not significant relative to the order quantity, the behavior
of (s,S) and (nQ,r) systems is similar to that of (Q,r) systems.
Acknowledgment
The research of the first author was supported in part by NSF grant DDM 9111183. The anthors
would also like to thank Professor Paul Zipkin for sharing part of his recent manuscript (Chapter 6
of Foundation of Inventory Management, Draft Version 0.1, November, 1991), in which proposition
3 of this paper is independently observed.
References
[1] Browne S. end P. Zipkin 1989 Inventory Models with Continuons, Stochastic Demands, Grad-
uate School of Business, Columbia University.
[2] Chen F. and Y.-S. Zheng(1991a) Evaluating the Performance of a Serial Inventory System
with Stochastic Demand, Working paper, Department of Decision Sciences, Wharton School,
University of Pennsylvania.
[3] Chen F. and Y.-S. Zheng(1991b) A Lower Bounding Framework for Stochastic Inventory Sys-
tems with Setup Costs Working paper, Department of Decision Sciences, Wharton School.
University of Pennsylvania.
[4] deBodt, M. A. and S. C. Graves(1985) Continuous Review Policies for a Multi-Echelon In-
ventory Problems with Stochastic Demand, Management Science, 31, 1286-1295.
15
[5] Federgruen A. and Y.-S. Zheng 1988 A Simple and Efficient Algorithm for Computing Optimal
(r, Q) Policies in Continuous-Review Stochastic Inventory Systems, Operations Research, to
appear.
[6] Gerchack 1990 Analytical Comparative Statics for the Continuous Review Inventory Mode&
Operations Research Letters V.9, 215-217.
[7] Gerchack and Mossman 1988 The Effect of demand mndomness on lot sizes, safety stocks
and costs, working paper, Department of Industrial and Operations Engineering, University of
Michigan.
[8] Hadley, G. and T. M. Whitin 1963 Analysis of Inventory Systems, Prentice-Hall, Englewood
Cliffs, NJ.
[9] Lee, H. and Nahmias, S. 1989 Single product, single-location models, Chapter 2 in Handbook in
Operations Research and Management Science, Vol. 4: Logistics of Production and Inventory
(eds. S. Graves, A. Rinnooy Kan and P. Zipkin), North Holland, Amsterdam.
[10] Rothschild, M. and J.E. Stiglitz 1970 Increasing Risk: a Definition, Journal of Economic
Theory, 2, 225-243.
[11] Roundy, R. 1985 98% Effective Integer-Ratio Lot- Sizing for One Warehouse Multi-retailer
Systems, Management Science, 31, 1416-1430.
[12] Roundy, R. 1986 A 98% Effective Lot-Sizing Rule for a Multi-Product, Multi-Stage Production
Inventory Systems, Mathematics of Operations Research, 11, 699-727.
[13] Zheng Y. S. 1989 On Properties of Stochastic Inventory Systems, Management Science, to
appear.
[14] Zheng Y.-S. 1990 A Simple Proof for Optimality of (s, S) Policies in Infinite Horizon Inventory
Systems Journal of Applied Probability, to appear.
[15] Zheng Y.-S. and F. Chen 1990 Inventory Policies with Quantized Ordering, Naval Research
Logistics, to appear.
[16] Zheng Y.-S. and A. Federgruen, 1991 Finding Optimal (s,S) Policies is About as Simple as
Evaluating a Single Policy Operations Research 39, 654-665.
[17] Zipkin. P. 1986 Stochastic Leadtimes in Continuous-rime Inventory Models, Navel Research
Logistics Quarterly, 33 763-774.
16
[18] Zipkin. P. 1991 Foundation of Inuentory Management, Version 1.0, Columbia University,
Manuscript to be published.
17
Ce = H(Q*
0
Q*
Figure 1
HO, A() — functions and the optimality condition
• INSEAD WORKING PAPERS SERIF.S
1988
88/01
88/02
8/1/03
/04/84
88/88
88/06
88187
88/08
101/09
88/10
88/11
Miehael LAWRENCE andSpyros MAKRIDAKIS
Spyms MAKRIDAKIS
larmes TEBOUL
Susan SCHNEIDER
Chartes wYrws7
Reinhanl ANGELMAR
Ingemar DIERICKXand Karci COOL
Reinhard ANGELMARand Susan SCHNEIDER
Bernard SINCLAIR-DESGAGNÉ
Bernard SINCLAIR-DESGAGNÉ
Bernard SINCLAIR-DESGAGNÉ
"Factors affectif* judgementsd forecans andconfidence intervals". January 1988.
"Predicting tressions and miter t'ondin/points". January 1988.
"De-induserialiee service for quality". January1988.
"National vs. corporate culture: implicationsfor humas rentame management". January1988.
"The sninging is Europe mut ofstep?", January 1988.
"Les conflits dans les canaux de(fignIention". January 1988.
"Competitive advantage: a resource hasedperspective', lanusry 1988.
*Issues in the study of organizationalcognition", February 1988.
"Prise formation and malle design throu8hhideus •. Fehruary 1088.
"The robustness of »me standard miction:tome forms", Fehruary 19811.
"When 8100011arY llrilmles are emeilihriumhidrfing strategy: The single-crossingproperty", Fehmary 1988.
8R/12 Spyms MAKRIDAKIS
88/13 Manfred KETS DE VRIES
88/14 Alain NOEL
RS/15 Anil DEOLALIKAR andLars-Hendrik ROLLER
lt8/16
Gabriel HAWAWINI
R8/17 Michael BURDA
88/18
Mich»! BURDA
88/19
M.I. LAWRENCE andSpyros MAKRIDAKIS
88/20 Jean DERMINE.Damien NEVEN andJ.F. THISSE
88/21 lames TEROUL
88/22 Lars-Hendrik RÔLLER
"% dom fines and managers in the 21,4century", Fehmary 1988
"A/mâle:nia ba Imminent:al lite: theorganization man revisited", February 1988.
"The interpretatiou of stralegies: a study ofthe impact of CEOs eu thecorporation". Math 1988.
"The production M' and rentras frettaindastrial innorMion: an ecomemetrieanalysis for a deve1oping country". December1987.
"Market 'Miette and egnity priting:international «idem sud implications forlebel investing", Math 1988.
"Meetesliilie 8998011.14 tees ofadjudant* and thenannevior of Europe»NoPlornent", Septrnapr 1987.
"Rellectioas en •Walgilitmtploymene inEurope", November 2987, revised Febniary1988.
"hathvidasal Win in Jelgeneeee ofconfidence". Mare 1988.
"rentoile Warens le mutuel fines. anegmlihrirm made", March 1988.
"De-iedustriaree service for quahly". March1988 (88/03 Revised).
*Prao« Quadrille Fauchions with amAppheatine to AT&T", May 1987 (Reviaed
March 1988).
B. Expen ECK/10 and
Herudg LANGOHR
Evereue S. GARDNER
and Spyrns MAKRIDAKIS
Sjur Didrik FLAM
ami Georges ZACCOUR
Mammy/ KR ISHNAN
Lors-Hendrik Rett.ult
Sumantra GHOSHAL and
C. A. BARTLETT
NareM IL h4ALIIOTRA,
Christian PINSON and
Arun K. /AIN
'Information (Mercure. menas of payaient.and fakeover mendia. Public and Private
tender («ers in France", July 1985, Sixthrevision, April 1988.
"The future of forecacting". April 1988.
"Serni-competitive Cournot equilihrimn inmultistage oligaprelies", Avril 1988.
"Entry gameivith revalut* capacity".April 19811
"Hie multinational corporation as a »imitait:perspectives Iront interorganizational
thenry". May 1988.
"Consumer cognitive tomplexity and thedintensionality of multidintensional scaling
erlarilturatirms". May 1988.
88/24
88/26
IG9/27
88128
811/29
88/30
Catherine C. ECKEL
"The financial faitout faon Chernohyl: risk
and Thini VERMAELEN perceptions and regulatory remonte". May19118,
11/1/31 Sumantra GHOSHAL and
*Creation, adoption. and diffusion ofChristopher BARTLETT
innovations by subsidiarien of multinationalcorporations", lune 1988.
88/32
Kama FERDOWS and
"International manufacturing: positimiingDavid SACKRIDER plants for surcots", lune 1988.
Rit1.13
Mihkel M. TOMBAK
*The importance of flexibility in
manufacturier". lune 1988.
811/34 Mihkel M. TOMBAK "Flexibrity: an important dimension inInagefachtliant". June 1988.
88/35 Mihkel M. TOMBAK "A strate* analyski of inventaient in flexible
mannfaduring systemeduly 1988.
/18/36 Vikas TIBREWALA and "A Predirtive Test of the NIM Medd thatBruce BUCHANAN Contrais for Non-stationarity", June 1988.
BR/37 Murugappa KRISHNAN "Reperde" Price-Liability Competition Ta
Lars-Hendrik RÔLLER Imprime Welfare", July 19118.
811/3* Manfred KETS DE VRIES "The Motiver* Rote of Easy : A Forgotten
Factor in Mrstrusteneet", Apte 88.
tift139 Manfred KETS DE VRIES "Ille Leader as Mirror t ChuintaReniions", July 1988.
88/40 Josef LAKONISHOK and "Annandens price behavier AroundThen VERMAELEN reperdante tender atm". Auges: 1988.
118/41 Charles WYPLOSZ "Asaymetry kt the FMTatajteaatiamal ortordeuse", Aune 1988.
88/42 Paul EVANS "Ornadisational deeelellitnt thetransnadonid enterminnulune 1988.
88/43 B. SINCLAIR-DESGAGNÉ "Grum dedeine autiout systeons int pimentBayesian rationality",egotember 1988.
88/44 Estero MAHMOUD and "lie aide of the art Md &More directionsSpyma MAKRIDAKIS in conibinim forecatts", September 1988.
SR/45 Robert KORA/CZYK "As eagairical investigation of internationaland Claude V1ALLET auget Friche. November 1986, revised
August 1988.
88146 Yves DOZ and "Ems iodent ta guitoune: a ormetsAmy SHUEN Framework for oalenerthips", Augura 1988.
*8/47 Alain BULTEZ,Els GUSBRECHTS,
"Asynnnetric cannitialiran hanta substitateitems lided by retenue, September 1988.
118/23 Sjur Didrik FLAM
"Fneolibres de Nash-Conne( dans le marchéand Georges ZACCOUR européen du Ras: un mn nh les solutions en
bonde ouverte et en feedhack ceiincident",
Mars 1988.
"Refkictimet on 'M'ait rmemploymene inEurope. II". April 1988 revised September1988.
"Information asymmetry end equity Wons'.September 1988.
"Mame» expert systems: front intentionentres »doline. October 1987.
"Technoinitv. work. and tlw organir.ation:the impact of expert systems". luly 1988.
Cornilion and arganizational usudysis:Mmes minding the garer. September 19101.
"Wkatever lutppened to the philosopher-king: the leader's addiction to power,September 1988.
"Strategic choke of Brade productiontechnologies and ...effare implications".October 1988
"Method of moutents tests of contingentdaims amet locking modela', October 1988.
"Sse-seeted portfolios »d the violation ofthe ramdam walk hypnithmic: Adclitionalempirical »Mente and implication for testsof »et pria» modela", lune 1988.
88/59 Martin K1LDUFF
88/60 Michel BURDA
101/61 Lars-Hendrik RÔLLER
88/62 Cynthia VAN HUILE,Tb» VERMAELEN andPaul DE WOUTERS
118/63 Fernando NASCIMENTOand Wilfried R.VANHONACKER
88/64 Kan. FERDOWS
88/65 Arnaud DE MEYERand Kasra FERDOWS
118/66 Nathalie DIERKENS
Paul S. ADLER andKasra FERDOWS
'The interpersonal «nem of dechionguidant a social compatis» approach toorganisational choke•, November 1988.
"h mismatch moly the probiem? Someestimes of the Chehvood Gate II »delwith US data", September 1988.
"Modelling »st structure: the Bell Systemrevisiter, November 1988.
"Itegideon, taxes and the market fercernera« »MM in Belgium", September1988.
"Strategic pricing elitilihestudiated consumerdiamides h a dynannetiopnly: a isumericalanalysa', October llie
"L'Isard» stralegicodlin fer internationalfatteritu •, December SM.
"Quality isp, technology done, October 1988
"A dichniden et met umemew ofistlineedan annuotry: the »ample of Myesand Midler modal er the importance of themuet Motta» et tienne, December 1981
'The chef hennie« effriter". December1988.
Philippe NAERT andPiet VANDEN ABEELE
/81/48 Michael BURDA
88/49 Nathalie DIERKENS
P41/50
Rob WEITZ andArnoud DE MEYER
88/51 Rob WEÎFZ
81/52 Susan SCHNEIDER andReinhard ANDELMAR
88/53 Manfred KETS DE VRIES
88/54
Lare-Hendrik RÔLLERand Mihkel M. TOMBAK
88/55
Plier BOSSAERTSand Pieux HILLION
118/S6 Pierre HILLION 88/67
1989
89/01
89/02
88/57
l41/58
Wilfried VANHONACKER 'Data transferalaity: estintating the renon»and Lydié PRICE effect of future mots based on historien,
IltsdnItY'. October 1988.
B. SINCI:AIR-DESGAGNÉ •Ameraing econoweic inequality", Novemberand Mihkel M. TOMBAK 1988.
Joyce K. BYRER and "lise impact of language *mies ee DSSTawfik JELASSI
digne, Jimmy 1989.
Louis A. LE BLANC
MM software seloction: • multiple criteliaand Town JELASSI
&chias methodoiage, lenuary 1989.
B. SINCLAIR-DESGAGNÉ strategies: 1", February 1989.
89/07 Damien 1. NEVEN "Structural adiustment in Farnuan retailbanking. Some view from industrialorganisation", lanunry 1919.
89/08 Arnaud DE MEYER and
"Trends in the due :puent of technology
Hellmut SCHÜTTE and finir effectn on the production structurein the European Community", lanuary 1989.
89/09 Damien NEVEN. "Brand praferation and entry detemence".Carmen MATUTES and Penalty 1989.
Marcel CORSTJENS
119/10
89/11
Nathalie DIERKENS.Bruno GERARD andPierre HILLION
Manfred KETS DE VRIESand Alain NOEL
°A market huard apprnath te the vibrationof the mets in place and the gmuth°paon:Inities of the ficm", December 1988.
"Under:tan/mg the leader-strategy interface:application of the stratepic relationshipinterview method". Fehruary 1989.
89/12 Wilfried VANHONACKER dynamic rupture une« whenthe data are nubject to differeat temporalafereltatiore, lanuary 1989.
89/03 Beth H. JONES andTamlik JELASSI
'Ne:tad:Won support: the «Tut; of computerintervention and conflict lent on hargainingutcmue", lanunry 1989.
"I,ading in:purement in manufarturingperformance: In aearch of a new theory",lanuary 1989.
"Shared hidery or nhared culture? Theeffects of lime, culture, and performance oninatitutionaliudina in aimulatednre.aniutione, lanuary 1989.
89/13 Manfred KETS DE VRIES
89/14
Reinhard ANGELMAR
89/15
Reinhard ANGELMAR
89/16
Wilfried VANHONACKER,Donald LEHMANN andFareena SULTAN
•Ibe imposer syndrome: a &quiet:*phenomenon in organizationd lire", February1989.
"Proded innovation: a tord far enrupMitiveadvantage", Mare 1989.
•Evalaating ■ Rem's prodact innovationperformance", mura 1919.
"Condining related and marne data in limerregrension modela", Febmary 1989.
som4 Kama FERDOWS andArnaud DE MEYER
89105
Martin K1LDUFF andReinhard ANGELMAR
89/06
Mihkel M. TOMBAK and "Coordinating manufacturin* and bruine«89/17
89/18
89/19
89/20
119121
89/22
89123
89/24
"Changement olgankationnel et réalitésculturel/es: entantes franco-andricairm",Mach 1939.
infonnetion anynumetry. market failure andjoint-vealuen: thug), nad evidence,Marck 1989.
Condreing relatent rid »orne data in Ruerregrembm medeteeiiiinined Match 1989.
"A rational ramdam indmvier made, ofchoke", Revimd 3fareh 1989.
"ledlerwe of maredaehring improvernentprogrammes on peetbnnalre", April 1989.
"What in the rale affleuriez inpnychasualysis?" April 1989.
"Fmaity rtdt puede and the priant* ofrenier «dam aide April 1989.
'The social denfteretion or redify:
Organinalirmiduadtkt as social dramezApril 1989.
Gilles AMADO,Claude FAUCHEUX andAndré LAURENT
Srinivaaan BALAK-RISFINAN andMitchell KOZA
Wilfried VANHONACKER,Donald LEHMANN andEmmena SULTAN
Wilfried VANHONACKERend Russell WINER
Arrmud de MEYER andKama FERDOWS
Manfred KETS DE VRIESand Sydney PERZOW
Robert KORAJCZYK andClaude VIALLET
Manin KILDUFF andMitchel ABOLAFIA
89/25 Roger BETANCOURT andDavid GAUTSCHI
89/26 Charles BEAN.Edmond MALINVAUD,Peter BERNHOLZ,Francenco GIAVAllIand Charles WYPLOSZ
89/27 David KRACKHARDT andMartin KILDUFF
89/28 Manin KILDUFF
89/29 Robert GOGEL andJean-Claude LARRECHE
89/30 Lars-Hendrik ROLLERand Mihkel M. TOMBAK
89/31 Michael C. BURDA andStefan GERLACH
89/32 Peter HAUG andTawfik /ELASSI
89/33 Bernard SINCLAIR-DESGAGNÉ
89134 Sumantra GHOSHAL andNittin NOHRIA
89/35
Lean DERMINE andPierre IIILLION
"Two meuglai characteristirs of reliamanets and their amimie comenuenres"Match 1989.
"Macroeconnmic peries for 1992: thetransition and aller". April 1989.
"Frientiship patterns and cuberaiattributions: the control of organizationaldiversity", April 1989.
"The interpersonal structure of &titillamakis*: a modal contrariants appmach Inorganitationid claire", Revised April 1989.
"The battiefield for 1992: omettra %tallethend geographic manne", May 1989.
"Conspetitior and Investment in Finit*Technologies", May 1989.
"Intertempond priera and the US (radebalance in durable gonds", luly 1989.
'Apparition and estimation of a mulecriant deckien support system for thedynamic Medina of U.S. manufactura*locations-, May 1989.
"Design flextinlity in monopsonistirindustriel", May 1989.
"Requisite variely verset sluwed vidons:managing corporste-division rtiMionships inthe M-Ferro eremenation", May 1989.
r*le teilles and the man« vals*of banks: The case of France 1971-1981",May 1989.
89/36 Martin KILDUFF
89/37 Manfred KETS DE VRIES
89/38 Manfred KETS DE VRIES
89/39 Robert KORAJCZYK andClaude VIALLET
89/40 Balaji CHAKRAVARTHY
89/42 Robert ANSON andTawlik IELASSI
89/43 Michael BURDA
89/44 Balaji CHAKRAVARTHYand Peter LORANGE
89/45 Rob WEITZ andAmoud DE MEYER
89/46 Marcel CORSTIEt4S,Carmen MATUTES andDamien NEVEN
89/47 Manfred KETS DE VRIESand Christine MEAD
89/48 Damien NEVEN andLem-Hendrik RÔLLER
•A disert:118nel apparat* te miel »Works:the case of organintinstal choke. May 1989.
"The organisation", foui: balancine aleader% harde, May 1989.
"The CFA blues", lune 1989.
" Aa empirital inventigatien of internationalmet riche. (Reviaed lune 1989).
•Martagetnevat system% fer innovation andprodnetivity", lune 1989.
"A devtiopment ?Menue fer computer-98001011•11 rwallirt atitillion", July 1989.
"A une an firingnitigind suturante henelitsin %guillotinai anmetiatiment", /une 1989.
"Strategic adouba»le nnolti-lweinessfirme, lune 1989.
*Mannatiog expert ..,Items: • framework andcase Mady", lune 1989.
"Faltry Enneregratera •, luly 1989.
"The global •tinention in leadership andorganisation: mues and contrevenir/1", April1989.
"European identifias end trade flows",Autun 1989.
89/41 B. SINCLAIR-DESGAGNE *The strategic sun* of prenons•, luneand Nathalie DIERKENS 1989.
89/49 Jean DERMINE
119/50 Jean DERMINE
119/51 Spyms MAKRIDAKIS
89/52 Arnoud DE MEYER
89/53 Spyroa MAKRIDAKIS
89/54 S. BALAKRISHNANand Mitchell KOZA
89/55 H. SCHLITTE
"Ilote, country control and mutuelrecognition", luly 1989.
"The specianzation of financial institutions.the EEC mode)", August 1989.
"Sliding simulation: e neve apprnach te Limeseries forecasting", July 1989.
-seberteaing develnpment cycle tintes: •mannfacturer's perspective. August 1989.
"Why comhining %sults?". July 1989.
*Organisation cons and e theory of jointventures". September 1989.
"Fawn-Japonese cooperation in informationtechnology", September 1989.
89/62 Arnoud DE MEYER(TM)
89/63 Enver YUCESAN and(TM) Lee SCHRUBEN
89/64 Enver YUCESAN and(TM) Lee SCHRUBEN
89/65 Suturera DUTTA and(TM. Piero BONISSONEAC, FIN)
89/66 B. SINCLAIR-DESGAGNÉ(TM.E,P)
89/67 Peter BOSSAERTS and(FIN) Pierre HILL/ON
"Technology strate*/ and international RADaperntions". October 1989.
"Equivalogre of simulation*: A graploapproach", November 1989.
Compiexity of simulation gondele: A araphthenretit apprentie, November 1989.
''MARS: A merl:ers and acquisitionsmanade" systtune, November 1989.
*On the reaulation of proceoreenentNovember 1989.
"Market miormignecture 'Mets ofRevenante« intervention in the forelegvienne market•, Dota aber 1989.
89/56 Wilfried VANHONACKER "On the practical usefednem of neetaaerutlysisand Lydia.PRICE mes". September 1989.
89/57 Taekwon KIM,Lars-Hendrik RÔLLERand Mihkel TOMBAK
89/58 Lars-Hendrik RÔLLER(FP,Thi) and Mihkel TOMBAK
89/59 Manfred KETS DE VRIES,(0I1) Daphna ZEVADI,
Alain NOEL andMihkel TOMBAK
89160 Enver YUCESAN and(TM) Lee SCHRUBEN
89/61 Suran SCHNEJDER and(An) Arnoud DE MEYER
"Market grevant and the diffusion ofundliprodeut technologies", September 1989.
"Strategic aspects of fleitelde productiontechnologies", October 1989.
"Locus of control and entrepreneurship: athree-country comparative study", October
1989.
"rantulation graples for design and analysis ofdberete event simulation modes", October
1989.
Interpreting end responding Io singeait.issues: The impact of national culture,October 1989.
1990
90/01 B. SINCLA1R-DESGAGNÉTM/F,P/AC
90/02 Michael BURDAEP
90/03 Arnoud DE MEYER
TM
90/04 Gabriel HAWAWINI andFIN/EP Erie RAIENDRA
90/05 Gabriel HAWAWINI andFIN/F,P Benrand IACQUILLAT
lhoavaidabie Moclauldlige, January 1990.
fflepeopenotie ColneolIllan, Conte ofAdjudant«, and thelbiloarionr of EuropeanManufacturing Fantileneent", lanuary 1990.
•Managegoeut of Counnunkatina inInternational lemme and Development',lanuary 1990.
"The Trnagronnitign or the %mnoFinancial Services Industry: Fon.Fragmentation to botegration*, lanuary 1990.
.E•rtell111 bey *latine: Tenant 1992and %your, Ume 1990.
90/06 Gabriel HAWAWINI and "Integration of European Equity Markets:FIN/EP Erie RAIENDRA beplicatimm of Sine:nal Change fer Key 90/17 Nathalie DIERKENS "Information Asymmetry and F.qvity
Market Participants tel and Beyond 1992".lanuary 1990.
FIN Reviaed lanuary 1990.
90/18 Wilfried VANHONACKER "Magagerial Draisine Raies and the90/07 Gabriel IlAWAWINI "Stock Market A/101111dieli and the Pricing of MKT F.alimadon of Dynainit Sales Restes»FIN/EP Fsmity on the Tokyo Stock Exrhange",
lanuary 1990.Model •, Revised lanuary 1990.
90/19 %th JONES and "Tbe KIWI of Computer Inlemention and90/08TM/EP
Tawfik JELASSI andB. SINCLAIR-DESGAGNÉ
"Modelling *ah MCDSS: What »Mn«Effiles?". January 1990.
TM Tawfik JELASSI Tati: Saurante ou Rariaining Unicorne",February 1990.
90/09 Albedo GIOVANNINI "Capital Controls and International Trade 90/20 Tawfik JELASSI, "An introdection ta Croup Draisine »dEP/I1N and lac WON PARK Finance", lanuary 1990. TM Gregory KERSTEN and Nrantiation Support", Fehnary 1990.
Stanley ZIONTS90/10 Joyce BRYFR and "The Impact of Language Theorim on MSTM 'nova JELASSI Dialog", ;gentry 1990. 90/21 Roy SMITH and "Recollait:radium of Global Sec:trille*
FIN Ingo WALTER Industry in the 199re.Fenaary 1990.9011I Enver YUCF.SAN *An Overview of Frequency DemainTM Mea:odelette for Simulation Sensitivity 90/22 logo WALTER •Farepaan Pinamitibligration mut Ils
Analysis", Januar, 1990. FIN Impticatiomt for the Uilltd States•, February1990.
90/12 Miehael BARDA "Feellaral Change. Unemployment Renefitsand Iligh Unemployment: A U.S.-European 90/23 Damien NEVEN "EEC lotettratioe Mem& 1992: SomeComparium", lanuary 1990. EP/SM Distrbutineal Aspacts", Revimd December
192990/13 Soumitra DUITA and •Apprandetate %menine about Temporal1/11 Shashi SHEKHAR Commtraints in Real Time Planning and 90/24 Lars Tyge NIELSEN "Positive Prime in cArm". lanuary 1990.
Search", /anuary 1990. FIN/EP
90/14TM
Albert ANGEHRN andHana-Jakoh LÜTH1
•Ireseal Interactive Modelling and IntelligentDSS: Petting llwory hen Practice". January
90/25FIN/EP
Lars Tyge NIELSEN "Elisa.» et Fmailihrione in CAPM",January 1990.
1990.90/26 Charles KADUSHIN and •Wily netwericiam Faits: Double lands »d
90/15TM
Arnaud DE MEYER,Dirk DESCHOOLMEESTER,Rudy MOENAERT and
"The Intered Technological Renewal of a%miens Unit with a Mature Technology".January 1990.
OB/BP Miehael BRIMM the Limilatiosta of Shed» Networke,February 1990.
Jan BARBE 90/27 Abbas FOROUGH1 and •NSS Sol:Mun Io Meer N'inaction1111 Tswfik IELASSI Sheaddim Mets', February 1990.
90/16 Richard LEVICH and "Tas-Driven Regolatory Drag: EuropeanFIN logo WALTER Financial Center: in the 1990's", lemme 90/211 Anmud DE MEYER 'Tic Manufacturing Contstiontiou te
1990. TM Innovation", February 1990.
90/40 Manfred KETS DE VRIES "Leaders « the Coach: The case of Roberto90/29 Nathalie DIERKENS "A Discuesion of Correct Mesures of OB Calvi', April 1990.I1N/AC Information Asymmetry", January 1990.
90/30 Lies Type NIELSEN "Te Expetted U$Ifty of Portfolios of9n/41
FIN/EPGabriel HAWAV/INI,117115k SWARY and
"Capital Market Reaction to theAnortarscement of Internat, Rauking
FIN/EP Assets", Mare 1990. lk HWAN JANG Legidatinn", Mach 1990.
90/31 David GAUTSCIII and "What Devinions U.S. Retail Manias?". 90/42 Joel STECKEL and "Crocs-Vandatind Remmena Marker inMKT/EP Roger BETANCOURT Fehmary 1990. MKT Wilfried VANHONACKER Marke/MI Research". (Revised April 1990).
90/32 Srinivamn BALAK- "Informatima Asymmetry, Adverse Selection 90/43 Ruben KORA1CZYK and "FAmity Ride Prends and the Peint of
SM RISHNAN and and John-Ventures: Throry and Evidence". FIN Claude VIALLET Foreign Excluante Risk', May 1990.
Mitchell KOZA Revised, la cary 1990.90/33 Carco SIEHL, 'The Rale of Rites of lei:ration in Service 90/44 Gilles AMADO, .01191dienould Chante nad CulturalOB David BOWEN and Deliver'''. Match 1990. 011 Claude FAUCHEUX and Rendes: Franco-American Contres", April
Christine PEARSON
90/45
André LAURENT
Soumitra DUTTA and
1990.
elategratint Case RIO« and Rode Rend
90134t1N/EP
Jean DERMINE "The Cakes fana Fitmpean RankineInter:ration, a Cali for a Pro-Active
TM Piero BONISSONE Reasoning: The tàoaulhstic Correction",May 1990.
Compention Poney". April 1990.90/46 Soma MAKRIDAKIS "Exponentiel Surmandswinerra Met of
90/35 Jae Won PARK •Changing Uncertahtty and the Time- TM and Michèle HIBON Initial Values and Leva Falletioes an Post-
EP Varying Risk Premier in the Tenu Structureof Nominal Inter'« Rates". Decenther 1989,Revised March 1990. 90/47 Lydia PRICE and
Semple Foreca tien Ancem".
Improper Samprame in IdifferilMKT Wilfried VANHONACKER Experimente: Linitalianme the Use of
90/36 Arnaud DE MEYER "An %Wied lame:tee of Meta-Arniyais Reonita9119191‘18
TM Masurfacturing Stratégies in European Updating", Reviaed May 1990.Industry", April 1990.
90/4* lm WON PARK "The Infornation in the Tenu Structure of
90/37TM/013/SM
William CATS-BARIL "Executive Information Systems: Developingas Approach Io Open the Possibles", April
EP latere* Rates: Out-andinsole ForecadingPerformance*, lune 1990.
1990.90/49 Soumitra DUTTA "Approenate Remet ky /valloRY
90/38 Wilfried VANHONACKER "Managerial bectent >barioler and the TM Answer Na Quinine', lune 1990.
MKT Estimation of Dynamic Sales RespmrseModela", (Revised Fentary 1990). 90/50
EPDaniel COHEN andchartes WYPLOSZ
"Price and Trade Fifeets et Exchange RatesFlactuations and die Nana of Poney
90/39
TM
Louis LE BLANC andTawfik JELASSI
'An Englue« and Section Metbodologyfor Expert System Shelh", May 1990.
Coonfonation", April 1990.
90/51 Michael BURDA and "Grass Labeur Market Flows in Vampe: 90/63 Sumwers GHOSHAL and "Organising Coussinet« Analyais Systeme,EP Chartes WYPLOSZ Some Stylized Falls". lune 1990. SM Eleanor WESTNEY Augias 1990
90/52 Lars Tyge NIELSEN "The Mie of Inlimite Menus". lune 1990. 90/64 Sumantra GHOSHAL "Intentai Differentiation and CorporateFIN SM Performance: Cam of the Multinational
Corporation", Angle 199090/53 Michael Borda "The Consequences of German &momieEP and Mnnelary Union". /une 1990. 90/65 Chades WYPLOSZ "A Note ou the Real Exclunme Rate Effect of
EP German Unification", Anon 199090/54 Damien NEVEN and "Rumens Financial Regulation:El' Colin MEYER Framework for Pulky Analysis". (Reviaed 90/66 Snumitra DUTTA and "Computer Support for Strategic and Tartkal
May 1990). TM/SE/11N Nem BONISSONE Munia" in Mergero and Acquisitions",September 1990
90/55 Michael BURDA and "Intertempond Prices and the US TradeEP
90/56
Stefan GERLACH
Damien NEVEN and
Balance". (Reviaed JuIy t990).
*The Structure and Determistants of Fast-West
90/67TNI/SE/F1N
Sombra DUTTA andPiero BONISSONE
ilategratkig Prier Canes and Expert Knowledge lna Menem and Ammiabitomn Re:domina System',September 1990
EP Lars-Hendrik RÔLLER Trade: A Preliminary Analysis of theManuficturbse Serine". lut), 1990 90/68 Saumura DUTTA P'renseumult leilhodology for Enlumina theami
TM/SE Business Impact et Atticial Intelligence90/57 fars Tyge NIELSEN Comma Knowledge of a Multivariate Aggregate ApOications", Sepresmar 1090FIN/EP/ Statistie". July 1990TM 90/69 Sonmitra DUTTA "A Medd Bir Temporal Remanie« kt Medical
TM Expert &Siffle% Sesternber 199090/511 Lam Tyge NIELSEN Cannna Knowledge of Price and Expected CosiFIN/EP/TM in an OliRopelktic Market". August 1990 90/70
TMAlbert ANGEHRN "'Triple C': A Mena Interactive MCDSS',
September 199090/59 Lean DERMINE and "Feemornies of Seule andFIN Lam-Hendrik RÔLLER Steve in the French Mutuel Fumés (SICAV) 90/71 Philip PARKER and "Campedtive Efforts in Diffistion Modela: An
Industry". Auguu 1990 MKT Hubert GATIGNON Empirical Analysée'. September 1990
90/60 Pen 1Z and 'An Interactive Group Occitan Aid for 90/72 Enver YÛCESAN 'Andy* tif Marli« Chia Ugine 5anndationTM Tintin JELASSI Muttiohjective Proldents: An Empirical TM Grapk Modela", October 1990
Autrement", September 1990
90/61 Pankaj CHANDRA and "Modela for the Emilasittion of Manufacturing90/73TM
Arnoud DE MEYER andKasra FERDOWS
"Remaniant the Bardera in Manufacturing",October 1990
TM Mihkel TOMBAK %adule, August 1990
90/62 Damien NEVEN and "Public relief Towards TV Break:Ming in the 90/74 Summum GHOSHAL and "Rognidte Cemplexity: O. Headquartem-FP Menno VAN DUK Netherlands", August 1990 SM Nitin NORRIA Subeithary Rebtirms in MNICs". October 1990
9onsMKT
Roser BETANCOURT andDavid GAUTSCHI
'Ibo Orrai et Relia Artividem Coarekals,Mensorment ma Evillente. October 1990
9047FIN/Er
Lam Tyne NIELSEN
911/70 Wilfried VANHONAC/CER 'Men Bond Doride* Behavione and the Yetinution 9011011 Susan C. SCHNEIDER andMKT of Dreemdaelta gemma» Modeae. 00/MKT Reinhard ANGELMAR
Revive/ October 1990»Wied F.R. KETS DE VRIES
tern Wilfried VANHONACKER nada; Ihe Kart &Bembo ai Site Respire as OBMKT Advertisima: Am Aarettalisn-ludemendent
Aeletendoliiee T. October 1990 90190 Philip PARKERMKT
90/18 Micked BURDA and *Embaume Rate Drineirs and CauveryEIP Stefan GERLACH Unification: The Ostmark - DM Rate.
October 1990
90/79 Mil GARA •Interencen ai* an Ustimown Noise Lied in aTM Bernes% haceur, October 1990
90/1111 Ale GARA and •Gaine Sarre Data I.• laterearet about hercha»TM Robert WIN/CUIR Rellanionet Omober 1990 1991
Tarvfd 1ELASSI "Dm niant ar INItnr: Bien et Orientations desTM Brevet Interactifs d'Aide II In Decisbee 9101 Luk VAN WASSENHOYE.
October 1990 ni/St Leonard FORTUIN andPaul VAN BEFJC
901113 Otaries WYPLOSZ Ideeetery Union rd Fiscal Poliry Diodes',"EP November 1990 91/113
7M/5111Lut VAN WASSF.NHOVE,Leonard FORTU1N and
9063 Nathalie DIUICENS and noiormatien Myestretry and Corporate Paul VAN BEEKnNrni Bernard SINCLAIR-DESGAGNE Commaitatiem Remdts of • Pilet Sonde,
Noverdber 1990 91103 Pekka HIETALA adFIN Tien ILOYMNIEMI
9014 Phifip M. PARKER "The Effort d Advertitina on Price and Quality:MKT Ibo Ormaehie Industry Rerithed• 91104 Lars Tyge NIELSEN
December 1990 FIN
Avijit GHOSH end •Opetri Tiadas and Lerma be Competitire 91105 Srs SCHNEIDERMKT Varna TIBREWALA lelerkeee November 1990 OB
*MMEPITM
Olivier CADOT andBernard SINCLAIR-DESGAONE
°nyder, and Stoss in roides; November 1990 MAKOB
Minfœtt Kers DE VRIES,Daum MILLER andAlain NOEL
•Faisten•• of EssualBwinas in CAMA: M'aberNasadif. Decendier 1990
`Cognai» in Organientioeud Andria: 11bo'sMien the Semer Revient December 1990
CE0 Celle* Ti gratta and OtherTes fier the Bard Rama; December 1990
'hire ihraticity Dr:amies mer the AdoptionLiterie: Am Empiriud Study; December 1910
'0perational Itamtemitffla Mont fer Marge«Thon %y Mielermary 1991
*Oparediond Remo* enrovirommotehinurop 1991
Dividend herease in Rem IssueThur, »I Bedonne towesery.1991
"Tweetued Separallma Parme Structure amiRelsemesse lantary 1191
9Mlegettiag beneterke ia Or .ekami PM
gledeeilledies the Leolereretep Welter«Applicage, et tbe Sieste* Relideeelip imervireMine Imam 1990 09111. mvised Apal 19901
91/07 Olivier CADOT "levain to Inmadvent Countriem: A farallosicalEr Sem," lanuary 1991 91/19
MKT
Vikas TIBREWALA end • Aggregate Test of Purtimse Regularite,Bruce BUCHANAN March 1991
91/08 Charles WYPLX/SZ "Pola-Refone Emt and West: CapitalEr Aemennlotioe and the Labour Mubility 91/20 Darius SABAVALA and Monitoring Short-Rome Changes in Purrhasing
Construisit," lanuary 1991 MKT Vika* TIBREWALA Behaviour", March 1991
91/09 Spyroe MAKRIDAKIS •What eau we Leoni from navrer, Felnuary 1991 91/21 Sumatra GHOSHAL, Internât Conammiration within biNns:TM SM Harry KORINE and lemme of Formel Structure Verses lalegrative
Gabriel SZULANSKI Promues*, April 199191/10 Luc Van WASSENHOVE end "Integrating Schedeing with Batching andTM C. N. P01111 Let-Seing: A Revive or Alliamilkulla and 91/22 David GOOD, "EC lekgratian nad Me Stream of the Fromm-
Causplenity •, Febnery 1991 EP Lers-Hendrik RÔLLER and American Aies* ladmetries: Implications ferRobin S1CKLFS Efficient" and Wren*, April 1991
91/11 Luc VAN WASSENHOVE et al. "Muid-Item in Caparitated Mugi-StageTM Serial System", February 1991 91/23 Spyros MAKRIDAKIS and "Kemmel SeeldRiagtlie Effect of Initial
TM Michèle HEION Vaine" and Lem Fewetimature Foot-Semple91/12 Albert ANGEHRN •Interpretadve Computer Intelâmame: A Link Forweerting Areemey;111.111 1991 (Revision ofTM between Umm, Modela and Metbods in ose. 90146)
February 199191/24 Louis LE BLANC and •A. %Orient ArresmarMWChoice Modela for
91/13EP
Michael BURDA •Ulm and 'Muet Markets à Czechariovidia andthe E."-GDR: A Twin Stedy", February 1991
1M Tawfik IELASS1 Software Eveleaden anifillkoMnr, May 1991
91/25 Luk N. VAN WASSENHOVE and "Tradaelle What Trtieothr April 1991
91/14 Roger BETANCOURT and 'ne Output of Rata At-livides: Fumai Shi/7m Charles CORBEITMKT David GAUTSCHI Evident •, February 1991
91/26 Luk N. VAN WASSENHOVE and "Sangle Media- Sdrifi bilai tenaillée Total Lat.98/15
OBManfred F.R. KETS DE VRIES •Expérang the Mytb about Ratinant Organiusiows
and Emcmives", March 19911M C.N. POTTS %kWh• April 1991
91/27 Nathalie DIERKENS •A Dimmion of Cornet Mandes of Informatisa91/16 Arnaud DE MEYER and •Faeteties of the Vehme: L'endive Senweary of FIN Asyremetry: 1be Lime or Myes and ISIMInf`sTM East. FERDOWS et.al. the 1990 Interea6unal Manufacturing Futures
Survey", March 1991Maint or Ibe Importance of the Amr( Sawcture ofthe Me. May 1991
91/17 Dirk CATTRYSSE, "Ileuriaties for Ibe Marrie letvizing and 91/20 Philip M. PARKER •A Note au 'Aéreribia« and the Prim lad QualityTM Roda KUIK,
Marc SALOMON and&Madelin Noble. laids Setup Times •, March 1991 MKT of Oplometrie Services', hume 1991
Luk VAN WASSENHOVE 91/29 Tswfik JELASSI and 'An t'aphte] Moly of an Interactive, SeamiamTM Abbas FOROUGH1 Orieded Compoterised %sertirai« Support System
91/18 C.N. POTTS end •Approximnalion Algorithmes fer Scinda« a Sm* (NSS)", lune 19911111 Luk VAN WASSENHOVE Machine M Milhatime Total Lute Work•,
Match 1991
91/30 Wilfried R. VANHONAC10ER and MM« Meta-Anallysis Rimes in Bayeniatt Updating:MKT Lydie J. PRICE lbe Erne Cal Profilent", lune 1991 91143 Sumatra OHOSHAL and %W in Trammieend Combattiez: The
SM Christopher BARTLETT Managemeat Challenge', September 199191131 Reraul KARJR and "leader Tratfieg Ruinaient muid the StockFIN Theo VERMAELEN Mana% Jase 1991 91/44 Summar* GHOSHAL and Inabilated Innevation I. the IfIfferantioded
SM Nilin NOHRIA Network. MnItinetietur, September 1991
91/32 Stman C. SCHNEIDER 'Orgamisadonel Sememaking: 1992• , lune 1991011 91/43 Philip M. PARKER "The F/feet et Adverfidad es Frite and Quality:
MKT As Fmapirical Study of Eye Examinalions, Sweet
91/33 Miction' C. BURDA and *Germe Trade Usinas gifler Umilication Third Lama muid Self-Decevers", September 1991EP Michael FUNKE Dere, Wace Marin/mea Mossopolistarr
lutte 1991 91/46 Philip M. PARKER *Prelog Santals in Mante whig tem*MKT Flatikifies". October 1991
91/34 Jean DERMINE *The BIS Noeud fer the Memerenleat of InterestFIN Rate Reit, Some ?Wells", lune 1991 91/47 Philip M. PARKER Sady of Price Ehiseleky Dynamite Usai
MKT Parsianonions Redmeneent/Naltiode Fareham
91/33FIN
Jean DERMINE "The Radeau of Finacial Servies in the F.C,Centrai:sten er %kraal Antemear lune 1991
Diffames Modela•, October 1991
91/414 H. tandis LABEL and 9Mourgerial Ineentive amillhaviromantal
91/36 Albert ANGEHRN •Suppertiat Modelaient Decktie« Mana: New EP/TM Bernant SINCLAIR-DESOAONE Cooludiemee. Oember I991
TM Perspeedves mad New Systems", Auget 199191/49 Bernard SINCLAIR-DESGAGNB "Me Net-Onler Afflua» MmItiendu
91/37 Mao WALTER and 'The latrodactim of Universel Bakin in Canada: TM FradgekAgent TreblearttOmber 1991
ET Hugh THOMAS An Emme Study", Auget 199191/30 Luk VAN WASSENHOVE end Mea Gien h Yeer blegataring Strelfear
911311 Ingo WALTER and "Natimml Ilad Global Canspetitivemeas of New York SM/TM Charles CORBETT October 1991
EP Anthony SAUNDERS City as a %amis! Center', Mea 199191/31 Piao M. PARKER Mimais Aatatlf Made Modela Sarre
91/39 Mg° WALTER andAnthony SAUNDERS
"Reeantiguratien of Rankine and Capital Marketshi Eastern Emme. Augura 1991
MKT Empiried Goddelinee, Odober 1991
91/32 Michel BURDA and 'Mana Caplet Imeatieent and Menti« lia an
91140 Luk VAN WASSENHOVE. 'A Set Fartitieming Renne fer the Gemerefued EP Charles WYPLOSZ Integrated Fitropee, October 1991
TM Dirk CATTRYSSE and Awdeament Profiles", August 1991Marc SALOMON 91/53 Michael BURDA end • aimer Marna and German Integration: Sente
EP Charles WYPLOSZ Ifiemette •, Ocaber 1991
91/41TM
Luk VAN WASSENHOVE,M.Y. KOVALYOU and
'A nie Pelyeandal Approwienation Stigma forSchee/Mg a Male Maitise to Minimise Total 91/34 Albert ANGEHRN •Sanie Adage: An Alternative Frimaire* for
C.N. POTTS Weigilted Lite Work", Annal 1991 TM Caentleter-Aided Raban Maldnor. October 1991
91/42 R. WEfTZ and "Solving A Mani-Ctiteria Allocation Freedom.:TM Tawfik IELASS1 A DIPCfRi011 Support System Apprends",
August 1991
91/55 Robin HOGARTH,EP/SM Claude MICHAUD,
"Leenevity of Business Firmus A Four-StaseFreinework for Analysis", November 1991
92/03OB
Manfred F.R. KETS DE VRIES 'Ibn Fansily Film An Owen', Maenso•,lanuary 1992
Yves DOZ andLudo VAN DER HEYDEN 92/04 Philippe HASPESLAGH and "Maine Acquisitions Work", /anuary 1992
SM David MM/SON91/56 Bernard SINCLAIR-DESGAGNETM/EP
"Aspirations an Emmen» Development',November 1991 92/05 Xavier DE GROOTE "Fledhally and Prend Dives* in Loteniap
TM Modela". lamas, 1992 (revised)91/57 Lydda PRICE 'Ibo Indirect Efforts of Neptive Information enMKT Attitude ange", November 1991 92/06 Theo VERMAELEN and "Enencial Innevatien: Self Tender Offen I.• the
FIN Kees COOLS January 199291/58 Manfred F. R. KETS DE VRIES "Leaders Who Go Cran", November 1991OB 92/07 Xavier DE GROOTE "lb. Fleoldlity of Production Prenne A
TM Gemmi Framework", January 1992 (rened)91/59 Paul A. L. EVANSOB
91/60 Xavier DE GROOTE
"Managemeat Development as Glue Technology",November 1991
`Flesildity nad MarketiegIblannfaceung
92/08TM
Luk VAN WASSENHOVE,Leo KROON andMarc SALOMON
•End and Approdemlion Ateritleas for theOperatiend Fimed ber ved Sebaddin Profilent",Jarasary 1992
TM Coordintin", November 1991 (revised)
91/61 Arnaud DE MEYER "Prend Development in ne Textile Markimery92/091M
Luk VAN WASSENHOVE,Roelof KUBC and
"Statistired Se r» MIllikne for lAtaingProlden", lennety
TM Industry". November 1991 Mare SALOMON
91/62 Philip PARICER and *Sperifying Cempatitive Efforts in Diffusion 92/10 Yves DOZ and •Repainap Ermandlinness: A Proroge ofMET Hubert GATIGNON Mn»: An Empirerai Anoblie, November 1991 SM Heinz THANHEISER Orgemisntiond Renewe •, Jamary 1992
91/63 Michael BURDA 'Sem New Indes ou the Interindmstry Wein 92/11 Enver YUCESAN and •Che the hernetability of Vesifying StretteralEP Sentare frein the Gemme Soeioneesesnir Pond•
December 199117S1 &bridon JACOBSON ?reperdes et pinne End Simulation Models",
February 1992
91/64 Jean DERMINE "InerrationnEntion of FInamen1 Mark». 92/12 Gabriel HAWAWINI "Valentin of Cie-Bender Meilen endFIN Ef&ioscy and Stanley', December 1991 FIN Andeilimer, Penny 1992
12,1 92/13 Spyros MAICRIDAICIS and ail. IdeCenepotiliseu A Budget Related1M Michèle HIBON et.al. Fapieieal Fonmens Study", Felnuary 1992
92/01 Wilfried VANHONACKER "CONPRO4DOGIT: A New Brand amoire Medd111KT/EPI7AI Imerporating a Coasideration Set Formation 92/14 Lydda PR/CE "Inde.' Cluster Ondin with NORMIX
Pronee, Jonas, 1992 MKT Population Atembenialp Prembalities",Febtuary 1992
92/02 Wilfried VANHONACKER "Ibn Drin» et tbe Considoration Set ForeudemMICT/EP/TM Promu A Radient Medelling Penipartivo
Sun Nemosical Rente", lersdary 1992