Directory UMM :Data Elmu:jurnal:I:International Journal of Production Economics:Vol67.Issue3.Oct2000:
Int. J. Production Economics 67 (2000) 235}252
Coordination of internal supply chains in vertically integrated
high-tech manufacturing organizations (HTMOs)
Armando Ugarte!,*, Shmuel Oren"
!i2 Technologies, 303 Twin Dolphin Drive, Suite 210, Redwood City, CA 94065, USA
"Department of Industrial Engineering and Operations Research, University of California at Berkeley, Berkeley, CA 94720, USA
Received 24 February 1998; accepted 19 January 2000
Abstract
This paper uses economic mechanisms to coordinate supply chains within High-Tech Manufacturing Organizations
(HTMOs). It models the one-shot initial production and allocation decisions involved in the production and marketing
of new technologies; these decisions are driven by the economic objectives of the "rm and of the employees with private
information } the experts. It analyzes and compares the e$ciency of three coordination policies: centralized command and
control, centralized revelation, and decentralized revelation. It shows that decentralized policies introduce an additional
cost, and it proposes rules of thumb for coordinating supply chains within "rms that use many experts. ( 2000
Published by Elsevier Science B.V. All rights reserved.
Keywords: Coordination; Firm organization and market structure; Vertical integration; Markets vs. hierarchies
1. Introduction
HTMOs are large and vertically integrated so as
to take advantage of economies of scale and scope,
reduce their time to market, and a!ord periodic
large capital investments. HTMOs have several
divisions running technologically complex operations. The internal transactions in large and complex organizations are characterized by
information asymmetries and lack of market competition [1].
HTMOs are continuously looking for improvements in their overall supply chain e$ciencies.
* Corresponding author.
E-mail addresses: armando}[email protected] (A. Ugarte),
[email protected] (S. Oren).
Companies such as Hewlett Packard (HP) and
IBM are continuously "ne tuning their organizations to better coordinate their internal supply
chains. Hewlett Packard (HP) fabricates semiconductors which it subsequently uses to build computers, printers, fax machines, medical devices, etc.
In the late 1980s, HP decentralized its organizational structure and created independent business
units that were asked to focus attention on improving their cost e$ciency and market responsiveness.
Similarly, IBM after achieving technological
leadership in semiconductor manufacturing expanded their production through forward integration to produce computers and other high-tech
products. In the early 1990s, however, IBM had to
down size and restructure itself into a less hierarchical organization in pursuit of higher e$ciency. The
success of HTMOs such as HP and IBM depends
0925-5273/00/$ - see front matter ( 2000 Published by Elsevier Science B.V. All rights reserved.
PII: S 0 9 2 5 - 5 2 7 3 ( 0 0 ) 0 0 0 2 2 - 0
236
A. Ugarte, S. Oren / Int. J. Production Economics 67 (2000) 235}252
on their technological leadership and the e$cient
coordination of their supply chains.
This paper evaluates the use of economic market
mechanisms to coordinate a HTMO's production
and marketing decisions of a new proprietary technology.1 In Section 2, We model the coordination
of production and allocation decisions during the
introduction of a new technology as decisions that
are driven by the economic objectives of the "rm
and of the employees with private information } the
experts.2 We investigate and compare the e$ciency
of a Centralized Command and Control policy,
Section 3; a Centralized Revelation policy, Section
4; and a Decentralized Revelation policy, Section 5.
In Section 6, we illustrate the e$ciency of the policies analyzed by means of a numerical example
consistent with our model. In Section 7, we generalize the e$ciency condition for the three policies and
show that decentralized policies introduce a decentralized e$ciency cost.3 Finally, we propose some
rules of thumb for coordinating internal supply
chains in HTMOs.
2. A coordination model for HTMOs
In the remainder of this paper we consider a
stylized HTMO consisting of a Headquarters division (HQ) and two vertically integrated production
divisions, Division-1 and Division-2. Division-1
produces an intermediate product using state-ofthe-art technology, such as integrated circuits; Division-2 uses part of the output from Division-1 to
assemble a "nal product, such as printers, computers, phones, etc. HQ coordinates the divisions
1 Our objective is not to replicate generic economics results
but rather to add structure to the models employed in the
economics literature so as to specialize and reinterpret these
results in a manufacturing context.
2 Private information represents the knowledge, intuition, experience, and e!ort of managers and experts; this information is
not ex-ante observable by the "rm.
3 This result rea$rms the results obtained by Melumad et al.
[2] hereafter referred as MMR 1995 } and Vaysman [3]; our
model expanded the e!ect of private information onto the operation decisions which have `supply chaina e$ciency connotations.
using information provided by the division managers, Manager-1 and Manager-2.
We make three important assumptions. First, we
assume that the initiative, knowledge, e!ort, experience, and intuition of the experts play a major role
in the development, design, production, and marketing of new technologies. Second, we assume that
the productivity of a new technology is uncertain
due to its immaturity and workers' heterogeneity in
mastering new technologies. Third, We assume that
expert employees are rational, risk neutral, and
utility-maximizing decision makers; their objective
is to maximize their income and/or to minimize
their disutility from e!ort, which we model as disutility costs.
2.1. Production characteristics
Division-2 uses inputs produced at Division-1 to
assemble and market a "nished product based on
a new technology. The demand for its "nished
product d(I, z (h )), with cumulative probability
2 2
distribution F (.; I, z ), has a "rst-order stochastic
d
2
dependency on marketing expenditures I and on
marketing productivity z (h ). Marketing produc2 2
tivity z (h ) depends on Manager-2's private
2 2
information parameter h , which accounts for
2
Manager-2's market information, connections, and
e!ectiveness.4
Division-1 operates a state-of-the-art production
facility with a capacity of K regular production
hours per period;5 of which k hours are sold to
s
external customers and k hours are used to
p
produce inputs for Division-2. The production of
inputs for Division-2, Mg(k , z (h , e))"k z N, is
p 1 1
p 1
done by means of a new proprietary technology
with uncertain production yield. Productivity
z (h , e) depends on Manager-1's private informa1 1
tion parameter h , and on an uncertain level of
1
production &noise' e. The parameter h accounts for
1
Manager-1's experience and e!ectiveness in bringing new technologies up to production maturity.6
Production noise e, with cumulative probability
4 Higher levels of h are desirable, Lz (h )/Lh '0.
2
2 2
2
5 K doe not include overtime hours.
6 Higher levels of h are desirable, Lz (h , e)/Lh '0.
1
1 1
1
A. Ugarte, S. Oren / Int. J. Production Economics 67 (2000) 235}252
distribution F (.), accounts for all the uncontrole
lable events that can a!ect production yields and
cycle time.7
2.2. Economic characteristics
HQ's objective is to maximize "rm's expected
pro"ts E[P(.)] from the new technology. Corporate
revenues result from: selling capacity k at a unit
s
pro"t of p dollars, selling Division-2's assembled
products at a unit price of p , and salvaging Divis2
ion-2's intermediate inputs in excess of demand
(g(k , z )!d(I, z ))` at a net unit gain of h dolp 1
2
1
lars.8 Corporate costs result from: production
penalizing
excess
demand
+2 c ]d,
i/1 i
(d(I, z )!g(k , z ))` at a cost of s per excess unit,
2
p 1
2
and from compensating the manager U . Expected
i
corporate pro"ts before compensating managers
are:9
E [P(k , k , I, hI ; h)]
d,e
s p
2
"pk # p ! + c E [d(I, z )]
s
2
i d,e
2
i/1
#h E [max(g(k , z )!d(I, z ), 0)]
1 d,e
p 1
2
!s E [!min(g(k , z )!d(I, z ), 0]!I,
2 d,e
p 1
2
(1)
E [P(k , k , I, hI ; hI )]
d,e
s p
2
"pk # p ! + c E [d(I, z )]
s
2
i d,e
2
i/1
g(kp ,z1 )
F (x)dx
#h E
d
1 e
0
=
FM (x)dx !I.
!s E
d
2 e
g(kp ,z1 )
In the above equation, price per unit of capacity at
Division-1 is positive p'0, price per unit of "nal
product produced at Division-2 is greater than
A
B
A
CP
CP
B
D
D
7 Productivity decreases with noise, Lz (h , e)/Le(0.
1 1
8 (a!b)`"max(a!b, 0).
9 Reported private information hI "(hI , hI ) is a decision vari1 2
able, whereas true private information h"(h , h ) is a para1 2
meter. The arguments of z and z are omitted for ease of
1
2
exposition.
237
production cost p !c !c !p/E [z (h , e)]'0,
2
1
2
e 1 1
there is an overstock cost in Division-1 for
the excess inputs produced for Decision-2
h (p/E [z (h , e)], and the excess demand pen1
e 1 1
alty cost at Division-2 is non-pro"table
s (p !c !c !p/E [z (h , e)].10
2
2
1
2
e 1 1
Managers are utility maximizers, rational, and
risk neutral; the economic utility for the Manager
of the ith Division is ; (U , < ),U !< (a , h ).
i i i
i
i i i
Managers' compensations U are determined by
i
HQ; their disutility or personal costs < (a , h )
i i 1
account for the time, e!ort, and forgone opportunity costs that a manager with private information
parameter h incurs when assigned production
i
activity a ;11 < (.) is assumed to be monotonic and
i
i
single crossing in h to guarantee at least one inceni
tive compatible solution [2]. Su$ciency conditions
for monotonicity and single crossing are satis"ed
when < (.) increases with higher levels of produci
tion activity (L< (a , h )/La '0); decreases with
i i i
i
higher levels of private information (L< (a , h )/
i i i
Lh (0); decreases marginally in production activi
ity and private information (L2< (a , h )/
i i i
Lh La (0); and is convex in production activity
i i
(L2< (a , h )/L2a '0).12 Disutility costs < (.) are
i i i
i
i
not observable to HQ since they depend on managers' private information h ; HQ's prior beliefs
i
about h are characterized by a cumulative probi
ability distribution F i (.: H ) where H ,[h , h ].
i
i
- 6
h
2.3. Coordination decisions
In general the objectives of the HQ and the
managers objectives are not compatible and both
have asymmetric access to information; these two
conditions create incentives for adverse-selection
and/or moral hazard in the behavior of the division
managers.13
10 Overstock cost does not consider inventory costs because
these are negligible.
11 a "k and a "I.
1
p
2
12 For weaker conditions see Milgrom and Shannon [4].
13 Moral harzard and/or adverse selection are the result of an
agency relationship that occurs whenever the Principal, HQ,
needs a service from a person or Agent (in our case the Manager)
who has private objectives that are not aligned with those of the
principal (in our case HQ) and is better informed than HQ [5].
238
A. Ugarte, S. Oren / Int. J. Production Economics 67 (2000) 235}252
HQ coordinates and decides on the operational
and the enforcement rules for the one-shot project
of releasing to the market a new technology,
consistent with its objectives and beliefs [6].14
The operational rules determine managers'
responsibilities and regulate the interactions between the divisions involved in the project. The
enforcement rules make managers accountable for
executing the operational rules by determining
divisions' performance measures and managers'
compensations U .
i
Managers actions and decisions obey a utility
maximization rationale with participation and
incentive compatibility conditions. Managers participate in HQ's contract if and only if their utility is
competitive, i.e., greater than their reservation utility ;M (without loss of generality, we set ;M "0.)
i
i
Managers' incentive compatibility condition
requires them to act and decide so as to maximize
their individual utilities. Incentive compatibility
implies than when managers report their private
information parameter hI , they report a parameter
i
value that maximizes their utility:
hI H3argmax ME j [; (U , hI , hI H(h ); h )]
d,e,h
i i i j j i
i
hI i
"E j [U !< (aH(hI , hI H(h )), h )]N.
d,e,h i
i
i i i j j
(2)
3. Centralized command and control (CCC) policy
This coordination policy is commonly observed
in the industry and results from formulations proposed in the Operations Management literature
[7}9], HQ implements the operational and
enforcement rules for this policy assuming that
managers are altruistic, i.e., hI H"h .15
i
i
14 HTMOs allocate many resources to these critical projects,
often hiring experts that join these companies with the mentality
of make-it or break-it.
15 HQ ignores that if managers report hI HOh , HQ cannot
i
i
detect the distortions: productivity z is ex-post observable but
1
depends on unobservable and random production noise e, and
productivity z cannot be accurately inferred from a single
2
realization of random demand.
Fig. 1. Flow of information and product in a CCC policy.
3.1. Coordination rules
HQ implements the following operational rules.
At time t"0, HQ determines managers' compensation U and ranking measures; at time t"0`,
i
HQ asks managers to report their private information, hI , which is equivalent to reporting their proi
ductivity; at time t"0``, HQ determines
production activities k , I; at time t"1, demand
p
d and pro"ts P are realized, and the managers are
compensated. Fig. 1 shows the #ow of information,
in dotted lines, and the #ow of product, in solid lines,
as implemented by the above operational rules.
HQ's enforcement rule, consistent with its
assumption about managers' altruism, sets managers' compensations as #at wages with pro"t sharing incentives, = #k P; and it sets subjective
i
i
managers' performance evaluation measures such
as initiative, quality commitment, productivity
contributions, and dependability.
3.2. HQ's decisions
HQ makes production and marketing decisions
with a pro"t maximizing rationale; in contrast, HQ
decides on the manager's wages = and pro"t
i
sharing fraction k P(.) using a labor market rationi
ale:
Find kH, kH, IH3 argmax E [P(k , k , I, hI ; hI )]
d,e
s p
p s
(3)
s.t. (i) k #k )K.
p
p
Since pro"ts from k are higher than the ones
p
from k , HQ sets kH"K!kH and solves an
p
s
s
unconstrained problem using "rst-order necessary
A. Ugarte, S. Oren / Int. J. Production Economics 67 (2000) 235}252
conditions for optimality.16 HQ selects the kH at
p
which Division-1's expected marginal costs of overstock equate Division-2's expected marginal costs
of understock:
p!h
1
LE [:g(kp ,z1 (hI 1 ,e))F (x; I, z )Lx]
e 0
d
2
Lk
kp /kHp
p
K
K
LE [:= p 1 I 1 F (x; I, z )Lx]
2
e g(k ,z (h ,e)) d
.
(4)
Lk
p
kp /kHp
HQ selects the IH at which expected marginal revenue equals the expected marginal cost from marketing projects:
"s
2
A
p !+ c !s
2
i
2
i
!(s !h )
2
1
B
LE [d(I, z )]
d
2
LI
K
3.2.2. Ezciency losses
E$ciency losses in this policy occur because
HQ's decisions use distorted productivity information, and because managers have no incentive to
report their true private information. HQ ignores
the fact that managers are utility maximizers with
valuable private information, and that they incur
disutility costs. Consequently, managers distort
their private information because their expected
marginal bene"ts from reporting truthfully is zero:
[P(aH(hI , h ), h , h ; h)]
dE
i j i j
k ] d,e,hj
i
dhI
i
hI i /hi
LE j [P(aH(hI , h ), h; h)] LaH
k
d,e,h
i j
"k ] +
,
i
LhI I i i
LaH
h
i
/h
k
k|i,j
(7)
K
K
I/IH
LE [:g(kHp ,z1 (hI 1 ,e))F (x; I, z )Lx]
d
2
e 0
LI
K
"1,
I/IH
(5)
3.2.1. Managers' decisions
Managers follow their utility maximizing objective and accept HQ's contract if their compensations are competitive, i.e.,
E j [U !< (aH, h )]*0.
i i i
d,e,h i
Managers that choose to participate then report
the private information hI H that maximizes their
i
utility. Managers' utilities are the sum of three
concave functions,
E[; ]"= #k E[P]#
i
i
i
(!E[< ]); therefore, their utilities would be maxii
mized when their expected marginal bene"ts equals
their expected marginal cost corresponding to the
reported private information:17
[P(aH(hI , hI H(h )), h , hI H(h ); h)]
dE
i j j
i j j
k ] d,e,hj
i
dhI
i
hI i /hI Hi
dE [< (aH(hI , hI H(h )), h )]
i
" hj i i i j j
.
dhI
I
IH
i
i
i
h /h
K
K
239
(6)
16 Second-order conditions are not needed since E [P(.)] is
d,e
assumed to be concave in k and I. Guarantees a global maxp
imum at any point that satis"es the "rst-order conditions.
17 If managers' compensation consist only of #at wages
U "= , then managers will report the lowest credible level of
i
i
private information hI H(h )"h because their marginal
i i
l
utility from reported private information is negative,
dE[;(U , hI ; h )]/dh "!E[< (aH(hI H, hI H), h )]/dhI (0.
i i i
i
i i i j i
i
but optimality requires that
LE j [P(aH(hI , h ), h; h)]
i j
d,e,h
"0 ∀k3i, j.
LaH
hI i /hi
k
To reduce their disutility costs, managers underreport their private information, i.e., hI H(h )(h . Coni i
i
sequently, HQ's production activity levels aH are
i
based on distorted private information, i.e., lower
estimates of productivity.
K
aH(hI H, hI H), aH(hI H, hI H) N argmax E [P(aH(hI H, hI H),
i i j
d,e
i i j j i j
(8)
aH(hI H, hI H), hI H; h] ∀ hI HO0
j i j
Comparing the e$ciency of this policy to the bench
mark e$ciency of the &"rst best' solution provides
a measure of the e$ciency losses of this policy,
given by Eq. (9). The "rst best solution would be
achieved if private information would not exist and
HQ would not need to align managers and "rms
objectives.
E[¸ ]"E [P(aH(h , h ), aH(h , h )), h , h ; h , h )]
i j i j
i i j j i j
CCC
d,e
!E [P(aH(hI H, hI H), aH(hI H, hI H), hI H, hI H; h , h )]'0.
i i j j i j i j i j
d,e
(9)
4. A centralized revelation (CR) policy
In this coordination policy, HQ maintains centralized control but does not assume that managers
are altruistic. In order to access private information
240
A. Ugarte, S. Oren / Int. J. Production Economics 67 (2000) 235}252
HQ must align the manager's objective with the
objective of the "rm, which is accomplished by
a direct revelation mechanism [2,3].18
4.1. Coordination rules
HQ sets forth the following operational rules: at
time t"0, it determines managers' compensations
UK H; at time t"0`, it asks managers to report their
i
private information parameters hI H; at time
i
t"0``, it makes production activity decisions; at
time t"1, demand d and pro"ts P are realized,
and managers are compensated. Fig. 2 shows the
#ow of information, in dotted lines, and the #ow of
product, in solid lines, for the above set of rules.
HQ designs the enforcement rules, determining
managers' compensations and performance evaluation measures, that maximize the utility of managers who subscribe to the above operational rules
and report their true private information.
4.2. HQ's decisions
HQ o!ers managers the minimum compensation
UK H that maximizes their utility when they are not
i
distorting their private information:19
max E [P(aH(hI ), hI ; hI )]!+2 E i [UK (hI ; h )]
i/1 d,e,h i i i
d,e
UK
i
subject to
(i) h "hI H3 argmax E jEi [UK (hI , h )
d,e,h
i i i
i
i
hI i |Hi
!< (a( H(hI , h ), h )] ∀(i, j),
i i i j i
(ii) E jE1 [UK (hI ; hI )
d,e,h
1 i i
!< (a( (h , h ), h )]*;M
∀(i, j).
i i i j j
i
The optimal managers' compensations UK H must
i
cover managers' disutility costs and pay them
informational
rents
[2].
This
results
18 Revelation mechanisms are based on the revelation principle for communication games with imperfect information [10].
19 Pro"ts before payment to the managers E[P] are de"ned
in Eq. (1).
Fig. 2. Flow of information and product in a CR policy.
from
assuming
that
E jEi [UK 1(hI ; h )]"
i i
d,e,h
E jEi [< (a( (h , h ), h )#¹(hI )], where ¹(hI ) are
d,e,h
i i i j i
i
i
managers' informational rents. To achieve managers' participation ¹(hI )*0, and to achieve inceni
tive compatibility ¹(hI ) must be equal to the second
i
term of Eq. (10).
C
P
UK H(hI ; h )"E j < (a( H(hI , h ), hI )
i i i j i
i i i
h
!
hI i L< (a8 H(t, h ), t)
j
i i
dt .
LhI
hl
i
D
(10)
HQ decides on the divisions' production activity
levels by solving an unconstraint optimization
problem that takes into account the expected optimal managers' compensation E i [UK H(hI , h )] also
h i i i
known as the virtual costs of the managers
HK (a( H, hI ):20
i i i
max E [P(kK , IK , hI ; hI )!HK (kK , hI )!HK (IK , hI )].
d,e
p
1 p 1
2
2
IK ,kK p
(11)
At the optimal capacity kK H, marginal expected cost
p
of understock and overstock are equal, but now
Manager-1's marginal virtual cost increases the
20 HK (a( H, hI )"E i [UK H(hI ; h )]"< (a8 , hI )!(L< (a( , hI )/LhI )
i i i
h
i i i
i i i
i i i
i
(FM i (hI )/f I i (hI ))"b (a )w (hI )!b (a )w@ (hI )(FM i (hI )/f I i (hI )) is conh i h i
i i i i
i i i i h i h i
vex in a as a result of the conditions imposed on < and F i .
i
i
h
A. Ugarte, S. Oren / Int. J. Production Economics 67 (2000) 235}252
241
marginal cost of understock.
4.4. Ezciency losses
LHK (k , hI )
p# 1 p 1
Lk
kp /kHp
p
The losses corresponding to this policy result
from having to pay managers informational rents
to access truthful information. The relative e$ciency measure of this policy, as compared to the "rstbest solution, is given by
K
!h
"s
2
LE [:g(kp ,z1 (hI 1 ,e))F (x; I, z )Lx]
d
2
e 0
1
Lk
kp /kHp
p
K
K
LE [:= p 1 I 1 F (x; I, z )Lx]
2
e g(k ,z (h ,e)) d
.
Lk
kp /kHp
p
(12)
At the optimal expenditures IK H the marginal expected costs are equal to the marginal expected
revenues from marketing expenditures, but now
Manager-2's revelation cost decreases expected
marginal revenue.
A
K
B
LE [d(I, z )]
d
2
p !+ c !s
2
i
2
LI
I/IH
i
!(s !h )
2
1
LE [:g(kHp ,z1 (hI 1 ,e))F (x; I, z )Lx]
d
2
e 0
LI
LHK (I, hI )
2
! 2
LI
K
K
I/IH
(13)
"1.
I/IH
C
¸K " E [P(aH(h), h; h)!+ < (aH, h )]
d,e
i i i
i
C
C
D
! E [P(a( H(h), h; h)!+ HK (a( H, h ]
d,e
i i i
i
"E
d,e
L< (a( , hI )
i i i
LhI
i
FM i (hI )
h i .
f I i (hI )
h i
D
D
(15)
If the production resources being allocated are
very expensive, paying for access to true private
information is more e$cient than underallocating
these resources. This is typically the case in
HTMOs which tend to use very expensive resources with a high rate of obsolescence that must
be utilized e$ciently. For instance, a modern production facility for integrated circuits costs around
one billion dollars; A single photolithography
machine costs around "ve million dollars [11].
4.3. Managers' decisions
5. A decentralized revelation (DR) policy
Each manager reports truthfully if truth-reporting is his/her best strategy under the assumption
that all other managers are also telling the truth. If
it is, then by induction truth-reporting is the best
strategy for all managers. The revelation compensation UK H(.) satis"es managers' participation condition for truth-reporting managers because
E[UK H(h)]'E[< (h)]. It also satis"es their incentive
i
i
compatibility condition because their utilities are
maximized when hI H"h ; their marginal expected
i
i
bene"ts and costs from hI are equal when hI H"h .
i
i
i
dE j [UK H(hI H; h )]
d,e,h i i i
dhI
hI Hi /hi
i
K
dE
[< ](a( H(hI H, h ), h )
" d,e,hj i i i j i
.
dhI
hI Hi /hi
i
K
(14)
Under this coordination policy the HQ delegates
all the local decisions to the divisional managers
and assumes that managers are sel"sh (rather than
altruistic).21 HQ in HTMOs may want to delegate
local decision for the following reasons: faster reaction to the urgency needs of many internal supply
chain decisions [12]; empowerment of well-informed
managers to make the best decisions[13]; and regulation of the monopolistic behavior of divisions controlling captive technologies [14,15].22
21 Arrow [1] proposed the decentralization of large organizations as a way to reduce the ine$ciencies due to asymmetric
information.
22 Decisions in HTMOs require increasingly more accurate
real-time technical and economic information to remain competitive.
242
A. Ugarte, S. Oren / Int. J. Production Economics 67 (2000) 235}252
k[ (i); and Division-1 decides on k[ (i). Pro"ts for each
s
p
division are:
Fig. 3. Flow of information and product in a DR policy.
5.1. Coordination rules
The operational rules for this policy are: at t"0,
HQ sets managers' responsibilities and compensation UK ; at t"0`, it asks the managers to report
i
their private information; at t"0``, it determines
the transfer price ¹(s, hI ) that Division-2 must pay
1
to Division-1 for its services S; at t"0```, Division-2 decides on I and S and Division-1 on k and
s
k ; at t"1, demand and pro"ts are realized. To
p
enforce the above operational rules, HQ speci"es
managers' responsibilities and compensations, and
the transfer price among the divisions. Fig. 3 shows
the product and information #ow implemented by
the above rules.
n\ (k[ (i), hI ; h )"¹(k[ (i), hI )#pk(i)!c g(k(i), z ),
s
1 p 1
p 1
1 s 1 1
n\ (I[ (i), k[ (i), hI ; h )
p 2 2
2
"p d(I[ (i); h )!(s #C )(d!g(k[ (i), z )`
p 1
2
2
2
1
#h (g(k[ (i), z )!d)`
p 1
1
(16)
!¹(k(i), hI )!I[ (i)!c d).
p 1
2
In case (ii) S"Q, Division-2 decides on I[ (i), Q; and
Division-1 decides on k[ (i), k . Pro"ts for each diviss p
ion are:
n\ (k[ (ii), hI ; h )
1 p 1 1
"¹(h[ , hI )#pk[ (ii)!c Q#h (g(k[ (ii), z )!Q)`
p 1
s
1
1
1
(ii)
!s (Q!g(k[ , z ))`,
2
p 1
n\ (I[ (ii), Q, hI ; h )
2
2 2
"p d(I[ (ii); h )!(s #c )(d!Q)`
2
2
2
1
#h (Q!d)`!¹(Q, hI !I[ (ii)!c d. (17)
1
1
2
HQ also decides on the transfer price that Division-2 pays Division-1 in exchange for S. Vaysman
[3] showed that an e$cient transfer price must
transfer the production as well as the virtual costs
associated with S:24
A
5.2. HQ's decisions
HQ decides on managers' responsibilities by separating the "rm pro"t maximization function into
several divisional pro"t maximatization functions,
and by giving each manager the authority and
decision domain needed to maximize its local
pro"ts [6]. In our model, decentralization can be
implemented in two ways depending on the services
S that Division-2 orders from Division-1: S can be
capacity hours k (case i) or it can be inputs Q (case
p
ii).23 In case (i) S"k[ (i), Division-2 decides on I[ (i),
p
23 Hereafter, superscripts (i) and (ii) refer respectively to case
(i) and case (ii).
B
c
]k[ (i)#H[ (k[ (i), hI ),
¹(i)(k[ , hI )(i)" p# 1
p
1 p 1
p 1
E [z ]
e 1
(18)
¹(ii)(Q, hI )"c Q#pF(Q)#H[ (F(Q), hI ).
1
1
1
1
HQ must design the compensation U[ that satisi
"es managers' participation and incentive compatibility conditions in this policy. The simplest form of
a decentralized incentive compatible compensation
scheme is linear in divisional pro"ts [16]:
U[ "a (hI )n #b (hI ).
(19)
i
i i i
i i
The slope a must induce managers to replicate
i
HQ's decisions by making managers' optimization
conditions the same as HQ's conditions.25 The
24 F(Q)"k[ (ii) represents Manager-1's capacity allocation dep
cision as a function of Q.
25 LE [+ n\ (a\ , hI ; h )!+ H[ (a\ , hI )]/La "0"LE [a (hI )
d,e i i i i i
i i i i
i
d,e i i
n\ (a\ , hI ; h )#b (hI )!< (a\ , h )]/La
i i i i
i i
i i i
i
A. Ugarte, S. Oren / Int. J. Production Economics 67 (2000) 235}252
required a
distributes divisional pro"ts
i
proportionally to the ratio of manager's marginal
disutility costs to HQs marginal virtual costs:
d< (a\ , hI )/da\
i.
a (hI )" i i i
i i
dH[ (a\ , hI )/da\
i i i
i
(20)
The intercept b must induce incentive compatibili
ity. Intuitively, the compensation under this policy
must be equal to or greater than the compensation
under the centralized revelation policy.26 But decentralization increases managers' expected marginal disutility cost because they have to make all
the local decisions. The decentralized informational
rents must cover the increase in managers' disutility
costs, i.e., b (h ) must be increased by27
i i
P
hI i
hl
a (t)
i
LE j [n (a\ H(t, h ), t, h ; hI )]
j
j i dt.
h i i
LhI
i
The decentralized revelation compensation
U[ H pays managers for their net contribution to
i
divisional pro"ts a (n !E[n]), for their disutility
i i
costs, and for the value of their private information:
U (n\ , hI )
i i i
The increase in informational rents due to decentralization causes an increase in the decentralized
managers' virtual costs:
E j [U[ H]"H[ (a\ , hI )
i i i
h i
"< (a\ , hI )
i i i
L< (a\ , hI )
Ln (a\ , hI ; hI ) FM i (hI )
h i .
i i i !a (hI ) i i i i
!
i i
LhI
f i (hI )
LhI
i
h i
i
(22)
A
B
5.3. Managers' decisions
Managers make participation, reporting, and
production activity decisions. The decentralized
revelation payment U[ H induces managers to participate and align their objectives with the objectives of the "rm; the previous section shows how
this payment induces managers to participate and
to report their true private information. To make
production activity decisions, managers solve:
max [a (hI )E [n\ (a\ , hI ; h )]!E [< (a\ , h )]#b (hI )
i i d,e i i i i
d,e i i i
i i
a\ i
"a (hI )E [n\ (a\ , hI ; hI )!H[ (a\ , hI )]#b (hI )]
i i d,e i i i i
i i i
i i
(23)
Whereas HQ would have solved:
"a (hI )(n\ (a\ , hI ; h )!E [n\ (a\ H(hI ), hI ; hI )])
i i i i i i
d,e i i i i i
#E
d,e
P
hI i
#
243
h
-
C
a (hI )
i i
hi L< (a\ H(t), t)
i i
dt
LhI
hi
P
< (a\ H(hI ), hI )!
i i i i
I
LE [n (a\ H(hI ), t; t)]
d,e i i i
dt.
LhI
i
D
(21)
26 Hence b *!a (h )E [n (a\ H(hI ), hI ; hI )]#UK (hI ; h ) where
i
i i d,e i i i i i
i i i
E [n (a\ H(hI ), hI ; hI )] are the pro"ts realized if HQ had made the
d,e i i i i i
decisions, and UK is the centralized revelation compensation (Eq.
i
(10)).
27 MMR [2] and Vaysman [3] concluded that the informational rents in centralization and decentralization need not be
di!erent. This because they did not model did not model the
production uncertainty and the e!ect of private information on
production decisions.
max E [n\ (a\ , hI ; h )#n\ (a\ , hI ; hI )
d,e 1 1 1 1
2 2 2 2
a\ 1 ,a\ 2
!H[ (a\ , hI )!H[ (a\ , hI )].
(24)
1 1 1
2 2 2
a has been chosen to make the above two maximizai
tion problems equivalent.
In Case (i), Manager-1 selects k[ (i)"K!k[ (i); this
p
s
decision does increase Manager-1's virtual costs because the decision does not increase his/her disutility
costs.28 Manager-2 selects k[ H(i), I[ H(i); these decisions
p
increase Manager-2's disutility costs and consequently his/her virtual costs.29 The increase in Manager-2's virtual costs is separable and independent
28 a "0, H[ "HK , U[ (i)"U[ .
1
1
1 1
1
29 a O0, H[ 'HK , U[ (i)'UK .
2
2
2 2
2
244
A. Ugarte, S. Oren / Int. J. Production Economics 67 (2000) 235}252
of production activity decisions; as a result, Manager-2 selects the same production activity levels as in
the centralized revelation policy k[ H(i)"kK H and
p
p
I[ H(i)"IK H.
In case (ii), Manager-1 selects k(ii)(Q) so that Divisp
ion-1's marginal cost of understock and overstock are
equal; this decision does not consider Division-2's
demand uncertainty.30
The exclusion of Division-1's uncertainty in Division-2's decisions, due to decentralization, decreases
Division-2's perceived marginal costs of overstock
and understock leading to ine$cient allocations
(I[ (Hii)'IK (H)) and (k[ (Hii)(QH)'k[ (H)).
p
p
LH[ (ii)(k[ (Hii), hI )
1
p# 1 p
Lk
p
L:e6 (g(k[ (Hii), z (hI , x))!Q) f (x)dx
p
1 1
e
!h eQ
1
Lk
p
L:eQ (Q!g(k[ (Hii), z (hI , x))) f (x)dx
p
1 1
e
"s el
.
(25)
2
Lk
p
The above decision increases Manager-1's marginal
disutility costs and hence his/her informational
rents.31 Manager-2 selects I(ii) and Q not taking into
account the production uncertainty at Division-1 and
ignoring the e!ect of his/her decisions on Division-1's
understock and overstock costs. Manager-2 selects
QH so that Division-2's expected marginal costs of
overstock and understock are equal:
In Case (i), the losses ¸(i) are higher than in the
Centralized Revelation Policy due to the increase in
Manager-2's informational rent.32 In Case (ii), the
losses ¸(ii) are higher than in the Centralized Revelation Policy due to an increase in mangers' informational rents and due to overallocation of production
resources. The decoupling of divisional uncertainties
in Case (ii) leads to a distortion of expected marginal
stockout, overstock, and investment calculations:
Manager-1 does not account for understock costs
when d*Q, and Manager-2 does not account for
costs when Q'd(g(ii) . Consequently, Manager-2
(Q)
expects unrealistic higher marginal revenues from investment and over allocates resources.
pLF(Q) LH[ (**)(F(Q), hI )
1
# 1
LQ
LQ
!h F (QH; I[ H(**), z )"s FM (QH; I[ H(**), z ).
(26)
1 d
2
2 d
2
It selects I[ H(ii) so that Division-2's expected marginal
revenues and costs from investment are equal:
LE [d(I[ H(ii), z )]
2
(p !+ c !s ) d
2
i
2
LI
i
L:QHF (x; I[ H(ii), z )dx]
2
!(s !h ) 0 d
2
1
LI
LH[ (ii)(I[ Hii, hI )
2 "1.
! 2
LI
5.4. Ezciency losses
5.4.1. Rectifying ezciency losses in Case (ii)
To rectify e$ciency losses in Case (ii), Division-2's
price structure can be modi"ed, (p , h , s )N
2 1 2
(p@ , h@ , s@ ) so as to induce Manager-2 to internalize
2 1 2
the e!ect of his/her decision on Division-1. Manager2 needs to take into consideration that when d(Q
and g(k[ H, z )(Q and expected salvage revenues are
p 1
lower; and when Q(d, Q(g(k[ H, z ) expected
p 1
stock-out costs are also lower:33
p@ "p P[d)g(kK H, z )Dd(Q]
2
2
p 1
A
p
# p !s !+ c !
2
2
i E [z ]
e 1
i
B
]P[d'g(kK , zH)Dd(Q],
p 1
(27)
30 Here g(k[ (Hii), z(hI ,e ))"Q and [e , e ] is the support for the
p
1 Q
- 6
distribution F (.). The solution to this equation determines
e
F "kH(**) which is needed to determine the transfer price,
(Q)
p
¹(Q; hI ).
1
31 a(ii)'0, H[ (**)*HK (*), and U(**)'U(* ).
1
1
1
1
1
32 This case is just like the Centralized Revelation Policy,
except that Manager-2 makes all the decisions instead of HQ.
33 To compute these prices, one can use the probability structure characterized in the Centralized Revelation Policy. For
example,
FM (g(k[ H 1 ; IH, hI )!FM (Q; IK H, hI )
p,z )
2
d
2
P[d'g(k[ H, z )D (Q]" d
p 1 d
F (Q; IH, hI )
d
2
A. Ugarte, S. Oren / Int. J. Production Economics 67 (2000) 235}252
h@ "h P[d)g(kK H, z )Dd(Q]
p 1
1
1
#0P[d'g(kK H, z )Dd(Q],
p 1
s@ "s P[d'g(kK H, z )Dd(Q]
p 1
2
2
p
P[d)g(kK H, z )Dd'Q].
# +c#
p 1
i E [z ]
e
1
i
A
245
vaging a unit of inputs to Division-2 h "10.
1
The costs parameters are:
per unit production cost at the divisions
c "c "45,
1
2
and penalty cost per unit of Division-2's backlogged demand s "170
2
B
(28)
The above price recti"cation prevents Division-2
from overexpending and from operating at a high
probability of stock-out because it decreases Division-2's decentralized marginal expected revenues.
6. Numerical example
The following examples is primarily intended to
illustrate the comparative e$ciency of the three policies studied in this paper. However, the functional
forms used in the example are su$ciently rich to be
considered as a "rst-order approximate model of
a manufacturing/marketing organization, which with
proper parameterization can be used to set compensation and transfer prices.
f Division-1's production of inputs for Division-2 is
g((k , z(hI , e))"k ](z1(hI , e)"z (hI , 0)!e);
p
1
p
1
1 1
(z (hI , 0)"z8 #c hI ) is the theoretical productiv1 1
1
1 1
ity, z8 "0.6 is the productivity upper bound with1
out private information is, c "0.25 is a constant
1
of proportionally, and e3[0, z (hI , 0)] is the uni1 1
formly distributed uncontrollable production
noise.
Division-2's demand d(I, z ) is exponentially
2
distributed with mean E [d(I, z (hI ))]"
d
2 2
(r1(hI )]r (I)); r "500,000 ln (I/500,000), and
2
2
2(I)
r 2 "0.125h #0.0625.
2
1(h )
f Managers' disutility costs are < (a , h )"
i i i
g a (1.5!h ), where g "1 and g "0.1 are
i i
i
1
2
proportionality constants. Managers' private information parameter h 3[h , h ]"[0.2, 1.2] is
i
l u
uniformly distributed.
f The revenue parameters for the "rm are:
price per unit of Division-2's "nal product
p "275,
2
price per unit of Division-1's capacity sold in the
external market p"29, and net pro"ts after sal-
6.1. Using the CCC policy
Fig. 4 show HQ's production decisions in this
policy kH and IH as increasing functions of manp
agers' reported private information hI , hI .
1 2
Fig. 5 show managers' reporting strategy hI ,
1
hI when the CCC policy o!ers then U "= #
2
i
i
k E [P]; even a high k does not deter
i d,e
i
managers from distorting their private information.34
Fig. 6, from Eq. (9), show the e$ciency losses of
this policy when compared with the e$ciency of the
"rst-best solution.35
6.2. Using CR policy
Fig. 7 shows HQ's optimal capacity kK H(hI ) and
p
marketing expenditures and IK H(hI ) decisions when
using the CR policy.
Fig. 8 shows managers' expected utility as functions of their reporting strategy (hI H, h ). The comi i
pensation that HQ o!ers managers, Eq. (10), is
maximized when managers report hI H"h .
i
i
Fig. 9 shows the e$ciency losses when using the
CR policy according to Eq. (15). In this example,
losses when using the CR policy are lower
than when using the CCC policy; paying for
access to true private information is more e$cient
than underallocating expensive production
resources. Our model re#ects the fact that HTMOs
34 Here, global pro"t sharing incentives are creating the conditions for free riding [14].
35 The "rst-best solution is the solution that can be obtained
when private information does not exist; HQ does not have to
align managers' objectives to "rms' objectives and hence compensates managers only for their participation.
246
A. Ugarte, S. Oren / Int. J. Production Economics 67 (2000) 235}252
Fig. 4. CCC Capacity kH(hI ) and marketing expenditures IH(hI )"$.
p
Fig. 5. Managers' reporting strategy hI (k , h ) when U "= #k E [P].
i i i
i
i
i d,e
use very expensive resources with a high rate of
obsolescence, which have to be utilized very
e$ciently.36
36 A modern production facility for integrated circuit costs
around one billion dollars; a single photolithography machine
costs around "ve million dollars [11].
6.3. Using DR policy
In Case (i), DR and CR allocations are the same;
whereas in Case (ii), DR allocations are greater as
shown in Fig. 10.
Fig. 11 illustrate the e$ciency losses in a
DR policy. Losses in case (ii) are greater
than in case (i), because in case (ii) activity
A. Ugarte, S. Oren / Int. J. Production Economics 67 (2000) 235}252
247
7. Conclusion
Our results have theoretical and practical implications.
7.1. Theoretical results
We have found desirable conditions for each
policy.
Fig. 6. E$ciency Losses ¸ "$.
k
allocations and compensations are higher and
more ine$cient.
Fig. 12 shows a reduction in the e$ciency losses
in Case (ii) after rectifying prices (¸(ii){); now
the losses in both cases are similar. This "gure
also shows that even after the price recti"cation,
the e$ciency losses of the DR policy are lower
than in the CCC policy but higher than in the
CR policy.
f When private information does not exist centralized command and control policies are superior.
f When private information exists but it does not
a!ect operational decisions there are two situations. If the production resources are inexpensive, the centralized command and control policy
is superior, because it does not have to pay
informational rents in exchange for true private
information. If the production resources are
expensive, the centralized revelation policy is
superior, because it relies on true private
information.
f When private information exists and it a!ects
operational decisions across the divisions in the
chain, the decentralized revelation policy is superior but it requires carefully designated internal markets; it requires compensations based on
Fig. 7. CR capacity kK H(hI ) and marketing expenditures IK H(hI )"$.
p
248
A. Ugarte, S. Oren / Int. J. Production Economics 67 (2000) 235}252
Fig. 8. Managers' expected utility in a CR policy.
tralization is less e$cient than centralization if
private information a!ects interim operational
decisions, thus increasing managers' personal costs
and rents. The e$ciency losses due to decentralization can be recti"ed: Bushnell and Oren [17] and
Gilbert and Riordan [18] have shown that
competition can reduce the capacity to extract
informational rents, and we have shown that
internal prices can induce divisions to account for
the global impact of their decisions, i.e., decentralization costs.
7.2. Practical results
Fig. 9. E$ciency losses in a CR policy.
performance and private information, and
it also requires transfer prices that fairly allocate
production, information, and decentralization
costs.
Our work added operational uncertainties to the
models of MMR [2] and Vaysman [3]. We show
that even under unlimited communication, decen-
In practice, the level of abstraction used
in this research is not needed because private information and disutility costs are not measurable,
but they should not be ignored. The following
are rules of thumb based on the insights
derived from our model and analysis that can be
used to minimize the losses due to asymmetric
information:
f In organizations with complex operations, delegate the decisions to the better informed
workers; delegation must be accompanied by
incentives, performance evaluation measures,
A. Ugarte, S. Oren / Int. J. Production Economics 67 (2000) 235}252
249
Fig. 10. DR capacity k[ H(ii) and marketing I[ H(ii)"$.
p
Fig. 11. E$ciency losses ¸(i) and ¸(ii) in a DR policy.
and mechanisms geared to achieve incentive
compatibility.37
f Use economic instead of technical measures of
performance; they induce a direct focus on value-
added contributions and uncover the hidden ine$ciencies characteristic of internal supply
chains with captive technologies.38
37 Delegation is like decentralization; it gives its best results
when there is private information that a!ects operational decisions.
38 We have show that the rewards in the CCC policies are
based on qualitative performance evaluations and that they fail
to achieve incentive compatability.
250
A. Ugarte, S. Oren / Int. J. Production Economics 67 (2000) 235}252
are outside the organization's control, i.e., suppliers
and customers. The mechanisms will be designed to
increase quality, improve delivery performance,
and reduce demand #uctuations.
8. Uncited References
The following works are also of interest to the
reader: [19}80].
References
Fig. 12. DR e$ciency losses ¸(ii){ for the recti"ed Case (ii).
f Discourage `free ridinga by rewarding global
productivity using global performance measures
and local productivity using local performance
measures.39
f Base rewards on a combination of estimated and
observed performance to improve the e$ciency
outcomes of planning decisions.40
7.3. Future research
Large organizations, public and private, are
viewing themselves as supply chains connecting
suppliers and customers; they are modeling their
operations as a chain of functions, events, transactions, and decisions that occur in the #ow of their
product or services from suppliers to customers.
A natural addition to this research would be to
expand the model to analyze the coordination of
production for several periods where learning of
private information is possible in each period. The
model will also consider the design of market mechanism to coordinate supply chain operations that
39 The CCC policy in our example paid high rewards based on
global pro"ts but it failed to induce the right behavior.
40 The revelation compensation in the DR policy is based on
expected and realized pro"ts to fully induce incentive compatibility.
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[42] M. Hag
Coordination of internal supply chains in vertically integrated
high-tech manufacturing organizations (HTMOs)
Armando Ugarte!,*, Shmuel Oren"
!i2 Technologies, 303 Twin Dolphin Drive, Suite 210, Redwood City, CA 94065, USA
"Department of Industrial Engineering and Operations Research, University of California at Berkeley, Berkeley, CA 94720, USA
Received 24 February 1998; accepted 19 January 2000
Abstract
This paper uses economic mechanisms to coordinate supply chains within High-Tech Manufacturing Organizations
(HTMOs). It models the one-shot initial production and allocation decisions involved in the production and marketing
of new technologies; these decisions are driven by the economic objectives of the "rm and of the employees with private
information } the experts. It analyzes and compares the e$ciency of three coordination policies: centralized command and
control, centralized revelation, and decentralized revelation. It shows that decentralized policies introduce an additional
cost, and it proposes rules of thumb for coordinating supply chains within "rms that use many experts. ( 2000
Published by Elsevier Science B.V. All rights reserved.
Keywords: Coordination; Firm organization and market structure; Vertical integration; Markets vs. hierarchies
1. Introduction
HTMOs are large and vertically integrated so as
to take advantage of economies of scale and scope,
reduce their time to market, and a!ord periodic
large capital investments. HTMOs have several
divisions running technologically complex operations. The internal transactions in large and complex organizations are characterized by
information asymmetries and lack of market competition [1].
HTMOs are continuously looking for improvements in their overall supply chain e$ciencies.
* Corresponding author.
E-mail addresses: armando}[email protected] (A. Ugarte),
[email protected] (S. Oren).
Companies such as Hewlett Packard (HP) and
IBM are continuously "ne tuning their organizations to better coordinate their internal supply
chains. Hewlett Packard (HP) fabricates semiconductors which it subsequently uses to build computers, printers, fax machines, medical devices, etc.
In the late 1980s, HP decentralized its organizational structure and created independent business
units that were asked to focus attention on improving their cost e$ciency and market responsiveness.
Similarly, IBM after achieving technological
leadership in semiconductor manufacturing expanded their production through forward integration to produce computers and other high-tech
products. In the early 1990s, however, IBM had to
down size and restructure itself into a less hierarchical organization in pursuit of higher e$ciency. The
success of HTMOs such as HP and IBM depends
0925-5273/00/$ - see front matter ( 2000 Published by Elsevier Science B.V. All rights reserved.
PII: S 0 9 2 5 - 5 2 7 3 ( 0 0 ) 0 0 0 2 2 - 0
236
A. Ugarte, S. Oren / Int. J. Production Economics 67 (2000) 235}252
on their technological leadership and the e$cient
coordination of their supply chains.
This paper evaluates the use of economic market
mechanisms to coordinate a HTMO's production
and marketing decisions of a new proprietary technology.1 In Section 2, We model the coordination
of production and allocation decisions during the
introduction of a new technology as decisions that
are driven by the economic objectives of the "rm
and of the employees with private information } the
experts.2 We investigate and compare the e$ciency
of a Centralized Command and Control policy,
Section 3; a Centralized Revelation policy, Section
4; and a Decentralized Revelation policy, Section 5.
In Section 6, we illustrate the e$ciency of the policies analyzed by means of a numerical example
consistent with our model. In Section 7, we generalize the e$ciency condition for the three policies and
show that decentralized policies introduce a decentralized e$ciency cost.3 Finally, we propose some
rules of thumb for coordinating internal supply
chains in HTMOs.
2. A coordination model for HTMOs
In the remainder of this paper we consider a
stylized HTMO consisting of a Headquarters division (HQ) and two vertically integrated production
divisions, Division-1 and Division-2. Division-1
produces an intermediate product using state-ofthe-art technology, such as integrated circuits; Division-2 uses part of the output from Division-1 to
assemble a "nal product, such as printers, computers, phones, etc. HQ coordinates the divisions
1 Our objective is not to replicate generic economics results
but rather to add structure to the models employed in the
economics literature so as to specialize and reinterpret these
results in a manufacturing context.
2 Private information represents the knowledge, intuition, experience, and e!ort of managers and experts; this information is
not ex-ante observable by the "rm.
3 This result rea$rms the results obtained by Melumad et al.
[2] hereafter referred as MMR 1995 } and Vaysman [3]; our
model expanded the e!ect of private information onto the operation decisions which have `supply chaina e$ciency connotations.
using information provided by the division managers, Manager-1 and Manager-2.
We make three important assumptions. First, we
assume that the initiative, knowledge, e!ort, experience, and intuition of the experts play a major role
in the development, design, production, and marketing of new technologies. Second, we assume that
the productivity of a new technology is uncertain
due to its immaturity and workers' heterogeneity in
mastering new technologies. Third, We assume that
expert employees are rational, risk neutral, and
utility-maximizing decision makers; their objective
is to maximize their income and/or to minimize
their disutility from e!ort, which we model as disutility costs.
2.1. Production characteristics
Division-2 uses inputs produced at Division-1 to
assemble and market a "nished product based on
a new technology. The demand for its "nished
product d(I, z (h )), with cumulative probability
2 2
distribution F (.; I, z ), has a "rst-order stochastic
d
2
dependency on marketing expenditures I and on
marketing productivity z (h ). Marketing produc2 2
tivity z (h ) depends on Manager-2's private
2 2
information parameter h , which accounts for
2
Manager-2's market information, connections, and
e!ectiveness.4
Division-1 operates a state-of-the-art production
facility with a capacity of K regular production
hours per period;5 of which k hours are sold to
s
external customers and k hours are used to
p
produce inputs for Division-2. The production of
inputs for Division-2, Mg(k , z (h , e))"k z N, is
p 1 1
p 1
done by means of a new proprietary technology
with uncertain production yield. Productivity
z (h , e) depends on Manager-1's private informa1 1
tion parameter h , and on an uncertain level of
1
production &noise' e. The parameter h accounts for
1
Manager-1's experience and e!ectiveness in bringing new technologies up to production maturity.6
Production noise e, with cumulative probability
4 Higher levels of h are desirable, Lz (h )/Lh '0.
2
2 2
2
5 K doe not include overtime hours.
6 Higher levels of h are desirable, Lz (h , e)/Lh '0.
1
1 1
1
A. Ugarte, S. Oren / Int. J. Production Economics 67 (2000) 235}252
distribution F (.), accounts for all the uncontrole
lable events that can a!ect production yields and
cycle time.7
2.2. Economic characteristics
HQ's objective is to maximize "rm's expected
pro"ts E[P(.)] from the new technology. Corporate
revenues result from: selling capacity k at a unit
s
pro"t of p dollars, selling Division-2's assembled
products at a unit price of p , and salvaging Divis2
ion-2's intermediate inputs in excess of demand
(g(k , z )!d(I, z ))` at a net unit gain of h dolp 1
2
1
lars.8 Corporate costs result from: production
penalizing
excess
demand
+2 c ]d,
i/1 i
(d(I, z )!g(k , z ))` at a cost of s per excess unit,
2
p 1
2
and from compensating the manager U . Expected
i
corporate pro"ts before compensating managers
are:9
E [P(k , k , I, hI ; h)]
d,e
s p
2
"pk # p ! + c E [d(I, z )]
s
2
i d,e
2
i/1
#h E [max(g(k , z )!d(I, z ), 0)]
1 d,e
p 1
2
!s E [!min(g(k , z )!d(I, z ), 0]!I,
2 d,e
p 1
2
(1)
E [P(k , k , I, hI ; hI )]
d,e
s p
2
"pk # p ! + c E [d(I, z )]
s
2
i d,e
2
i/1
g(kp ,z1 )
F (x)dx
#h E
d
1 e
0
=
FM (x)dx !I.
!s E
d
2 e
g(kp ,z1 )
In the above equation, price per unit of capacity at
Division-1 is positive p'0, price per unit of "nal
product produced at Division-2 is greater than
A
B
A
CP
CP
B
D
D
7 Productivity decreases with noise, Lz (h , e)/Le(0.
1 1
8 (a!b)`"max(a!b, 0).
9 Reported private information hI "(hI , hI ) is a decision vari1 2
able, whereas true private information h"(h , h ) is a para1 2
meter. The arguments of z and z are omitted for ease of
1
2
exposition.
237
production cost p !c !c !p/E [z (h , e)]'0,
2
1
2
e 1 1
there is an overstock cost in Division-1 for
the excess inputs produced for Decision-2
h (p/E [z (h , e)], and the excess demand pen1
e 1 1
alty cost at Division-2 is non-pro"table
s (p !c !c !p/E [z (h , e)].10
2
2
1
2
e 1 1
Managers are utility maximizers, rational, and
risk neutral; the economic utility for the Manager
of the ith Division is ; (U , < ),U !< (a , h ).
i i i
i
i i i
Managers' compensations U are determined by
i
HQ; their disutility or personal costs < (a , h )
i i 1
account for the time, e!ort, and forgone opportunity costs that a manager with private information
parameter h incurs when assigned production
i
activity a ;11 < (.) is assumed to be monotonic and
i
i
single crossing in h to guarantee at least one inceni
tive compatible solution [2]. Su$ciency conditions
for monotonicity and single crossing are satis"ed
when < (.) increases with higher levels of produci
tion activity (L< (a , h )/La '0); decreases with
i i i
i
higher levels of private information (L< (a , h )/
i i i
Lh (0); decreases marginally in production activi
ity and private information (L2< (a , h )/
i i i
Lh La (0); and is convex in production activity
i i
(L2< (a , h )/L2a '0).12 Disutility costs < (.) are
i i i
i
i
not observable to HQ since they depend on managers' private information h ; HQ's prior beliefs
i
about h are characterized by a cumulative probi
ability distribution F i (.: H ) where H ,[h , h ].
i
i
- 6
h
2.3. Coordination decisions
In general the objectives of the HQ and the
managers objectives are not compatible and both
have asymmetric access to information; these two
conditions create incentives for adverse-selection
and/or moral hazard in the behavior of the division
managers.13
10 Overstock cost does not consider inventory costs because
these are negligible.
11 a "k and a "I.
1
p
2
12 For weaker conditions see Milgrom and Shannon [4].
13 Moral harzard and/or adverse selection are the result of an
agency relationship that occurs whenever the Principal, HQ,
needs a service from a person or Agent (in our case the Manager)
who has private objectives that are not aligned with those of the
principal (in our case HQ) and is better informed than HQ [5].
238
A. Ugarte, S. Oren / Int. J. Production Economics 67 (2000) 235}252
HQ coordinates and decides on the operational
and the enforcement rules for the one-shot project
of releasing to the market a new technology,
consistent with its objectives and beliefs [6].14
The operational rules determine managers'
responsibilities and regulate the interactions between the divisions involved in the project. The
enforcement rules make managers accountable for
executing the operational rules by determining
divisions' performance measures and managers'
compensations U .
i
Managers actions and decisions obey a utility
maximization rationale with participation and
incentive compatibility conditions. Managers participate in HQ's contract if and only if their utility is
competitive, i.e., greater than their reservation utility ;M (without loss of generality, we set ;M "0.)
i
i
Managers' incentive compatibility condition
requires them to act and decide so as to maximize
their individual utilities. Incentive compatibility
implies than when managers report their private
information parameter hI , they report a parameter
i
value that maximizes their utility:
hI H3argmax ME j [; (U , hI , hI H(h ); h )]
d,e,h
i i i j j i
i
hI i
"E j [U !< (aH(hI , hI H(h )), h )]N.
d,e,h i
i
i i i j j
(2)
3. Centralized command and control (CCC) policy
This coordination policy is commonly observed
in the industry and results from formulations proposed in the Operations Management literature
[7}9], HQ implements the operational and
enforcement rules for this policy assuming that
managers are altruistic, i.e., hI H"h .15
i
i
14 HTMOs allocate many resources to these critical projects,
often hiring experts that join these companies with the mentality
of make-it or break-it.
15 HQ ignores that if managers report hI HOh , HQ cannot
i
i
detect the distortions: productivity z is ex-post observable but
1
depends on unobservable and random production noise e, and
productivity z cannot be accurately inferred from a single
2
realization of random demand.
Fig. 1. Flow of information and product in a CCC policy.
3.1. Coordination rules
HQ implements the following operational rules.
At time t"0, HQ determines managers' compensation U and ranking measures; at time t"0`,
i
HQ asks managers to report their private information, hI , which is equivalent to reporting their proi
ductivity; at time t"0``, HQ determines
production activities k , I; at time t"1, demand
p
d and pro"ts P are realized, and the managers are
compensated. Fig. 1 shows the #ow of information,
in dotted lines, and the #ow of product, in solid lines,
as implemented by the above operational rules.
HQ's enforcement rule, consistent with its
assumption about managers' altruism, sets managers' compensations as #at wages with pro"t sharing incentives, = #k P; and it sets subjective
i
i
managers' performance evaluation measures such
as initiative, quality commitment, productivity
contributions, and dependability.
3.2. HQ's decisions
HQ makes production and marketing decisions
with a pro"t maximizing rationale; in contrast, HQ
decides on the manager's wages = and pro"t
i
sharing fraction k P(.) using a labor market rationi
ale:
Find kH, kH, IH3 argmax E [P(k , k , I, hI ; hI )]
d,e
s p
p s
(3)
s.t. (i) k #k )K.
p
p
Since pro"ts from k are higher than the ones
p
from k , HQ sets kH"K!kH and solves an
p
s
s
unconstrained problem using "rst-order necessary
A. Ugarte, S. Oren / Int. J. Production Economics 67 (2000) 235}252
conditions for optimality.16 HQ selects the kH at
p
which Division-1's expected marginal costs of overstock equate Division-2's expected marginal costs
of understock:
p!h
1
LE [:g(kp ,z1 (hI 1 ,e))F (x; I, z )Lx]
e 0
d
2
Lk
kp /kHp
p
K
K
LE [:= p 1 I 1 F (x; I, z )Lx]
2
e g(k ,z (h ,e)) d
.
(4)
Lk
p
kp /kHp
HQ selects the IH at which expected marginal revenue equals the expected marginal cost from marketing projects:
"s
2
A
p !+ c !s
2
i
2
i
!(s !h )
2
1
B
LE [d(I, z )]
d
2
LI
K
3.2.2. Ezciency losses
E$ciency losses in this policy occur because
HQ's decisions use distorted productivity information, and because managers have no incentive to
report their true private information. HQ ignores
the fact that managers are utility maximizers with
valuable private information, and that they incur
disutility costs. Consequently, managers distort
their private information because their expected
marginal bene"ts from reporting truthfully is zero:
[P(aH(hI , h ), h , h ; h)]
dE
i j i j
k ] d,e,hj
i
dhI
i
hI i /hi
LE j [P(aH(hI , h ), h; h)] LaH
k
d,e,h
i j
"k ] +
,
i
LhI I i i
LaH
h
i
/h
k
k|i,j
(7)
K
K
I/IH
LE [:g(kHp ,z1 (hI 1 ,e))F (x; I, z )Lx]
d
2
e 0
LI
K
"1,
I/IH
(5)
3.2.1. Managers' decisions
Managers follow their utility maximizing objective and accept HQ's contract if their compensations are competitive, i.e.,
E j [U !< (aH, h )]*0.
i i i
d,e,h i
Managers that choose to participate then report
the private information hI H that maximizes their
i
utility. Managers' utilities are the sum of three
concave functions,
E[; ]"= #k E[P]#
i
i
i
(!E[< ]); therefore, their utilities would be maxii
mized when their expected marginal bene"ts equals
their expected marginal cost corresponding to the
reported private information:17
[P(aH(hI , hI H(h )), h , hI H(h ); h)]
dE
i j j
i j j
k ] d,e,hj
i
dhI
i
hI i /hI Hi
dE [< (aH(hI , hI H(h )), h )]
i
" hj i i i j j
.
dhI
I
IH
i
i
i
h /h
K
K
239
(6)
16 Second-order conditions are not needed since E [P(.)] is
d,e
assumed to be concave in k and I. Guarantees a global maxp
imum at any point that satis"es the "rst-order conditions.
17 If managers' compensation consist only of #at wages
U "= , then managers will report the lowest credible level of
i
i
private information hI H(h )"h because their marginal
i i
l
utility from reported private information is negative,
dE[;(U , hI ; h )]/dh "!E[< (aH(hI H, hI H), h )]/dhI (0.
i i i
i
i i i j i
i
but optimality requires that
LE j [P(aH(hI , h ), h; h)]
i j
d,e,h
"0 ∀k3i, j.
LaH
hI i /hi
k
To reduce their disutility costs, managers underreport their private information, i.e., hI H(h )(h . Coni i
i
sequently, HQ's production activity levels aH are
i
based on distorted private information, i.e., lower
estimates of productivity.
K
aH(hI H, hI H), aH(hI H, hI H) N argmax E [P(aH(hI H, hI H),
i i j
d,e
i i j j i j
(8)
aH(hI H, hI H), hI H; h] ∀ hI HO0
j i j
Comparing the e$ciency of this policy to the bench
mark e$ciency of the &"rst best' solution provides
a measure of the e$ciency losses of this policy,
given by Eq. (9). The "rst best solution would be
achieved if private information would not exist and
HQ would not need to align managers and "rms
objectives.
E[¸ ]"E [P(aH(h , h ), aH(h , h )), h , h ; h , h )]
i j i j
i i j j i j
CCC
d,e
!E [P(aH(hI H, hI H), aH(hI H, hI H), hI H, hI H; h , h )]'0.
i i j j i j i j i j
d,e
(9)
4. A centralized revelation (CR) policy
In this coordination policy, HQ maintains centralized control but does not assume that managers
are altruistic. In order to access private information
240
A. Ugarte, S. Oren / Int. J. Production Economics 67 (2000) 235}252
HQ must align the manager's objective with the
objective of the "rm, which is accomplished by
a direct revelation mechanism [2,3].18
4.1. Coordination rules
HQ sets forth the following operational rules: at
time t"0, it determines managers' compensations
UK H; at time t"0`, it asks managers to report their
i
private information parameters hI H; at time
i
t"0``, it makes production activity decisions; at
time t"1, demand d and pro"ts P are realized,
and managers are compensated. Fig. 2 shows the
#ow of information, in dotted lines, and the #ow of
product, in solid lines, for the above set of rules.
HQ designs the enforcement rules, determining
managers' compensations and performance evaluation measures, that maximize the utility of managers who subscribe to the above operational rules
and report their true private information.
4.2. HQ's decisions
HQ o!ers managers the minimum compensation
UK H that maximizes their utility when they are not
i
distorting their private information:19
max E [P(aH(hI ), hI ; hI )]!+2 E i [UK (hI ; h )]
i/1 d,e,h i i i
d,e
UK
i
subject to
(i) h "hI H3 argmax E jEi [UK (hI , h )
d,e,h
i i i
i
i
hI i |Hi
!< (a( H(hI , h ), h )] ∀(i, j),
i i i j i
(ii) E jE1 [UK (hI ; hI )
d,e,h
1 i i
!< (a( (h , h ), h )]*;M
∀(i, j).
i i i j j
i
The optimal managers' compensations UK H must
i
cover managers' disutility costs and pay them
informational
rents
[2].
This
results
18 Revelation mechanisms are based on the revelation principle for communication games with imperfect information [10].
19 Pro"ts before payment to the managers E[P] are de"ned
in Eq. (1).
Fig. 2. Flow of information and product in a CR policy.
from
assuming
that
E jEi [UK 1(hI ; h )]"
i i
d,e,h
E jEi [< (a( (h , h ), h )#¹(hI )], where ¹(hI ) are
d,e,h
i i i j i
i
i
managers' informational rents. To achieve managers' participation ¹(hI )*0, and to achieve inceni
tive compatibility ¹(hI ) must be equal to the second
i
term of Eq. (10).
C
P
UK H(hI ; h )"E j < (a( H(hI , h ), hI )
i i i j i
i i i
h
!
hI i L< (a8 H(t, h ), t)
j
i i
dt .
LhI
hl
i
D
(10)
HQ decides on the divisions' production activity
levels by solving an unconstraint optimization
problem that takes into account the expected optimal managers' compensation E i [UK H(hI , h )] also
h i i i
known as the virtual costs of the managers
HK (a( H, hI ):20
i i i
max E [P(kK , IK , hI ; hI )!HK (kK , hI )!HK (IK , hI )].
d,e
p
1 p 1
2
2
IK ,kK p
(11)
At the optimal capacity kK H, marginal expected cost
p
of understock and overstock are equal, but now
Manager-1's marginal virtual cost increases the
20 HK (a( H, hI )"E i [UK H(hI ; h )]"< (a8 , hI )!(L< (a( , hI )/LhI )
i i i
h
i i i
i i i
i i i
i
(FM i (hI )/f I i (hI ))"b (a )w (hI )!b (a )w@ (hI )(FM i (hI )/f I i (hI )) is conh i h i
i i i i
i i i i h i h i
vex in a as a result of the conditions imposed on < and F i .
i
i
h
A. Ugarte, S. Oren / Int. J. Production Economics 67 (2000) 235}252
241
marginal cost of understock.
4.4. Ezciency losses
LHK (k , hI )
p# 1 p 1
Lk
kp /kHp
p
The losses corresponding to this policy result
from having to pay managers informational rents
to access truthful information. The relative e$ciency measure of this policy, as compared to the "rstbest solution, is given by
K
!h
"s
2
LE [:g(kp ,z1 (hI 1 ,e))F (x; I, z )Lx]
d
2
e 0
1
Lk
kp /kHp
p
K
K
LE [:= p 1 I 1 F (x; I, z )Lx]
2
e g(k ,z (h ,e)) d
.
Lk
kp /kHp
p
(12)
At the optimal expenditures IK H the marginal expected costs are equal to the marginal expected
revenues from marketing expenditures, but now
Manager-2's revelation cost decreases expected
marginal revenue.
A
K
B
LE [d(I, z )]
d
2
p !+ c !s
2
i
2
LI
I/IH
i
!(s !h )
2
1
LE [:g(kHp ,z1 (hI 1 ,e))F (x; I, z )Lx]
d
2
e 0
LI
LHK (I, hI )
2
! 2
LI
K
K
I/IH
(13)
"1.
I/IH
C
¸K " E [P(aH(h), h; h)!+ < (aH, h )]
d,e
i i i
i
C
C
D
! E [P(a( H(h), h; h)!+ HK (a( H, h ]
d,e
i i i
i
"E
d,e
L< (a( , hI )
i i i
LhI
i
FM i (hI )
h i .
f I i (hI )
h i
D
D
(15)
If the production resources being allocated are
very expensive, paying for access to true private
information is more e$cient than underallocating
these resources. This is typically the case in
HTMOs which tend to use very expensive resources with a high rate of obsolescence that must
be utilized e$ciently. For instance, a modern production facility for integrated circuits costs around
one billion dollars; A single photolithography
machine costs around "ve million dollars [11].
4.3. Managers' decisions
5. A decentralized revelation (DR) policy
Each manager reports truthfully if truth-reporting is his/her best strategy under the assumption
that all other managers are also telling the truth. If
it is, then by induction truth-reporting is the best
strategy for all managers. The revelation compensation UK H(.) satis"es managers' participation condition for truth-reporting managers because
E[UK H(h)]'E[< (h)]. It also satis"es their incentive
i
i
compatibility condition because their utilities are
maximized when hI H"h ; their marginal expected
i
i
bene"ts and costs from hI are equal when hI H"h .
i
i
i
dE j [UK H(hI H; h )]
d,e,h i i i
dhI
hI Hi /hi
i
K
dE
[< ](a( H(hI H, h ), h )
" d,e,hj i i i j i
.
dhI
hI Hi /hi
i
K
(14)
Under this coordination policy the HQ delegates
all the local decisions to the divisional managers
and assumes that managers are sel"sh (rather than
altruistic).21 HQ in HTMOs may want to delegate
local decision for the following reasons: faster reaction to the urgency needs of many internal supply
chain decisions [12]; empowerment of well-informed
managers to make the best decisions[13]; and regulation of the monopolistic behavior of divisions controlling captive technologies [14,15].22
21 Arrow [1] proposed the decentralization of large organizations as a way to reduce the ine$ciencies due to asymmetric
information.
22 Decisions in HTMOs require increasingly more accurate
real-time technical and economic information to remain competitive.
242
A. Ugarte, S. Oren / Int. J. Production Economics 67 (2000) 235}252
k[ (i); and Division-1 decides on k[ (i). Pro"ts for each
s
p
division are:
Fig. 3. Flow of information and product in a DR policy.
5.1. Coordination rules
The operational rules for this policy are: at t"0,
HQ sets managers' responsibilities and compensation UK ; at t"0`, it asks the managers to report
i
their private information; at t"0``, it determines
the transfer price ¹(s, hI ) that Division-2 must pay
1
to Division-1 for its services S; at t"0```, Division-2 decides on I and S and Division-1 on k and
s
k ; at t"1, demand and pro"ts are realized. To
p
enforce the above operational rules, HQ speci"es
managers' responsibilities and compensations, and
the transfer price among the divisions. Fig. 3 shows
the product and information #ow implemented by
the above rules.
n\ (k[ (i), hI ; h )"¹(k[ (i), hI )#pk(i)!c g(k(i), z ),
s
1 p 1
p 1
1 s 1 1
n\ (I[ (i), k[ (i), hI ; h )
p 2 2
2
"p d(I[ (i); h )!(s #C )(d!g(k[ (i), z )`
p 1
2
2
2
1
#h (g(k[ (i), z )!d)`
p 1
1
(16)
!¹(k(i), hI )!I[ (i)!c d).
p 1
2
In case (ii) S"Q, Division-2 decides on I[ (i), Q; and
Division-1 decides on k[ (i), k . Pro"ts for each diviss p
ion are:
n\ (k[ (ii), hI ; h )
1 p 1 1
"¹(h[ , hI )#pk[ (ii)!c Q#h (g(k[ (ii), z )!Q)`
p 1
s
1
1
1
(ii)
!s (Q!g(k[ , z ))`,
2
p 1
n\ (I[ (ii), Q, hI ; h )
2
2 2
"p d(I[ (ii); h )!(s #c )(d!Q)`
2
2
2
1
#h (Q!d)`!¹(Q, hI !I[ (ii)!c d. (17)
1
1
2
HQ also decides on the transfer price that Division-2 pays Division-1 in exchange for S. Vaysman
[3] showed that an e$cient transfer price must
transfer the production as well as the virtual costs
associated with S:24
A
5.2. HQ's decisions
HQ decides on managers' responsibilities by separating the "rm pro"t maximization function into
several divisional pro"t maximatization functions,
and by giving each manager the authority and
decision domain needed to maximize its local
pro"ts [6]. In our model, decentralization can be
implemented in two ways depending on the services
S that Division-2 orders from Division-1: S can be
capacity hours k (case i) or it can be inputs Q (case
p
ii).23 In case (i) S"k[ (i), Division-2 decides on I[ (i),
p
23 Hereafter, superscripts (i) and (ii) refer respectively to case
(i) and case (ii).
B
c
]k[ (i)#H[ (k[ (i), hI ),
¹(i)(k[ , hI )(i)" p# 1
p
1 p 1
p 1
E [z ]
e 1
(18)
¹(ii)(Q, hI )"c Q#pF(Q)#H[ (F(Q), hI ).
1
1
1
1
HQ must design the compensation U[ that satisi
"es managers' participation and incentive compatibility conditions in this policy. The simplest form of
a decentralized incentive compatible compensation
scheme is linear in divisional pro"ts [16]:
U[ "a (hI )n #b (hI ).
(19)
i
i i i
i i
The slope a must induce managers to replicate
i
HQ's decisions by making managers' optimization
conditions the same as HQ's conditions.25 The
24 F(Q)"k[ (ii) represents Manager-1's capacity allocation dep
cision as a function of Q.
25 LE [+ n\ (a\ , hI ; h )!+ H[ (a\ , hI )]/La "0"LE [a (hI )
d,e i i i i i
i i i i
i
d,e i i
n\ (a\ , hI ; h )#b (hI )!< (a\ , h )]/La
i i i i
i i
i i i
i
A. Ugarte, S. Oren / Int. J. Production Economics 67 (2000) 235}252
required a
distributes divisional pro"ts
i
proportionally to the ratio of manager's marginal
disutility costs to HQs marginal virtual costs:
d< (a\ , hI )/da\
i.
a (hI )" i i i
i i
dH[ (a\ , hI )/da\
i i i
i
(20)
The intercept b must induce incentive compatibili
ity. Intuitively, the compensation under this policy
must be equal to or greater than the compensation
under the centralized revelation policy.26 But decentralization increases managers' expected marginal disutility cost because they have to make all
the local decisions. The decentralized informational
rents must cover the increase in managers' disutility
costs, i.e., b (h ) must be increased by27
i i
P
hI i
hl
a (t)
i
LE j [n (a\ H(t, h ), t, h ; hI )]
j
j i dt.
h i i
LhI
i
The decentralized revelation compensation
U[ H pays managers for their net contribution to
i
divisional pro"ts a (n !E[n]), for their disutility
i i
costs, and for the value of their private information:
U (n\ , hI )
i i i
The increase in informational rents due to decentralization causes an increase in the decentralized
managers' virtual costs:
E j [U[ H]"H[ (a\ , hI )
i i i
h i
"< (a\ , hI )
i i i
L< (a\ , hI )
Ln (a\ , hI ; hI ) FM i (hI )
h i .
i i i !a (hI ) i i i i
!
i i
LhI
f i (hI )
LhI
i
h i
i
(22)
A
B
5.3. Managers' decisions
Managers make participation, reporting, and
production activity decisions. The decentralized
revelation payment U[ H induces managers to participate and align their objectives with the objectives of the "rm; the previous section shows how
this payment induces managers to participate and
to report their true private information. To make
production activity decisions, managers solve:
max [a (hI )E [n\ (a\ , hI ; h )]!E [< (a\ , h )]#b (hI )
i i d,e i i i i
d,e i i i
i i
a\ i
"a (hI )E [n\ (a\ , hI ; hI )!H[ (a\ , hI )]#b (hI )]
i i d,e i i i i
i i i
i i
(23)
Whereas HQ would have solved:
"a (hI )(n\ (a\ , hI ; h )!E [n\ (a\ H(hI ), hI ; hI )])
i i i i i i
d,e i i i i i
#E
d,e
P
hI i
#
243
h
-
C
a (hI )
i i
hi L< (a\ H(t), t)
i i
dt
LhI
hi
P
< (a\ H(hI ), hI )!
i i i i
I
LE [n (a\ H(hI ), t; t)]
d,e i i i
dt.
LhI
i
D
(21)
26 Hence b *!a (h )E [n (a\ H(hI ), hI ; hI )]#UK (hI ; h ) where
i
i i d,e i i i i i
i i i
E [n (a\ H(hI ), hI ; hI )] are the pro"ts realized if HQ had made the
d,e i i i i i
decisions, and UK is the centralized revelation compensation (Eq.
i
(10)).
27 MMR [2] and Vaysman [3] concluded that the informational rents in centralization and decentralization need not be
di!erent. This because they did not model did not model the
production uncertainty and the e!ect of private information on
production decisions.
max E [n\ (a\ , hI ; h )#n\ (a\ , hI ; hI )
d,e 1 1 1 1
2 2 2 2
a\ 1 ,a\ 2
!H[ (a\ , hI )!H[ (a\ , hI )].
(24)
1 1 1
2 2 2
a has been chosen to make the above two maximizai
tion problems equivalent.
In Case (i), Manager-1 selects k[ (i)"K!k[ (i); this
p
s
decision does increase Manager-1's virtual costs because the decision does not increase his/her disutility
costs.28 Manager-2 selects k[ H(i), I[ H(i); these decisions
p
increase Manager-2's disutility costs and consequently his/her virtual costs.29 The increase in Manager-2's virtual costs is separable and independent
28 a "0, H[ "HK , U[ (i)"U[ .
1
1
1 1
1
29 a O0, H[ 'HK , U[ (i)'UK .
2
2
2 2
2
244
A. Ugarte, S. Oren / Int. J. Production Economics 67 (2000) 235}252
of production activity decisions; as a result, Manager-2 selects the same production activity levels as in
the centralized revelation policy k[ H(i)"kK H and
p
p
I[ H(i)"IK H.
In case (ii), Manager-1 selects k(ii)(Q) so that Divisp
ion-1's marginal cost of understock and overstock are
equal; this decision does not consider Division-2's
demand uncertainty.30
The exclusion of Division-1's uncertainty in Division-2's decisions, due to decentralization, decreases
Division-2's perceived marginal costs of overstock
and understock leading to ine$cient allocations
(I[ (Hii)'IK (H)) and (k[ (Hii)(QH)'k[ (H)).
p
p
LH[ (ii)(k[ (Hii), hI )
1
p# 1 p
Lk
p
L:e6 (g(k[ (Hii), z (hI , x))!Q) f (x)dx
p
1 1
e
!h eQ
1
Lk
p
L:eQ (Q!g(k[ (Hii), z (hI , x))) f (x)dx
p
1 1
e
"s el
.
(25)
2
Lk
p
The above decision increases Manager-1's marginal
disutility costs and hence his/her informational
rents.31 Manager-2 selects I(ii) and Q not taking into
account the production uncertainty at Division-1 and
ignoring the e!ect of his/her decisions on Division-1's
understock and overstock costs. Manager-2 selects
QH so that Division-2's expected marginal costs of
overstock and understock are equal:
In Case (i), the losses ¸(i) are higher than in the
Centralized Revelation Policy due to the increase in
Manager-2's informational rent.32 In Case (ii), the
losses ¸(ii) are higher than in the Centralized Revelation Policy due to an increase in mangers' informational rents and due to overallocation of production
resources. The decoupling of divisional uncertainties
in Case (ii) leads to a distortion of expected marginal
stockout, overstock, and investment calculations:
Manager-1 does not account for understock costs
when d*Q, and Manager-2 does not account for
costs when Q'd(g(ii) . Consequently, Manager-2
(Q)
expects unrealistic higher marginal revenues from investment and over allocates resources.
pLF(Q) LH[ (**)(F(Q), hI )
1
# 1
LQ
LQ
!h F (QH; I[ H(**), z )"s FM (QH; I[ H(**), z ).
(26)
1 d
2
2 d
2
It selects I[ H(ii) so that Division-2's expected marginal
revenues and costs from investment are equal:
LE [d(I[ H(ii), z )]
2
(p !+ c !s ) d
2
i
2
LI
i
L:QHF (x; I[ H(ii), z )dx]
2
!(s !h ) 0 d
2
1
LI
LH[ (ii)(I[ Hii, hI )
2 "1.
! 2
LI
5.4. Ezciency losses
5.4.1. Rectifying ezciency losses in Case (ii)
To rectify e$ciency losses in Case (ii), Division-2's
price structure can be modi"ed, (p , h , s )N
2 1 2
(p@ , h@ , s@ ) so as to induce Manager-2 to internalize
2 1 2
the e!ect of his/her decision on Division-1. Manager2 needs to take into consideration that when d(Q
and g(k[ H, z )(Q and expected salvage revenues are
p 1
lower; and when Q(d, Q(g(k[ H, z ) expected
p 1
stock-out costs are also lower:33
p@ "p P[d)g(kK H, z )Dd(Q]
2
2
p 1
A
p
# p !s !+ c !
2
2
i E [z ]
e 1
i
B
]P[d'g(kK , zH)Dd(Q],
p 1
(27)
30 Here g(k[ (Hii), z(hI ,e ))"Q and [e , e ] is the support for the
p
1 Q
- 6
distribution F (.). The solution to this equation determines
e
F "kH(**) which is needed to determine the transfer price,
(Q)
p
¹(Q; hI ).
1
31 a(ii)'0, H[ (**)*HK (*), and U(**)'U(* ).
1
1
1
1
1
32 This case is just like the Centralized Revelation Policy,
except that Manager-2 makes all the decisions instead of HQ.
33 To compute these prices, one can use the probability structure characterized in the Centralized Revelation Policy. For
example,
FM (g(k[ H 1 ; IH, hI )!FM (Q; IK H, hI )
p,z )
2
d
2
P[d'g(k[ H, z )D (Q]" d
p 1 d
F (Q; IH, hI )
d
2
A. Ugarte, S. Oren / Int. J. Production Economics 67 (2000) 235}252
h@ "h P[d)g(kK H, z )Dd(Q]
p 1
1
1
#0P[d'g(kK H, z )Dd(Q],
p 1
s@ "s P[d'g(kK H, z )Dd(Q]
p 1
2
2
p
P[d)g(kK H, z )Dd'Q].
# +c#
p 1
i E [z ]
e
1
i
A
245
vaging a unit of inputs to Division-2 h "10.
1
The costs parameters are:
per unit production cost at the divisions
c "c "45,
1
2
and penalty cost per unit of Division-2's backlogged demand s "170
2
B
(28)
The above price recti"cation prevents Division-2
from overexpending and from operating at a high
probability of stock-out because it decreases Division-2's decentralized marginal expected revenues.
6. Numerical example
The following examples is primarily intended to
illustrate the comparative e$ciency of the three policies studied in this paper. However, the functional
forms used in the example are su$ciently rich to be
considered as a "rst-order approximate model of
a manufacturing/marketing organization, which with
proper parameterization can be used to set compensation and transfer prices.
f Division-1's production of inputs for Division-2 is
g((k , z(hI , e))"k ](z1(hI , e)"z (hI , 0)!e);
p
1
p
1
1 1
(z (hI , 0)"z8 #c hI ) is the theoretical productiv1 1
1
1 1
ity, z8 "0.6 is the productivity upper bound with1
out private information is, c "0.25 is a constant
1
of proportionally, and e3[0, z (hI , 0)] is the uni1 1
formly distributed uncontrollable production
noise.
Division-2's demand d(I, z ) is exponentially
2
distributed with mean E [d(I, z (hI ))]"
d
2 2
(r1(hI )]r (I)); r "500,000 ln (I/500,000), and
2
2
2(I)
r 2 "0.125h #0.0625.
2
1(h )
f Managers' disutility costs are < (a , h )"
i i i
g a (1.5!h ), where g "1 and g "0.1 are
i i
i
1
2
proportionality constants. Managers' private information parameter h 3[h , h ]"[0.2, 1.2] is
i
l u
uniformly distributed.
f The revenue parameters for the "rm are:
price per unit of Division-2's "nal product
p "275,
2
price per unit of Division-1's capacity sold in the
external market p"29, and net pro"ts after sal-
6.1. Using the CCC policy
Fig. 4 show HQ's production decisions in this
policy kH and IH as increasing functions of manp
agers' reported private information hI , hI .
1 2
Fig. 5 show managers' reporting strategy hI ,
1
hI when the CCC policy o!ers then U "= #
2
i
i
k E [P]; even a high k does not deter
i d,e
i
managers from distorting their private information.34
Fig. 6, from Eq. (9), show the e$ciency losses of
this policy when compared with the e$ciency of the
"rst-best solution.35
6.2. Using CR policy
Fig. 7 shows HQ's optimal capacity kK H(hI ) and
p
marketing expenditures and IK H(hI ) decisions when
using the CR policy.
Fig. 8 shows managers' expected utility as functions of their reporting strategy (hI H, h ). The comi i
pensation that HQ o!ers managers, Eq. (10), is
maximized when managers report hI H"h .
i
i
Fig. 9 shows the e$ciency losses when using the
CR policy according to Eq. (15). In this example,
losses when using the CR policy are lower
than when using the CCC policy; paying for
access to true private information is more e$cient
than underallocating expensive production
resources. Our model re#ects the fact that HTMOs
34 Here, global pro"t sharing incentives are creating the conditions for free riding [14].
35 The "rst-best solution is the solution that can be obtained
when private information does not exist; HQ does not have to
align managers' objectives to "rms' objectives and hence compensates managers only for their participation.
246
A. Ugarte, S. Oren / Int. J. Production Economics 67 (2000) 235}252
Fig. 4. CCC Capacity kH(hI ) and marketing expenditures IH(hI )"$.
p
Fig. 5. Managers' reporting strategy hI (k , h ) when U "= #k E [P].
i i i
i
i
i d,e
use very expensive resources with a high rate of
obsolescence, which have to be utilized very
e$ciently.36
36 A modern production facility for integrated circuit costs
around one billion dollars; a single photolithography machine
costs around "ve million dollars [11].
6.3. Using DR policy
In Case (i), DR and CR allocations are the same;
whereas in Case (ii), DR allocations are greater as
shown in Fig. 10.
Fig. 11 illustrate the e$ciency losses in a
DR policy. Losses in case (ii) are greater
than in case (i), because in case (ii) activity
A. Ugarte, S. Oren / Int. J. Production Economics 67 (2000) 235}252
247
7. Conclusion
Our results have theoretical and practical implications.
7.1. Theoretical results
We have found desirable conditions for each
policy.
Fig. 6. E$ciency Losses ¸ "$.
k
allocations and compensations are higher and
more ine$cient.
Fig. 12 shows a reduction in the e$ciency losses
in Case (ii) after rectifying prices (¸(ii){); now
the losses in both cases are similar. This "gure
also shows that even after the price recti"cation,
the e$ciency losses of the DR policy are lower
than in the CCC policy but higher than in the
CR policy.
f When private information does not exist centralized command and control policies are superior.
f When private information exists but it does not
a!ect operational decisions there are two situations. If the production resources are inexpensive, the centralized command and control policy
is superior, because it does not have to pay
informational rents in exchange for true private
information. If the production resources are
expensive, the centralized revelation policy is
superior, because it relies on true private
information.
f When private information exists and it a!ects
operational decisions across the divisions in the
chain, the decentralized revelation policy is superior but it requires carefully designated internal markets; it requires compensations based on
Fig. 7. CR capacity kK H(hI ) and marketing expenditures IK H(hI )"$.
p
248
A. Ugarte, S. Oren / Int. J. Production Economics 67 (2000) 235}252
Fig. 8. Managers' expected utility in a CR policy.
tralization is less e$cient than centralization if
private information a!ects interim operational
decisions, thus increasing managers' personal costs
and rents. The e$ciency losses due to decentralization can be recti"ed: Bushnell and Oren [17] and
Gilbert and Riordan [18] have shown that
competition can reduce the capacity to extract
informational rents, and we have shown that
internal prices can induce divisions to account for
the global impact of their decisions, i.e., decentralization costs.
7.2. Practical results
Fig. 9. E$ciency losses in a CR policy.
performance and private information, and
it also requires transfer prices that fairly allocate
production, information, and decentralization
costs.
Our work added operational uncertainties to the
models of MMR [2] and Vaysman [3]. We show
that even under unlimited communication, decen-
In practice, the level of abstraction used
in this research is not needed because private information and disutility costs are not measurable,
but they should not be ignored. The following
are rules of thumb based on the insights
derived from our model and analysis that can be
used to minimize the losses due to asymmetric
information:
f In organizations with complex operations, delegate the decisions to the better informed
workers; delegation must be accompanied by
incentives, performance evaluation measures,
A. Ugarte, S. Oren / Int. J. Production Economics 67 (2000) 235}252
249
Fig. 10. DR capacity k[ H(ii) and marketing I[ H(ii)"$.
p
Fig. 11. E$ciency losses ¸(i) and ¸(ii) in a DR policy.
and mechanisms geared to achieve incentive
compatibility.37
f Use economic instead of technical measures of
performance; they induce a direct focus on value-
added contributions and uncover the hidden ine$ciencies characteristic of internal supply
chains with captive technologies.38
37 Delegation is like decentralization; it gives its best results
when there is private information that a!ects operational decisions.
38 We have show that the rewards in the CCC policies are
based on qualitative performance evaluations and that they fail
to achieve incentive compatability.
250
A. Ugarte, S. Oren / Int. J. Production Economics 67 (2000) 235}252
are outside the organization's control, i.e., suppliers
and customers. The mechanisms will be designed to
increase quality, improve delivery performance,
and reduce demand #uctuations.
8. Uncited References
The following works are also of interest to the
reader: [19}80].
References
Fig. 12. DR e$ciency losses ¸(ii){ for the recti"ed Case (ii).
f Discourage `free ridinga by rewarding global
productivity using global performance measures
and local productivity using local performance
measures.39
f Base rewards on a combination of estimated and
observed performance to improve the e$ciency
outcomes of planning decisions.40
7.3. Future research
Large organizations, public and private, are
viewing themselves as supply chains connecting
suppliers and customers; they are modeling their
operations as a chain of functions, events, transactions, and decisions that occur in the #ow of their
product or services from suppliers to customers.
A natural addition to this research would be to
expand the model to analyze the coordination of
production for several periods where learning of
private information is possible in each period. The
model will also consider the design of market mechanism to coordinate supply chain operations that
39 The CCC policy in our example paid high rewards based on
global pro"ts but it failed to induce the right behavior.
40 The revelation compensation in the DR policy is based on
expected and realized pro"ts to fully induce incentive compatibility.
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