Directory UMM :Data Elmu:jurnal:I:International Journal of Production Economics:Vol67.Issue3.Oct2000:

*Corresponding author.

E-mail addresses: armando}ugarte@i2.com (A. Ugarte), oren@ieor.berkeley.edu (S. Oren).

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 opera-tions. The internal transactions in large and

com-plex organizations are characterized by

information asymmetries and lack of market com-petition [1].

HTMOs are continuously looking for improve-ments in their overall supply chain e$ciencies.

Companies such as Hewlett Packard (HP) and IBM are continuously"ne tuning their organiza-tions to better coordinate their internal supply chains. Hewlett Packard (HP) fabricates semicon-ductors which it subsequently uses to build com-puters, printers, fax machines, medical devices, etc. In the late 1980s, HP decentralized its organiza-tional structure and created independent business units that were asked to focus attention on improv-ing their cost e$ciency and market responsiveness. Similarly, IBM after achieving technological leadership in semiconductor manufacturing ex-panded their production through forward integra-tion to produce computers and other high-tech products. In the early 1990s, however, IBM had to down size and restructure itself into a less hierarchi-cal organization in pursuit of higher e$ciency. The success of HTMOs such as HP and IBM depends

1Our 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.

2Private information represents the knowledge, intuition, ex-perience, and e!ort of managers and experts; this information is not ex-ante observable by the"rm.

3This result rea$rms the results obtained by Melumad et al. [2] hereafter referred as MMR 1995}and Vaysman [3]; our model expanded the e!ect of private information onto the op-eration decisions which have`supply chainae$ciency connota-tions.

4Higher levels ofh₂are desirable,Lz

2(h2)/Lh2'0. 5Kdoe not include overtime hours.

6Higher levels ofh₁are desirable,Lz

1(h1,e)/Lh1'0.

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 tech-nology.1In 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.2We 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 pol-icies analyzed by means of a numerical example consistent with our model. In Section 7, we general-ize the e$ciency condition for the three policies and show that decentralized policies introduce a decen-tralized e$ciency cost.3Finally, 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 divis-ion (HQ) and two vertically integrated productdivis-ion divisions, Division-1 and Division-2. Division-1 produces an intermediate product using state-of-the-art technology, such as integrated circuits; Div-ision-2 uses part of the output from Division-1 to assemble a "nal product, such as printers, com-puters, phones, etc. HQ coordinates the divisions

using information provided by the division man-agers, Manager-1 and Manager-2.

We make three important assumptions. First, we assume that the initiative, knowledge, e!ort, experi-ence, and intuition of the experts play a major role in the development, design, production, and mar-keting 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 dis-utility 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

2(h2)), with cumulative probability

distributionF

d(.;I,z2), has a"rst-order stochastic

dependency on marketing expenditures Iand on marketing productivityz

2(h2). Marketing

produc-tivity z

2(h2) depends on Manager-2's private

information parameter h₂, which accounts for 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

s hours are sold to

external customers and k

p hours are used to

produce inputs for Division-2. The production of inputs for Division-2, Mg(k

p,z1(h1,e))"kpz1N, is

done by means of a new proprietary technology with uncertain production yield. Productivity z₁(h₁,e) depends on Manager-1's private informa-tion parameter h₁, and on an uncertain level of production&noise'e. The parameterh₁accounts for Manager-1's experience and e!ectiveness in bring-ing new technologies up to production maturity.6

7Productivity decreases with noise,Lz

1(h1,e)/Le(0.

8(a!b)`"max(a!b, 0).

9Reported private informationhI"(hI₁,hI₂) is a decision vari-able, whereas true private information h"(h₁,h₂) is a para-meter. The arguments of z

1 and z2 are omitted for ease of exposition.

10Overstock cost does not consider inventory costs because these are negligible.

11a

1"kpanda2"I.

12For weaker conditions see Milgrom and Shannon [4]. 13Moral 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].

distribution F_e(.), accounts for all the uncontrol-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"tsE[P_{(.)] from the new technology. Corporate}

revenues result from: selling capacity k

s at a unit

pro"t of p dollars, selling Division-2's assembled products at a unit price ofp

2, and salvaging

Divis-ion-2's intermediate inputs in excess of demand (g(k

p,z1)!d(I,z2))`at a net unit gain ofh1

dol-lars.8 Corporate costs result from: production

+2

i/1ci]d, penalizing excess demand

(d(I,z

2)!g(kp,z1))`at a cost ofs2per excess unit,

and from compensating the managerU

i. Expected

corporate pro"ts before compensating managers are:9

In the above equation, price per unit of capacity at Division-1 is positivep'0, price per unit of"nal product produced at Division-2 is greater than

production costp

2!c1!c2!p/Ee[z1(h1,e)]'0,

there is an overstock cost in Division-1 for the excess inputs produced for Decision-2 h

1(p/Ee[z1(h1,e)], and the excess demand

pen-alty cost at Division-2 is non-pro"table s

2(p2!c1!c2!p/Ee[z1(h1,e)].10

Managers are utility maximizers, rational, and risk neutral; the economic utility for the Manager of the ith Division is ;

i(Ui,<i),Ui!<i(ai,hi).

Managers' compensations U

i are determined by

HQ; their disutility or personal costs <

i(ai,h1)

account for the time, e!ort, and forgone opportun-ity costs that a manager with private information parameter h_i incurs when assigned production activitya

i;11<i(.) is assumed to be monotonic and

single crossing inh

ito guarantee at least one

incen-tive compatible solution [2]. Su$ciency conditions for monotonicity and single crossing are satis"ed when<

i(.) increases with higher levels of

produc-tion activity (L<

i(ai,hi)/Lai'0); decreases with

higher levels of private information (L<

i(ai,hi)/

Lh

i(0); decreases marginally in production

activ-ity and private information (L2<

i(ai,hi)/

Lh_iLa

i(0); and is convex in production activity

(L2<

i(ai,hi)/L2ai'0).12 Disutility costs <i(.) are

not observable to HQ since they depend on man-agers' private information h_i; HQ's prior beliefs about h_i are characterized by a cumulative prob-ability distributionF_h

i(.:Hi) whereHi,[h-,h6].

2.3. Coordination decisions

14HTMOs allocate many resources to these critical projects, often hiring experts that join these companies with the mentality of make-it or break-it.

15HQ ignores that if managers reporthIH_iO_h

i, HQ cannot detect the distortions: productivityz

1is ex-post observable but depends on unobservable and random production noisee, and productivity z

2 cannot be accurately inferred from a single realization of random demand.

Fig. 1. Flow of information and product in a CCC policy.

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 be-tween the divisions involved in the project. The enforcement rules make managers accountable for executing the operational rules by determining divisions' performance measures and managers' compensationsU

i.

Managers actions and decisions obey a utility maximization rationale with participation and incentive compatibility conditions. Managers par-ticipate in HQ's contract if and only if their utility is competitive, i.e., greater than their reservation util-ity ;M

i (without loss of generality, we set;M i"0.)

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 parameterhI_i, they report a parameter value that maximizes their utility:

hIH

i3argmax_hI_i

ME

d,e,hj[;i(Ui,hIi,hIHj(hj);hi)]

"E

d,e,hj[Ui!<i(aHi(hIi,hIHj(hj)),hi)]N. (2)

3. Centralized command and control(CCC)policy

This coordination policy is commonly observed in the industry and results from formulations pro-posed in the Operations Management literature [7}9], HQ implements the operational and enforcement rules for this policy assuming that managers are altruistic, i.e.,hIH_i"_h

i.15

3.1. Coordination rules

HQ implements the following operational rules. At timet"0, HQ determines managers' compen-sation U

i and ranking measures; at time t"0`,

HQ asks managers to report their private informa-tion,hI_i, which is equivalent to reporting their pro-ductivity; at time t"0``, HQ determines production activities k

p,I; at time t"1, demand

dand pro"tsP_{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 man-agers'compensations as#at wages with pro"t shar-ing incentives, =

i#kiP; and it sets subjective

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 =

i and pro"t

sharing fractionk_iP(.) using a labor market ration-ale:

FindkH_p,kH_s,IH3argmax E

d,e[P(k_s,k_p,I,hI;hI)]

s.t. (i)k

p#kp)K.

(3)

Since pro"ts from k

p are higher than the ones

from k

s, HQ sets kHs"K!kHp and solves an

16Second-order conditions are not needed sinceE

d,e[P(.)] is

assumed to be concave ink

pandI. Guarantees a global max-imum at any point that satis"es the"rst-order conditions.

17If managers' compensation consist only of #at wages

U

i"=i, then managers will report the lowest credible level of

private information hIH_i(h_i)"h_l because their marginal utility from reported private information is negative, dE[;(U

i,hIi;hi)]/dhi"!E[<i(aiH(hIHi,hIHj),hi)]/dhIi(0.

conditions for optimality.16 HQ selects the kH

p at

which Division-1's expected marginal costs of over-stock equate Division-2's expected marginal costs of understock:

HQ selects theIHat which expected marginal rev-enue equals the expected marginal cost from mar-keting projects:

3.2.1. Managers'decisions

Managers follow their utility maximizing objec-tive and accept HQ's contract if their compensa-tions are competitive, i.e.,

E

d,e,hj[Ui!<i(aHi,hi)]*0.

Managers that choose to participate then report the private information hIH

i that maximizes their

utility. Managers' utilities are the sum of three

concave functions, E[;

i]"=i#kiE[P]#

(!E[<

i]); therefore, their utilities would be

maxi-mized when their expected marginal bene"ts equals their expected marginal cost corresponding to the reported private information:17

k_i]dEd,e,hj[P(aH(hIi,hIHj(hj)),hi,hIHj(hj);h)]

3.2.2. Ezciency losses

E$ciency losses in this policy occur because HQ's decisions use distorted productivity informa-tion, 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:

k_i]dEd,e,hj[P(aH(hIi,hj),hi,hj;h)]

but optimality requires that

LE

d,e,hj[P(aH(hIi,hj),h;h)]

LaH

k

K

hI_i/hi

"0∀k3i,j.

To reduce their disutility costs, managers underre-port their private information, i.e.,hIH_i(h_i)(_h

i.

Con-sequently, HQ's production activity levels aH_i are based on distorted private information, i.e., lower estimates of productivity.

aH

i(hIHi,hIHj),aHj(hIHi,hIjH)NargmaxEd,e[P(a_iH(hIH_i,hIH_j),

aH_j(hIH_i,hIH_j),hIH;h]_∀hIHO0 (8)

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.

4. A centralized revelation(CR)policy

18Revelation mechanisms are based on the revelation prin-ciple for communication games with imperfect information [10]. 19Pro"ts before payment to the managersE[P_{] are de"ned}

in Eq. (1).

Fig. 2. Flow of information and product in a CR policy.

20HK_i(a(H_i,hI_i)"E

hi[UKH_i(hI_i;h_i)]"<_i(a8_i,hI_i)!(L<_i(a(_i,hI_i)/LhI_i) (FM_hi(hI_i)/f

hI_i(hI_i))"b_i(a_i)w_i(hI_i)!b_i(a_i)w@_i(hI_i)(FM_hi(hI_i)/f_hI_i(hI_i)) is con-vex ina

ias a result of the conditions imposed on<iandFhi.

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

timet"0, it determines managers'compensations

UK_H

i; at timet"0`, it asks managers to report their

private information parameters hIH_i; at time

t"0``, it makes production activity decisions; at

time t"1, demand dand 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 evalu-ation measures, that maximize the utility of man-agers 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

i that maximizes their utility when they are not

distorting their private information:19

max

UK

i E

d,e[P(aH(hI),hI;hI)]!+_i2/1Ed,e,hi[UKi(hIi;hi)]

subject to

(i) h_i"_hI_H

i3argmax

hI_i|H

i E

d,e,hjEi[UKi(hIi,hi)

!<

i(a(Hi(hIi,hj),hi)] ∀(i,j),

(ii) E

d,e,hjE1[UK1(hIi;hIi)

!<

i(a(i(hi,hj),hj)]*;M i ∀(i,j).

The optimal managers' compensations UK_H

i must

cover managers' disutility costs and pay them

informational rents [2]. This results

from assuming that E

d,e,hjEi[UK1(hIi;hi)]" E

d,e,hjEi[<i(a(i(hi,hj),hi)#¹(hIi)], where ¹(hIi) are managers' informational rents. To achieve man-agers'participation¹(hI_i)*0, and to achieve incen-tive compatibility¹(hI_i) must be equal to the second term of Eq. (10).

UK_H

i(hIi;hi)"Ehj

C

<i(a(Hi(hIi,hj),hIi)

!

P

h

I_i

hl

L<

i(a8Hi(t,hj),t)

LhI_i dt

D

. (10)

HQ decides on the divisions'production activity levels by solving an unconstraint optimization problem that takes into account the expected opti-mal managers' compensation E_h

i[UKHi(hIi,hi)] also known as the virtual costs of the managers HK

i(a(Hi,hIi):20

max

IK,kK_p

E

d,e[P(kK_p,IK,hI;hI)!HK 1(kKp,hI1)!HK 2(IK,hI2)].

(11)

21Arrow [1] proposed the decentralization of large organiza-tions as a way to reduce the ine$ciencies due to asymmetric information.

22Decisions in HTMOs require increasingly more accurate real-time technical and economic information to remain com-petitive.

marginal cost of understock.

p#LHK 1(kp,hI1)

At the optimal expenditures IKH the marginal ex-pected costs are equal to the marginal exex-pected revenues from marketing expenditures, but now Manager-2's revelation cost decreases expected marginal revenue.

4.3. Managers'decisions

Each manager reports truthfully if truth-report-ing 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 compen-sationUK_H(.) satis"es managers'participation condi-tion for truth-reporting managers because E[UK_H

i(h)]'E[<i(h)]. It also satis"es their incentive

compatibility condition because their utilities are maximized when hIH

i"hi; their marginal expected

bene"ts and costs fromhI_i are equal whenhIH

4.4. Ezciency losses

The losses corresponding to this policy result from having to pay managers informational rents to access truthful information. The relative e$cien-cy measure of this polie$cien-cy, as compared to the "rst-best solution, is given by

¸K"

C

E

If the production resources being allocated are very expensive, paying for access to true private information is more e$cient than underallocating these resources. This is typically the case in HTMOs which tend to use very expensive re-sources with a high rate of obsolescence that must be utilized e$ciently. For instance, a modern pro-duction facility for integrated circuits costs around one billion dollars; A single photolithography machine costs around"ve million dollars [11].

5. A decentralized revelation(DR)policy

Fig. 3. Flow of information and product in a DR policy.

23Hereafter, superscripts (i) and (ii) refer respectively to case (i) and case (ii).

The operational rules for this policy are: att"0, HQ sets managers'responsibilities and compensa-tionUK

i; at t"0`, it asks the managers to report

their private information; att"0``, it determines the transfer price¹(s,hI₁) that Division-2 must pay to Division-1 for its servicesS; att"0```, Divis-ion-2 decides onIandSand Division-1 onk

s and

k

p; at t"1, demand and pro"ts are realized. To

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.

5.2. HQ's decisions

HQ decides on managers'responsibilities by sep-arating 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 Sthat Division-2 orders from Division-1:Scan be capacity hoursk

p. Pro"ts for each

divis-ion are:

HQ also decides on the transfer price that Divis-ion-2 pays Division-1 in exchange forS. Vaysman [3] showed that an e$cient transfer price must transfer the production as well as the virtual costs associated withS:24

¹(i)(k[

HQ must design the compensationU[

ithat

satis-"es managers'participation and incentive compati-bility conditions in this policy. The simplest form of a decentralized incentive compatible compensation scheme is linear in divisional pro"ts [16]:

U[

i"ai(hIi)ni#bi(hIi). (19)

26Henceb_i*!_a

i(hi)Ed,e[ni(a\Hi(hIi),hIi;hIi)]#UKi(hIi;hi) where

E

d,e[ni(a\Hi(hIi),hIi;hIi)] are the pro"ts realized if HQ had made the decisions, andUK

iis the centralized revelation compensation (Eq. (10)).

27MMR [2] and Vaysman [3] concluded that the informa-tional 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.

28a₁"0,H[

1"HK1,U[(i)1"U[1.

29a₂O0,H[₂'HK₂,U[_(i)

2'UK2.

required a_i distributes divisional pro"ts proportionally to the ratio of manager's marginal disutility costs to HQs marginal virtual costs:

a

The interceptb_imust induce incentive compatibil-ity. Intuitively, the compensation under this policy must be equal to or greater than the compensation under the centralized revelation policy.26 But de-centralization increases managers' expected mar-ginal 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

The decentralized revelation compensation

U[_H

i pays managers for their net contribution to

divisional pro"ts a

i(ni!E[n]), for their disutility

costs, and for the value of their private information:

U

The increase in informational rents due to decen-tralization causes an increase in the decentralized managers'virtual costs:

5.3. Managers'decisions

Managers make participation, reporting, and production activity decisions. The decentralized revelation payment U[_{H induces managers to}

par-ticipate and align their objectives with the objec-tives 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

Whereas HQ would have solved:

max

ihas been chosen to make the above two

maximiza-tion problems equivalent.

In Case (i), Manager-1 selectsk[(i)

s"K!k[(pi); this

30Hereg(k[(_pHii),z(hI₁,e_Q))"Qand [e_-,e₆] is the support for the distribution F

e(.). The solution to this equation determines

F

(Q)"kHp(**)which is needed to determine the transfer price,

¹(Q;hI₁).

31a(ii)₁ '0,H[(₁**)*HK(₁*), andU_(**)

1 'U(1*).

32This case is just like the Centralized Revelation Policy, except that Manager-2 makes all the decisions instead of HQ.

33To compute these prices, one can use the probability struc-ture characterized in the Centralized Revelation Policy. For example,

of production activity decisions; as a result, Man-ager-2 selects the same production activity levels as in the centralized revelation policy k[H(i)

p "kKHp and

I[H(i)"IKH.

In case (ii), Manager-1 selectsk(ii)

p (Q) so that

Divis-ion-1's marginal cost of understock and overstock are equal; this decision does not consider Division-2's demand uncertainty.30

The above decision increases Manager-1's marginal disutility costs and hence his/her informational rents.31Manager-2 selectsI(ii)andQnot 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:

pLF_(Q)

It selectsI[H(ii)so that Division-2's expected marginal revenues and costs from investment are equal:

(p

The exclusion of Division-1's uncertainty in Divis-ion-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)

p (QH)'k[(pH)).

5.4. Ezciency losses

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 Revel-ation Policy due to an increase in mangers' informa-tional 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 whenQ'd(g(₍ii)

Q). Consequently, Manager-2

expects unrealistic higher marginal revenues from in-vestment and over allocates resources.

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

2,h1,s2)N

(p@₂,h@₁,s@₂) so as to induce Manager-2 to internalize the e!ect of his/her decision on Division-1. Manager-2 needs to take into consideration that whend(Q andg(k[H

p,z1)(Qand expected salvage revenues are

lower; and when Q(d, Q(g(k[H

p,z1) expected

stock-out costs are also lower:33

34Here, global pro"t sharing incentives are creating the con-ditions for free riding [14].

35The"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 com-pensates managers only for their participation.

h@₁"h

The above price recti"cation prevents Division-2 from overexpending and from operating at a high probability of stock-out because it decreases Divis-ion-2's decentralized marginal expected revenues.

6. Numerical example

The following examples is primarily intended to illustrate the comparative e$ciency of the three pol-icies studied in this paper. However, the functional forms used in the example are su$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 compen-sation and transfer prices.

f Division-1's production of inputs for Division-2 is

g((k

p,z(hI1,e))"kp](z1(hI1,e)"z1(hI1, 0)!e);

(z

1(hI1, 0)"z81#c1hI1) is the theoretical

productiv-ity,z8₁"0.6 is the productivity upper bound with-out private information is,c₁"0.25 is a constant of proportionally, ande3[0,z

1(hI1, 0)] is the

uni-formly distributed uncontrollable production noise.

Division-2's demandd(I,z

2) is exponentially

distributed with mean E

d[d(I,z2(hI2))]"

(r1(hI₂)]r

2(I));r2(I)"500,000 ln (I/500,000), and

r_1(h

2)"0.125h2#0.0625.

f Managers' disutility costs are <

i(ai,hi)"

g_ia

i(1.5!hi), where g1"1 and g2"0.1 are

proportionality constants. Managers'private in-formation parameter h_i3[h_l,h_u]"[0.2, 1.2] is uniformly distributed.

f The revenue parameters for the"rm are:

price per unit of Division-2's "nal product p

2"275,

price per unit of Division-1's capacity sold in the external marketp"29, and net pro"ts after

sal-vaging a unit of inputs to Division-2h

1"10.

The costs parameters are:

per unit production cost at the divisions c

1"c2"45,

and penalty cost per unit of Division-2's back-logged demands

2"170

6.1. Using the CCC policy

Fig. 4 show HQ's production decisions in this policy kH_p and IH as increasing functions of man-agers'reported private informationhI₁,hI₂.

Fig. 5 show managers' reporting strategy hI₁,

hI₂ when the CCC policy o!ers then U

i"=i#

k

iEd,e[P]; even a high k_i does not deter

managers from distorting their private informa-tion.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 kKH_p(hI) and marketing expenditures and IKH(hI) decisions when using the CR policy.

Fig. 8 shows managers' expected utility as func-tions of their reporting strategy (hIH

i,hi). The

com-pensation that HQ o!ers managers, Eq. (10), is maximized when managers reporthIH

i"hi.

Fig. 4. CCC CapacitykH_p(hI) and marketing expendituresIH(hI)"$.

Fig. 5. Managers'reporting strategyhI_i(k_i,h_i) whenU

i"=i#kiEd,e[P].

36A modern production facility for integrated circuit costs around one billion dollars; a single photolithography machine costs around"ve million dollars [11].

use very expensive resources with a high rate of obsolescence, which have to be utilized very e$ciently.36

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. 6. E$ciency Losses¸

k"$.

Fig. 7. CR capacitykKH_p(hI) and marketing expendituresIKH(hI)"$.

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.

7. Conclusion

Our results have theoretical and practical im-plications.

7.1. Theoretical results

We have found desirable conditions for each policy.

f When private information does not exist

central-ized command andcontrol policiesare superior.

f When private information exists but it does not

a!ect operational decisions there are two situ-ations. If the production resources are inexpen-sive, the centralized commandandcontrol 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

Fig. 8. Managers'expected utility in a CR policy.

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-tralization is less e$cient than cendecen-tralization if private information a!ects interim operational decisions, thus increasing managers'personal costs and rents. The e$ciency losses due to decentraliz-ation 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., decentraliz-ation costs.

7.2. Practical results

In practice, the level of abstraction used in this research is not needed because private in-formation 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,

Fig. 10. DR capacityk[H_p(ii)and marketingI[H(ii)"$.

Fig. 11. E$ciency losses¸_(i)and¸_(ii)in a DR policy.

38We have show that the rewards in the CCC policies are based on qualitative performance evaluations and that they fail to achieve incentive compatability.

37Delegation is like decentralization; it gives its best results when there is private information that a!ects operational deci-sions.

and mechanisms geared to achieve incentive compatibility.37

f Use economic instead of technical measures of

performance; they induce a direct focus on

Fig. 12. DR e$ciency losses¸_(ii){for the recti"ed Case (ii).

39The CCC policy in our example paid high rewards based on global pro"ts but it failed to induce the right behavior.

40The revelation compensation in the DR policy is based on expected and realized pro"ts to fully induce incentive compati-bility.

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, transac-tions, 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 mech-anism to coordinate supply chain operations that

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.

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