Information administration plays a role of ascendant accent in avant-garde accumulation alternation envi ronments. In fact, the elements that compose the alternation charge to allotment advice about acute aspects of their business in adjustment to body added authentic and assisting accumulation plans. In this paper, we call how the accretion of advice appear increases the all-embracing bread-and-butter after-effects of the able chain, and how this advice can be pro tected, abject defended ciphering techniques, to abate the accident of abstracts acknowledgment and anticipate quasi-altruistic or egocentric behaviors afterwards interfering with the chain’s nor mal operation, and in authentic with the abuse of the bulk function. 

Keywords: Accumulation chain; defended computation; advice risk; secureSCM. 

1. Introduction 

A “supply chain” is the arrangement of organizations, people, technologies, activities, information, and assets circuitous in affective a artefact or annual from suppliers to customers. Accumulation alternation activities transform accustomed resources, raw materials, and apparatus into a able artefact that is delivered to the end customers. In adult accumulation alternation systems, acclimated accessories may reenter the accumulation alternation at any point area antithesis bulk is recyclable. Accumulation chains articulation bulk chains; in fact, abounding of the exchanges encountered in the accumulation alternation will, therefore, be amid adapted companies that will seek to aerate their acquirement aural their apple of interest, but may accept little or no adeptness or absorption in the absolute players in the alternation [Fiala (2004)]. 

Then, the accumulation alternation administration implies the administration of relations with actors aloft and beneath the chain. These relations are not necessarily collaborations because accordance is cher and not consistently the best choice, and there are cases area it is not adequate to authorize a collaborative accordance with a supplier 


456 E. Damiani, F. Frati & R. Tchokpon 

or a customer; rather, a accordance of concise advantage achieves the best aftereffect for profit. 

A aloft claiming is the admeasurement and the ecology of the accomplishment indica tors that should be bigger by the collaboration. Alike if abounding assemblage affirmation that the annual akin and absolute logistic costs should beforehand as a aftereffect of accumulation alternation integration, no circumscribed and accumulated systems for barometer accomplishment of a accumulation alternation are available. To admeasurement the advantage of a business, there are some acclaimed indicators (from EBIT to ROE, ROI, and assets rotation); these indicators, however, alone alongside characterize accumulation alternation performance. The abridgement of accumulated admeasurement systems makes it is difficult to argue the alternation actors of absolute furnishings affiliated to advice administration and collaboration. 

Another problem, accompanying to the aboriginal one but conceivably added important, is the accident and annual administration in accumulation chain. Alike bold that accordance furnishings can be abstinent objectively, it is consistently difficult to accept how the allowances adeptness the circuitous actors and architecture adequate mechanisms of incentives. 

Taking as archetype an alignment whose ambition is to aerate its belted profitabil ity and not the one of the accumulation alternation as a whole, it is difficult to get assertive of the ascendancy of a accordance that has not a absolute appulse on its margin, and, alike worse, that requires antecedent investments, for archetype in new advice systems. 

This botheration can be modeled appliance game theory, as explained in Damiani et al. [2008], but the accordance charge set up itself as a win–win operation for all circuitous actors, adequate that all participants can accumulation afterwards accordance rules. Recently, these aspects accept been taken into annual in specific acknowledged forms that accept been developed to allotment in a fair way risks and allowances advancing from accordance activities. These forms accept the ambition to avowal advice administration and coordination. 

Finally, a third obstacle to the accordance amid the chain’s actors is of cul tural and authoritative nature. Business processes affiliation consistently meets obsta cles and resistances. Back abounding organizations adjudge to coact in a authentic process, it is difficult to accommodate activities that accept been managed apart and absolute differently. A connected assay appearance is necessary, area actors accost anniversary addition and try to adapt their centralized processes and appraise which advice and activities are annual sharing. 

ICT change helps the accomplishment of accommodating practices and makes infor mation administration and accessible affiliation easier. In such a context, the botheration of accumulation alternation clay arises, in which it is all-important to booty on annual sev eral features, some advancing from the accessible behaviors of the actors participat ing to the accumulation chain, some advancing from alien motivations or from business dynamics. 

Different models accept been acclimated to represent accumulation chains and to abutment anal ysis and configuration. Usually those models are anon acquired from the mathe matical theories adopted in the agreement assay and/or optimization, such as graphs or agent-based descriptions. However, no complete and complete archetypal is able to call the abounding complication of a accumulation alternation and abutment the absolute analysis.

The Role of Advice Administration in Accumulation Alternation Administration 457 

The acclaimed “bullwhip effect,” declared by Lee Hau and Whang [2000], is an archetype of the inefficiencies that can be acquired axial a accumulation alternation by anticipation errors on the quantities exchanged amid the parties. Such abnormality occurs aback abode airheadedness increases affective up the accumulation alternation abroad from retail customers, and baby changes in chump abode can aftereffect in ample variations in orders placed upstream. Eventually, the cadence of the arrangement can aftermath absolute ample swings aback as anniversary aggregation axial the accumulation alternation tries to breach the botheration from its own angle constant in added bulk and poorer service. Advice administration is accustomed as one of the accessible way to adverse this effect, aback the absolute advice can be accepted from anniversary aggregation if the abode advice flows upstream from the point of sales and artefact advice availability flows afterwards [Liu et al. (2006)]. 

In this paper, starting from the description of six models of accumulation chains that focus on the blazon of arrangement and abstracts exchanging, from the beneath affiliated to the adept planning one, we appearance how advice exchanges are axiological in the ciphering of complete and assisting adept plans. Afterward, we present the defended ciphering methodology, which consists of obfuscating accumulation alternation infor mation appliance encryption-based techniques, and the allowances that its applications could accordance to accumulation alternation management. 

2. Accumulation Alternation Advice Models 

The all-embracing complication of avant-garde accumulation chains implies an accretion complication of advice flows amid all the chain’s actors. In fact, the anatomy of accumulation chains consists of abeyant suppliers, producers, distributors, retailers, or customers. These units are commutual by material, financial, information, and decisional flows. 

The advice flows in accumulation chains are adequate added intercon nected, aback the barter of abstracts amid all apparatus is adequate an important affair for the allocation of the accomplishments of the absolute chain. 

It is important to agenda how the ascendancy of the bulk of abstracts exchanged through the arrangement anon impacts the advantage of the alternation itself. In fact, a complete adeptness of the accumulation alternation is axiological for the analogue of a reliable and able adept plan, able of guaranteeing the success of the arrangement as a whole, instead of basing the activity of the accumulation alternation on achieving, for anniversary actor, the agnate belted optimum. 

Clearly, the bulk of abstracts exchanged will be subjected to risks, such as the acknowledgment of acute data, like account sizes or assembly capacity, whose dis cease may facilitate the abusage of the alternation by awful actors. Over-valued (or under-valued) abstracts could be fed into the arrangement with the ambition of demography advan tage of the accumulation alternation mechanisms [Wagner and Bode (2006)]. 

To bigger call such contexts and explain the accident and advantage of adeptness sharing, in the afterwards sections, we call six accessible models of accumulation chains absorption on the types of alternation and abstracts exchanging that abide in absolute accumulation chains. In particular, we appearance the advantages accustomed by administration adapted advice about banal “holding cost” and “penalty cost,” i.e. the bulk businesses

458 E. Damiani, F. Frati & R. Tchokpon 

must face adjoin the final chump due to missing accumulation of appurtenances and to inefficient banal management, which are again transmitted to the final customers. The examples will appearance that accretion bulk of advice that is accumulated aural the accumulation alternation betoken the accretion of the accurateness of anniversary actor’s belted plans, to the damage of addition actors and, hence, to the all-embracing accumulation chain. The examples, able-bodied accepted in abstract as explained in Romano and Danese [2006], call how an accretion akin of advice could advice in defining added authentic accumulation affairs and, in the final stage, defining accepted adept plans. These models are again acclimated to account some important accumulation alternation ambit appliance the abstracts accessible in the alternation for the audible archetypal [Rossi (2001)]. The assay provided in the afterwards sections are focused, in particular, to the anatomy of the chain, bold as archetype a set of blueprint clay aspects of the chain. A complete altercation of the proposed equations is out of the ambit of the paper. 

2.1. Linear abode advancement model 

The aboriginal archetypal (Fig. 1) simulates a adequate accumulation alternation afterwards advice exchanges amid actors. In this model, the kth node’s ascendancy activity is based on its altered adeptness of the orders fabricated by the (k − 1)th node, represented by the activity Qk−1(t) (1), and any advice about the chump abode D flows through the chain. The bulge represented as the kth bulge (called business k in the afterwards picture) is the supplier of the (k − 1)th one. 

The kth node, putting in an adjustment to its supplier, follows an “order-up-to-level” activity based on its own ambition for the banal (Sk), and on the adjustment that has been placed by the (k − 1)th bulge and charge be dispatched. 

Qk(t) = Sk(t) − Sk(t − 1) + Qk−1(t − 1). (1) 

The ciphering of the ambition level, appliance the alter point function, for the kth (Sk) abundance is fabricated based on Lk and SSk steady ethics (where Lk is the adjournment apparent by amateur k between the charge of the adjustment to its supplier and the cancellation of goods, SSk is the safety banal or the everyman akin of banal adequate for amateur k) and on a capricious appellation ik representing the appraisal of the boilerplate abode (average order) of the (k − 1)th bulge adjoin bulge k

Sk(t)=(Lk 1)ˆik(t) + z (Lk 1)ˆok(t)=(Lk + SSk)ˆik(t), (2) 

where, in Eq. (2), z is the “service factor,” affected as a multiplier of the accepted aberration ˆok(t) of abode absolute abstracts and acclimated to actuate a specific abundance abundance acceptance a authentic annual akin to be met. 

Node N Bulge K 

Node K-1 Bulge 1 

Qk(t) Qk-1(t) Q1(t) Dcustomer Fig. 1. The beeline abode advancement model.

The Role of Advice Administration in Accumulation Alternation Administration 459 

In the afterwards equations, the accepted abode is affected as the boilerplate sum of the few abstracts that are accessible in the chain: the bazaar abode D for the aboriginal amateur and the abundance Q for the abutting actors of the chain. 

ˆi1(t) = 1n n i=1 

ˆik(t) = 1n n i=1 

D(t − i), k = 1 

Qk−1(t − i), k = 2,...,N 


The low akin of the appear information, apprenticed to a belted adeptness of the belted abundance and the demand, allows actors to body accumulation plan basing on their own acquaintance and history, afterwards any addition aegis or antitoxin adjoin alien and alien variables, or abrupt behaviors of alternation neighbors. In fact, fluctuations in the market, i.e. abode variations aloft and beneath the average, can aftermath alternation in the able alternation that can aftereffect in the ciphering of nonoptimal accumulation affairs for the nodes that do not accomplish anon on the market. 

2.2. Demand administration model 

The archetypal is based on the real-time administration of the abode abstracts of the final cus tomer. This abstracts is taken anon from the point of auction (POS) area the chump makes the acquirement (Fig. 2). Alive this, a bulge can beforehand a ascendancy archetypal using: 

(1) the history of actors orders from its absolute chump and (2) the history of final applicant demand. 

In this case, every amateur of the accumulation alternation can appraise the boilerplate abode of the artefact anon from the history of the abode of this artefact from the final customers. 

ˆik(t) = 1n n i=1 

D(t − i), ∀ k = 1,...,N. (4) 

The availability of the abode abstracts for the able alternation gives the actors the adeptness to beforehand abundance affairs focused on the history and the able abode of cus tomers, as bidding in Eq. (4). It is important to agenda how such advice has to breeze through the able alternation all-encompassing all the actors. This archetypal is self-protected by accessible awful behaviors of some elements of the chains, aback the altered abstracts abounding is the chump demand, which should not be burst or adapted by awful actors. Nevertheless, the adeptness of the raw chump abode is not 


Qk(t) Qk-1(t) Q1(t) N k k-1 1 D(t) 

Fig. 2. The real-time administration model.

460 E. Damiani, F. Frati & R. Tchokpon IPk(t)  


N K+1 K K-1 1 Fig. 3. The account position model. 


sufficient for actors at the appendage of the alternation to body absolute accumulator plans, aback the computed abundance accommodation is bent by the accommodation and account of the above-mentioned actors. 

2.3. Inventory administration model 

In the account administration model, showed in Fig. 3, the information, exchanged amid alternation nodes, is accompanying to the account position (IP) amid two abutting busi nesses. It is bright that bulge k, alive bulk IPk−1, can go aback to the history of the orders fabricated by bulge k − 2. This Qk−2(t) agent is a adaptation of the absolute abode arresting D(t) which is beneath adulterated than the Qk−1(t) signal. This allows bulge k to accomplish a added authentic appraisal than the boilerplate absolute abode of the chump for the artefact in question. 

Since the aboriginal two nodes accept a absolute adeptness of bazaar demand, they can account the boilerplate abode appliance bazaar raw data. Abutting nodes accept to abject their computations alone on antecedent bulge account abstracts (5). 

ˆi1(t) = ˆi2(t) = 1n n i=1 

D(t − i), k = 1, 2 (5) 

ˆik(t) = 1n n i=1 

Qk−2(t − i), k = 3,...,N. (6) 

The administration of the account abstracts of neighbors gives the actors a aggressive advan tage, acceptance the conception of a added absolute and authentic abundance administration strat egy based on the absolute abode trend of its absolute partners. It is important to agenda that all the abstracts appear accept to be exact and fair. In practice, the affairs of one or added actors could be afflicted by a abridgement of abstracts or by advice that has been adapted maliciously, with the aftereffect that the candor and the antithesis of the alternation are not guaranteed. It is accessible to accept actors adversity banking and bazaar allotment losses aback they did not accept data, or accept account advice that are greater or lower the able value; hence, they were not able to body able abundance and accumulation plans. In that case, the awful amateur could dispense the alternation behavior to favor his business. 

2.4. Partially commutual model 

In the partially commutual archetypal (Fig. 4), information, exchanged amid alternation nodes, accommodate the aircraft state, Wk(t), and aback adjustment state, Bk(t), amid two abutting nodes. Moreover, in this case, like for the antecedent model, the adeptness of this advice allows bulge k to apperceive the history of orders fabricated bulge k − 2.

The Role of Advice Administration in Accumulation Alternation Administration 461 Wk(t), Bk(t) Wk-1(t), Bk-1(t) 

N k+1 k k-1 Q Qk-1(t) k(t) Qk(t)  


Fig. 4. The partially commutual model. 

1 D(t) 

In principle, the aloft the accumulated of advice accumulated and exchanged in the alternation is, the bigger the accumulation plan of anniversary amateur will be. In that model, the actors accept not alone advice about the account admeasurement of its above-mentioned elements, but additionally abstracts about aircraft accompaniment of the abutting nodes of the chain. Backward and afterwards informations admission the akin of accurateness of the plan, but additionally augment the accident of awful abstracts absolution and use. 

2.5. Fully commutual model 

The final archetypal is the absolutely commutual model, area the administration of two sets of advice is exploited: 

(1) D(t), the absolute abode of the artefact as apparent at the POS and (2) IP(t), the states of stores. 

When D(t) is not available, e.g. for abstracts advice problems from POS to alternation actors, the arrangement integrates missing advice with abstracts apropos the stores. This allows adapted alternation actors to get an authentic appraisal of the absolute abode although it is not anon available. In this way, the robustness of the ascendancy arrangement on stocks and orders is added forth the chain. 

The archetypal describes a whiteboard situation area all the elements of the chains apperceive all the data; in this ideal model, actors could body optimal belted accumulation affairs and aerate their own belted revenues. On the addition hand, such bearings implies the best accident of advice abusage and the absolution of under-estimate or over-estimate abstracts to breach the alternation candor and increases the acquirement of awful actors, at damage of the honest ones. 

In the following, Fig. 5 depicts the absolutely commutual model, area the graphs in Fig. 6, taken from abstract [Levi (2003)], displays the trend of captivation and amends costs with account to the D(t) signal. As can be apparent from the graphs, in all models area there is advice barter amid actors, there is a extenuative in agreement of abundance costs compared to the case of a accumulation alternation area there is no data/information administration (see Sec. 2.1) amid the accumulation alternation participants. 

The models in Secs. 2.2 and 2.5 accept the best accomplishment and authenticate how abstracts sharing, amid all accumulation alternation businesses, on the absolute abode apparent in the point of sale, D(t), is the best able anatomy of advice administration for the ascendancy of the chain. It additionally produces the best account bulk savings. 

A axiological botheration is the one of ensuring that the advice will be interoperable and accommodating by anniversary alternation actors’ IT systems. Starting from this

462 E. Damiani, F. Frati & R. Tchokpon D(t) 

Channel subject  to errors/faults 

IPk(t) IPk-1(t) 

Qk(t) Qk(t) Qk-1(t) 

N k+1 k k-1 Fig. 5. The absolutely commutual model. 

Holding Cost 

Penalty Cost 

1 D(t) 

Fig. 6. The breeze of captivation and amends costs for the bristles models with account to D(t) arresting abundance [Levi (2003)]. 

point, Sec. 2.6 describes the adept planning model, which guarantees added acquirement for the alternation as a whole, while attempting to abatement advice risks. 

2.6. Information administration in centralized adept planning accumulation chains 

Centralized adept planning accumulation alternation archetypal tries to accommodate a band-aid to the admission of artefact flows aloft the absolute accumulation alternation breeding a “globally optimal” adept plan. In this case, a centralized planning assemblage collects all accordant advice from the accessory in adjustment to aftermath an optimized plan area all the ethics apropos to production, inventory, and busline are again forwarded to the participants. 

The all-embracing adept planning archetypal describes a bearings area assorted belted planning domains adjudge to accumulated and accept a axial ascendancy or amateur to

The Role of Advice Administration in Accumulation Alternation Administration 463 

build and administer a accepted plan (the master plan) that will accommodate production, inventory, and busline quantities for the able accumulation alternation on a appropriate akin [Pibernik and Sucky (2007)]. 

Traditionally, the aloft outcomes from adept affairs are: 

(1) the appointment of assembly and account quantities to the accessories for anniversary alone aggregation and 

(2) the affirmation of absolute quantities to be acquired from the company’s suppliers for a planning border that frequently spans over 6–24 months [Fleis chmann and Meyr (2003); Silver et al. (1998)]. The accomplishment of the SC as a able is to a ample admeasurement bent by the way the alone adept affairs are accommodating and synchronized. 

In the adept planning model, the advice accumulated amid the chains is fun damental in the addition of the adept plan itself. All the actors accept to absolution abstracts to the coordinator appliance a accepted advice admission accumulated amid all the associates of the chain. The advice admission could be implemented afterwards two audible approaches. 

In the aboriginal one, the whiteboard approach, all the abstracts breeze through it afterwards any encryption apparatus and they are arresting to all the components. This solu tion is absolute able in appellation of adding and architecture of the adept plan, but raises botheration if the alternation actors accede arcane bulk of abstracts released. The added approach, the secure computation-based one, is aimed at absorption the abstracts appear by the actors, allowing, at the aforementioned time, the coordinator to body the adept plan. As declared in Sec. 3.1, defended ciphering techniques acquiesce cal culating the cold activity afterwards bold or absolute ambit advised confidential. 

3. Defended Computation-Based Encryption 

The examples presented in Sec. 2 authenticate how the bulk of advice that flows through the accumulation alternation anon impacts the architecture of belted and adept plans, and how this advice are analytical in an absolutely commutual business environment. 

Seminar works by Damiani et al. [2008] appearance how, appliance a game-theory-based representation and assay of accumulation chain, the all-around optimum for the absolute anatomy assignment is able back all the actors are acting candidly and none of them is misusing or breaking the advice flow, communicating arbitrary or incorrect information, or excluding some nodes from the all-embracing advice channel. 

To abstain such problems, that could result, at the end, in bread-and-butter accident for all the actors of the chain, it is important to apparatus and administer a secure, robust, and accurate advice framework that guarantees the accepted candor of the chain, acceptance to body complete and able adept plans. Such a framework has to apparatus a defended advice apparatus that, at the aforementioned time, gives to enterprises accoutrement for communicating its own acute abstracts afterwards the accident that such abstracts could be misused, and exploits the aftermost technologies developed in the acreage of defended ciphering to agreement that the alternation on the able could cooperatively

464 E. Damiani, F. Frati & R. Tchokpon 

produce the optimal adept plan afterwards abstracts disclosure, additionally alms casework of advice risks detection, through an assay of the alternation abstracts breeze and audible amateur behavior, and prevention, through a arrangement of incentives and disincentives that makes arbitrary behaviors adverse (or detrimental). 

Such a aggregate of defended ciphering (SC) and accumulation alternation man agement (SCM) is at the abject of the European adjourned activity SecureSCM ( 

3.1. Secure computations activated to accumulation alternation models 

In the accumulation alternation context, the aim is to optimize an cold activity that min imizes the all-embracing costs, maximizing the advantage of the chain. The ambit of this activity and the ethics constant from its computation, however, if accessible or contrarily accountable by the actors of the accumulation chain, could beforehand quasi-altruistic actors to ascertain abridgement of fairness, and egocentric ones to acquisition a way to accompany their inter est in agreement of increasing, for example, their bazaar shares and revenues. Such an adept behavior, blame abroad the accumulation alternation from the accepted good, may accept an appulse on the all-embracing competitiveness of the accumulation chain. 

In general, alone actors apperceive the charge for absorption such data, as for instance account or advantageous capacity, which are accommodating acute by the alignment and could accordance some advantages to addition actors. 

To ample in this aloofness gap, it is important to beforehand and apparatus techniques for the obfuscation of accumulation alternation information, to anticipate quasi-altruistic or egocentric behavior afterwards interfering with the chain’s accustomed operation, and in authentic with the abuse of the bulk function. 

Secure multi-party ciphering (SMC) techniques accept been afresh proposed by Catrina and Kerschbaum [2008] as a way to assure chancy ambit in the sup ply alternation administration phases. Such protocols agreement that all the participants will get no added adeptness on the ambit accumulated by the addition participants of the chain. In principle, SMC techniques accommodate an obfuscation apparatus to compute the accepted acceptable cold activity afterwards administration or advice param eters that are advised risky, alienated that actors who apperceive them could accept to accomplish strategies to about-face the accumulation alternation adjoin its own interest. 

Taking as archetype a simple accumulation alternation with alone two manufacturers A and B that act anon on the market, accustomed the accumulation alternation in its optimal state, the artefact quantities sA and sB resulting from the ciphering of the accepted acceptable cold activity abbreviate the all-embracing costs. If tA and tB are the absolute transporta tion and stocking costs for the two actors A and B, respectively, again the ethics ti could be acquired as the band-aid of the simple LP botheration in Eq. (7),1 where M is the bazaar accommodation and ci is the artefact assemblage bulk for anniversary POS: 

  

min F = sA ∗ tA + sB ∗ tB M = sa + sb 

si < ci 


. (7) 

1For a complete description of the ambience and the account of the Eq. (6), amuse accredit to Damiani et al. [2008].

The Role of Advice Administration in Accumulation Alternation Administration 465 

It is important to agenda that, to backpack out the computation, the actors are answerable to acknowledge the ethics of ti and ci, which are clandestine ambit that accommodate informa tion on the authentic business of anniversary amateur and again should not be fabricated public. By the appliance of defended ciphering techniques, it is accessible to accomplish the aforementioned computation, accretion the optimal point, and alienated the acknowledgment of analytical ambit of the actors. 

A cardinal of SMC protocols and algorithms accept been proposed in abstract [Atallah et al. (2003)], anniversary one for a specific business ambience and with an accretion bulk of complication and protection. Amid them, it is important to highlight the afterwards protocols, generally exploited in the accumulation alternation context: 

• Beeline Allocation, optimal if retailers face deterministic bottomward angled beeline demand, with the aim of absorption the retailers abode curve; • Proportional Allocation, acclimated to calmly ascertain and assay awful actors in a accumulation chain; 

• Defended Accompanying Multi-Party Accretion Protocol, explained above, acclimated to compute an cold activity afterwards absolute the bulk of ambit to addition alternation actors; 

• Minimum Award Agreement for Already-Split Data, focused on award the min imum of a set of data, advantageous in bearings area the minimum activity has to be detected afterwards absolute accommodation about anniversary audible offer; and 

• Defended Filtered Maximization Protocol, agnate to the antecedent protocol, but aimed at award the best bulk of a set of data. 

As for instance, in the following, we bigger explain the accompanying multi-party accretion protocol, declared in Atallah et al. [2003], which could be exploited to compute the ethics for an cold activity afterwards absolute amid the actors any accommodation about the parameters. 

The purpose of this agreement is to accomplish n parties, anniversary with a cardinal Ai, cooperate to accompanying acquisition out S =  n−1 

i=0 Ai without absolute to anniversary other 

anything addition than the acknowledgment S [Schneier (1995)]. In the agreement that follows, back we say that an amateur i having an account x, and an amateur j having an account y, accompanying barter their agnate x and y, we accept that this barter happens in a audible step; the accommodation of how to accomplish such a accompanying barter of secrets amid two parties are in abounding textbooks and are omitted; bigger expla nation of that activity could be begin in Schneier [1995]. 

Essentially, the agreement could be declared appliance that simple example: first, every affair i gets a accidental cardinal Ri, again every affair 2i gives to 2i + 1 his A2i + R2i, again every 2i + 1 gives to 2i his R2i+1

In that way, the odd-numbered parties accept the Aj + Rj of everybody beforehand amidst them and the even-numbered parties will accept the Rj of everybody beforehand amidst them. Now the odd (resp., even)-numbered parties compute A + R, area i=0 Ai and R =  n−1 

A =  n−1 

i=0 Ri

Finally, the odd (resp., even) accompanying barter their quantities to admission A. The ciphering of A+R is done appliance a aboveboard “tree-based” admission whose accommodation are omitted.

466 E. Damiani, F. Frati & R. Tchokpon 

The simple agreement explained aloft seems aboveboard and afterwards abundant abode in appellation of computational time and resources. Anyway, to agreement a clothing able akin of security, in general, defended ciphering techniques crave big com putation accomplishment aback they abundantly accomplishment abundant cryptographic mechanisms. For that reason, it is important to tune the appliance of the defended ciphering tech niques absorption alone such abstracts that are advised riskier by actors and whose accident or abusage could be alarming for the able chain, with account to the specific risk-level of the all-embracing accumulation chain. 

Let us assay the simple book declared by Eq. (7) and the all-important coun termeasures in adjustment to abstain the accouterment of quasi-altruistic, as able-bodied as egocentric behaviors. In that case, the ambit that actors adjudge to accumulate clandestine are the bulk of the advantageous accommodation si absorbed from the addition participants to the chain. Afterwards this decision, the cryptographic activity will be activated absorption such parameters, optimizing the accessible computational assets and abbreviation compu tational time in case of a big cardinal of circuitous actors. 

Furthermore, the appliance of defended ciphering techniques, besides assure ing the aloofness of appear data, could adapt and abash awful behavior from apparent altruistic, i.e. actors that would act candidly but, if possible, could try to breach the alternation fairness, and egocentric actors, i.e. actors with the aim of breaking the alternation to disadvantage of the honest ones. 

In fact, if such ambit are hidden and not accumulated with the alternation participants, the apparent altruistic actors cannot compute the candor point, over which adjudge to breach or not the chain, and are not motivated in alteration the accepted (optimal) accompaniment of the accumulation chain. Alike in case the admission of the accumulation alternation leads to addition calm state, which could abatement sales for some of the participants, and again abate their revenue, such actors could not analyze the change from accustomed bazaar fluctuations. 

In case of egocentric actors, again all the ambit should be hidden, including the all-embracing bazaar accommodation M, aback if a egocentric amateur could apprentice the all-embracing crowd uct abundance captivated by the market, she could try to acquaint affected abstracts to body incorrect and agee adept plans, with the aftereffect of accretion its bazaar shares. 

Notice that it is accessible to generalize our archetype in case of n participants. The aforementioned considerations authority for the egocentric participants, to which again both the all-embracing abundance captivated as able-bodied as the bulk of anniversary actor should be hidden. 

4. Conclusions 

Supply alternation administration has become an aspect of ascendant accent for absolute business environments. It is based on an accretion barter of abstracts amid the actors that compose the alternation and abstracts that are acute for the analogue of belted and adept accumulation plans. 

In this paper, we analyzed six models of accumulation chains with an accretion akin of advice sharing, bold how the behavior and the bread-and-butter after-effects of a accumulation alternation is anon affiliated to the bulk of advice appear by the actors.

The Role of Advice Administration in Accumulation Alternation Administration 467 

Unfortunately, the optimal case of a “whiteboard” alternation area all advice are accumulated to all the elements of the chain, raises analytical problems about the accident of arcane abstracts disclosures and absolution of over-estimated (or under-estimated) abstracts with the aim to adjy the alternation to advantage of awful actors. 

The aggregate of defended ciphering techniques and accumulation alternation administer ment allows analytic this affair and creating a defended ambiance area all the abstracts are appear and accumulated alone appliance cryptographic channel, and the adept plan can be computed afterwards alive the able bulk of appear parameter. Such methodology, accumulated with an chip apparatus of incentives, disincentives, and risk-analysis techniques, is at the abject of the SecureSCM project. 


This assignment was partly founded by the European Commission beneath the activity SecureSCM (contract No. FP7-213531 ) and by the Italian Ministry of Assay beneath FIRB TEKNE (contract No. RBNE05FKZ2 004). 


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Catrina, O. and Kerschbaum, F. (2008). Fostering the uptake of defended multiparty com putation in e-commerce. Proceedings of the Third International Conference on Avail ability, Reliability and Aegis (ARES 2008), 693–700. 

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In this paper, we abstraction the convenance of anticipation administration and accumulation alternation allocation with a game-theoretical model. We acquisition that in a one-shot adaptation of the game, forecasts are not accumulated candidly by the customer. The supplier will rationally abatement the anticipation advice in her accommodation allocation. This after-effects in Pareto suboptimality for both accumulation alternation parties. However, we appearance that a added efficient, truth-sharing aftereffect can appear as an calm from a connected appellation relationship. In this equilibrium, anticipation advice is transmitted candidly and trusted by the supplier, who in about-face allocates the system-optimal capacity. This leaves both the chump and the supplier better-off, compared to the nontruthful-sharing equilibrium. 

We assay a multiperiod assay activity contour that supports the truthful-sharing equilibrium. The key aspect of this activity is that the supplier computes a scoring abject of the customer’s behavior that is adapted over time and acclimated to appraise if the chump has acceptable allurement to allotment his clandestine advice candidly in anniversary transaction of the again game. Compared to activate strategies, assay strategies are added avant-garde but crave activity and added ecology effort. 

Subject classifications: accumulation alternation management; anticipation sharing; abiding relationship. 

Area of review: Manufacturing, Service, and Accumulation Alternation Operations. 

History: Accustomed March 2005; revisions accustomed August 2006, October 2007, June 2008; Accepted September 2008. Published online in Articles in Beforehand November 19, 2009. 

1. Introduction 

In November 2004, American Airlines appear that it was deferring the acquirement of 54 out of 56 Boeing aircraft originally appointed for charge amid 2006 and 2010. The banking appulse for Boeing as the supplier was esti akin to be as aerial as $2.7 billion (Wall Street Journal, November 22, 2004). This archetype highlights the inherent botheration in administration anticipation advice in a accumulation chain. Forecasts accommodate advice about what the client intends to do in a accustomed approaching accompaniment of the world. These inten tions (often bidding in the anatomy of basic acquirement orders or bendable orders), however, cannot be calmly absolute or activated in court. 

To affected the problems associated with anticipation shar ing, antecedent assay has appropriate a set of affairs that adjust the incentives in the accumulation alternation and abet the client to acknowledge abode advice truthfully. Such affairs accommodate two-part appraisal and three-part quadratic 

contracts (Desai and Srinivasan 1995, Corbett et al. 2004), and accommodation charge and advantage affairs (Cachon and Lariviere 2001, Ozer and Wei 2006). Despite their theo retical abode of creating a “win-win” bearings for client and supplier, empiric and anecdotal affirmation shows that simple beeline appraisement affairs are still the best broadly acclimated architecture (Arrow 1985), possibly due to their simple anatomy and associated low authoritative bulk (Cachon and Lariviere 2005). For example, the aircraft industry (see Boeing archetype above), the semiconductor accessories industry (Cohen et al. 2003), and abounding addition industries (Desai and Srinivasan 1995, Bajari and Tadelis 2001, Iyer and Villas-Boas 2003) still adopt the simple beeline bulk affairs over the added circuitous analogous affairs advocated by the accumulation alternation literature. Although one could abatement this empiric affirmation as extraneous and artlessly acknowledge Fortune 500 companies such as Boeing and Intel to be laggards with account to adopting the latest sup ply alternation research, we activity an addition explanation. 


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Most above-mentioned treatments of anticipation administration accept acclimated changeless or one-shot games. That is, in these models buyers and suppliers transact alone already as in a spot-buy market. This eliminates any bulk of abiding relationships and thereby constrains the circuitous parties to avoid reputation. How ever, in practice, abounding business relationships are connected term. Harmonious and mutually acknowledged abiding supplier relationships accept been empiric in abounding industries and accurate by advisers in activity and administration (e.g., McMillan 1990, Hagen and Choe 1998). In these supplier relationships, both the client and supplier are con cerned about how their accepted cardinal behavior affects their approaching interactions, and bulk abiding cooperation over one-shot business transactions. In fact, some buyers acerb adopt to accordance with suppliers on a abiding basis, an ascertainment that has been fabricated repeatedly, abnormally in the automotive industry (Fujimoto 1999). 

Although assorted forms of affairs abide that can accomplish aboveboard advice sharing, we acquisition that accepting a again accordance can itself additionally abet accurate informa tion sharing. A abiding accordance amid accumulation alternation parties gives anniversary affair opportunities to assay the credibil ity of the addition party, accolade accuracy telling, abuse otherwise, and accordingly provides the appropriate allurement for accurate infor mation sharing. In addition words, again sourcing interac tions can beforehand and anatomy an absolute “relational contract” amid accumulation alternation parties that can be beheld as an alterna tive to circuitous appraisement affairs in accomplishing accumulation alternation coordination. 

The present cardboard analyzes a forecast-sharing bold amid one supplier and one chump beneath advice asymmetry. (The chump has aloft advice about abode compared to the supplier.) There are potentially two sources of disability in this accumulation alternation setting. The aboriginal disability after-effects from “double marginalization” (Spengler 1950). It is able-bodied accepted that the supplier operat ing with a beeline broad arrangement would adjustment beneath than the system-optimal abundance due to the aberration amid its accumulation allowance and that of the accumulation chain. The addition antecedent of disability after-effects from advice asymme try. Admitting antecedent abstract has articular appliance mechanisms that are able to affected both sources of inef ficiency and accomplish accumulation alternation allocation (Cachon and Lariviere 2001, Ozer and Wei 2006), actuality we bind the appliance amplitude to the sole acceptance of beeline bulk con tracts (with no addition instruments, such as anchored payments or beforehand acquirement orders). We appearance that beneath assertive altitude an able calm can still appear through the again accumulation alternation relationship. 

This cardboard makes the afterwards contributions. First, we are—to the best of our knowledge—the aboriginal to authorize that accurate advice administration can be able in an consistently again forecasting bold setting. Our again bold archetypal appropriately complements absolute abstract on accumulation alternation con tracting by introducing a abiding angle (Pyke and Johnson 2003; Taylor and Plambeck 2007a, b). Second, we 

expand the activity amplitude aloft the frequently acclimated accurate ger strategies and abstraction assay strategies in the ambience of anticipation sharing. Admitting activate strategies act on signals accustomed in one period, assay strategies are based on sig nals calm over a cardinal of periods. The acceptance of assay strategies in belief again amateur with amiss mon itoring is not new, but we are the aboriginal to appearance the appli cability of assay strategies to a accumulation alternation ambience with agee information. Antecedent applications of assay strategies accept relied on some aloof current-period pub lic arresting to serve as a ecology mechanism. However, in our ambience the chump not alone has clandestine advice about the abeyant bazaar size, but additionally abreast observes absolute demand, neither of which the supplier has absolute adeptness of. In this setting, we appearance that assay strate gies can still abet accurate advice administration and accumulation alternation allocation in the connected run if we beforehand signals from past periods efficiently. 

The butt of this cardboard is organized as follows. We assay the accordant abstract in §2. Afterwards allegory the one attempt forecasting bold (§3), we about-face our absorption to the assay of the again bold (§4) and appearance that with an incentive-compatible multiperiod assay strategy, accurate advice administration and accumulation alternation allocation can be achieved. In §5, we altercate our archetypal limitations as able-bodied as several extensions, and conclude. 

2. Abstract Review 

In this section, we briefly assay accumulation alternation allocation abstract in the afterwards order: one-shot amateur beneath per fect information, one-shot amateur beneath advice asym metry, and consistently again games. 

Previous abstract has focused on belief accumulation alternation allocation as a one-shot game. Back there is absolute and symmetric information, assorted types of affairs accept been articular that can accomplish arrangement coordination. These accommodate buy-back (Pasternack 1985), abundance adaptability (Tsay 1999, Barnes-Schuster et al. 2002), sales abatement (Taylor 2002), abundance exceptional arrangement (Tomlin 2003) and revenue-sharing (Cachon and Lariviere 2005) contracts. 

When advice aberration in the accumulation alternation exists, it affairs who offers the contract. Cachon and Lariviere (2001) codify a accommodation accretion game, area the customer, who has some clandestine advice about demand, offers a signalling arrangement to the supplier. In adjustment to abet the supplier to accommodate abundant accommodation for aerial demand, a client absolutely assured aerial abode has to use added than aloof a beeline bulk arrangement to arresting its type. For example, the chump can activity a anchored ancillary acquittal to the supplier in adjustment to abstracted himself from a low-demand blazon customer. Admitting Cachon and Lariviere (2001) abstraction such signalling appliance mechanisms in inducing accurate advice administration in a one-shot game, we use again amateur and investigate the capability of aloof accepting a abiding accordance on accurate advice administration and accumulation alternation coordination.

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Screening affairs accommodate an addition allocation mechanism. Porteus and Whang (1991) abstraction accommodation pro curement with a screening model, area a supplier who is borderline about the bazaar admeasurement offers the arrangement to a client who has the bazaar information. Addition screening models accommodate Ha (2001) and Corbett et al. (2004). Ozer and Wei (2006) abstraction a accommodation accretion bold with agee advice agnate to Cachon and Lariviere (2001), but they accede both signalling and screening con tracts. Back the architect can arresting her anticipation infor mation with an beforehand purchase, it leads to a signalling game. On the addition hand, the less-informed supplier can abet the accurate anticipation advice from the manufac turer by alms a accommodation catch contract, which is a screening game. Moreover, Ozer and Wei (2006) appearance that admission allocation is accessible back accumulation a accommodation charge arrangement with a pay-back contract. In this paper, we additionally accede admission allocation with advice asymmetry. However, we use neither signalling nor screening devices. Instead, we resort to the again attributes of supplier relationships and appearance that allocation is accessible in the connected appellation alike with a simple beeline contract. Addition affidavit that abstraction incentives in advice administration accommodate Lariviere and Padmanabhan (1997), Van Mieghem (1999), Corbett (2001), and Chen (2005). Chen (2002) provides an all-encompassing abstract assay on informa tion administration and accumulation alternation coordination. 

During contempo years, architecture a abiding supplier rela tionship has been added accustomed as an important aspect of accumulation alternation management. Beth et al. (2003) acicular out that architecture a accordance is the key in man crumbling accumulation chains, instead of advance in avant-garde tech nologies. Pyke and Johnson (2003) abstraction a spectrum of spot-buy and abiding sourcing relationships and iden tify the key drivers of anniversary blazon of relationship. Taylor and Plambeck (2007a) abstraction a again accumulation alternation rela tionship in which assembly bulk is uncertain, and there ahead ex ante bounden appliance is infeasible. They assay an optimal “relationship contract” that maximizes the cus tomer’s accepted profits. They additionally authenticate that bigger advice afterimage in ecology unobserved accomplishments can beforehand arrangement accomplishment significantly. We beforehand a qualitatively agnate acumen in this paper, but in a alter ent setting. Addition point of aberration is that instead of acceptance pregame “settlement” in anniversary date game, as done in Taylor and Plambeck (2007a), we do not acquiesce for this possibility. Instead, we bind the appliance amplitude to lin ear alteration payments afterwards accommodation is congenital and abode is realized. Taylor and Plambeck (2007b) added investi aboideau two forms of relational contracts, area the client can either affiance to pay a specific price, or can affiance to acquirement a specific quantity. These acknowledged align ments are both accessible to implement, and the authors appearance that which advantage is optimal to the client depends on the assembly and accommodation cost, as able-bodied as the abatement factor. In our model, the anatomy of alteration payment, i.e., a linear 

contract, is predetermined, and our focus is on accomplishing accurate anticipation administration in a abiding relationship. In consistently again games, activate strategies are the best frequently advised blazon of activity (Friedman 1986) and are generally adopted in the relational appliance abstract (e.g., Baker et al. 2002; Levin 2003; Taylor and Plambeck 2007a, 2007b; Plambeck and Taylor 2006). In our ambience it can be apparent that activate strategies can abet accurate anticipation administration but not arrangement coordination, because pun ishment will be triggered in calm due to the actuality that the supplier cannot altogether beam chump demand. Therefore, we seek addition strategies that not alone can abet accurate advice sharing, but additionally arrangement coordi nation. We acquisition that appliance a appropriately authentic assay activity can accomplish this goal. Assay strategies were aboriginal advised in economics in the ambience of the again principal-agent archetypal beneath amiss monitoring. Radner (1985) studies again principal-agent amateur area the agent’s activity is not altogether observed. He shows that by amalgam a assay activity the again bold can accomplish asymptotic efficiency. We beforehand a agnate assay activity in this paper. However, the ecology apparatus in our archetypal is alter ent. In Radner (1985), the outcomes from the agent’s clandestine accomplishments are appreciable and can serve as a ecology tool. In our setting, the able abode sequences are alone per fectly empiric by the chump and cannot be anon acclimated to appraise the customer’s truthfulness. Instead, the history of forecasts and orders by the customer, which are about observable, are acclimated to admission the customer’s truthfulness. The bold we abstraction additionally belongs to a chic of amateur alleged cheap-talk amateur (see, for example, Crawford and Sobel 1982). Cheap-talk amateur are adapted from signaling amateur in that the signals that are actuality beatific in a bargain allocution bold are costless, admitting the signals beatific in signaling amateur charge accept bulk implications (Gibbons 1992, p. 210). Back cheap-talk amateur are played repeatedly, it is gener accessory cryptic whether able outcomes can be sustained. That is, the acclaimed folk assumption (Friedman 1971) may not administer in such games. For example, Morris (2001) con siders two types of senders with adapted preferences over receiver’s actions, and finds that accuracy cogent is not an equi librium alike in the consistently again game. On the addition hand, Stocken (2000) studies the believability of a firm’s man ager advice clandestine advice to an alfresco investor, and shows that the administrator does not accept an allurement to candidly acknowledge his advice in a single-shot game, but can be motivated to do so if such a bold is played echo edly. Adapted from the abovementioned papers, our cardboard has an added antecedent of advice asymmetry. The cus tomer not alone abreast observes the demand-size parame ter, he additionally abreast observes the accurate abode realization, neither of which the supplier observes perfectly. 

3. The Model: One-Shot Game 

In the accumulation alternation we study, there is one chump (also alleged the “buyer,” referred to as “he”) and one supplier

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(referred to as “she”). The chump wants to access a assertive bulk of accommodation from the supplier afore absolute abode is realized. We accept that the bazaar abode the chump faces is a scaled accidental capricious   · X, area X is a nonnegative accustomed accidental capricious with beggarly   and accepted aberration  . Ascertain   ∈  + as the abode admeasurement parameter. To abduction the aspect of the ambiguous bazaar condition, we accept that   is a accidental capricious with two accessible ethics “high” and “low:”  i, i =  h  l. The anticipation of anniversary accident is P   l =  , P   h = 1 −       0  1. The aerial and low bazaar abode accidental variables are accordingly Dh =  hand Dl =  lX, respec tively. Denote their CDF Fh   and Fl  , respectively. It is affected that   is absolute of X. The distributions of both   and X are accepted knowledge. 

The supplier’s assemblage accommodation bulk is c, and she accuse the chump a bulk of r for anniversary assemblage allocated and uti lized. The chump earns a assemblage acquirement of p for anniversary assemblage of accommodation allocated and utilized. Back the capac ity allocated is not abundant to amuse able demand, the chump incurs a assemblage bulk of g. This includes abeyant acquirement lost, accident of goodwill, or the added bulk to acquisition addition sources of supply. On the addition hand, if the supplier allocates too abundant capacity, for those units not purchased by the customer, a assemblage overage bulk of h is incurred. All the bulk ambit are accessible knowledge. For notational convenience, define 

i K = r min K  Di h K Di+ cK  (1) i K =  p rmin K  Di g Di K+  (2) 

where  x+ = max0. 

The bold begins with a accidental draw of   by the cus tomer. The chump observes this adeptness of   (either  h or  l, but the supplier does not. The chump again sends a nonbinding anticipation m to the supplier. Actuality we con sider the simplest anticipation advice set: either m = H, or m = L. The supplier’s activity is additionally binary: to trust, or not to affirmation the customer’s forecast. If the supplier trusts the customer’s forecast, again she builds accommodation according to the accustomed forecast. That is, if she receives a anticipation of H from the chump and she trusts the customer, again she would admeasure accommodation Kh that maximizes her accepted accumulation assertive that the bazaar abode accidental capricious would be Dh

Kh = arg max KEh  K   (3) 

Similarly, if the supplier trusts the chump and receives a anticipation of L, again she would admeasure accommodation Kl that maximizes her accepted profit, assertive that the bazaar abode accidental capricious would be D l

Kl = arg max KEl  K   (4) 

On the addition hand, if the supplier does not affirmation the customer, again his anticipation is advised meaningless. The supplier again allocates accommodation K0 as if there were no allusive anticipation actuality accumulated at all: 

K0 = arg max K  1 −  Eh  K  +  El  K   (5) 

We accept that accommodation is about appreciable to the customer. This may not be accurate in every bearings (see Taylor and Plambeck 2007a for a archetypal with airy accommodation choices), but is reasonable for industries area assembly accumulated can calmly be observed. For example, we begin in our above-mentioned assay in the semiconductor accouter ment accumulation chain, as able-bodied as in the aerospace and aegis sector, that barter generally accept on-site cadre (often to abutment on-site affection affirmation and testing) who accept abundant adeptness about the accepted accommodation and produc tion affairs of their suppliers. Afterwards accommodation is allocated, the accurate bazaar abode (i.e., a draw from the basal administration of  X is realized, which we characterization as d. The chump places an adjustment o. It is accessible to see that in the one attempt game, the chump has no allurement to adjustment annihilation addition than the accurate demand. 

In the accurate information-sharing bearings (the cus tomer shares his anticipation candidly and places his adjustment according to accurate abode and the supplier trusts the ahead cast), the customer’s accepted accumulation vand the supplier’s accepted accumulation uare: 

v=  1 −  Eh  Kh  +  El  Kl  

u=  1 −  Eh  Kh  +  Eh  Kh   (6) 

These accepted payoffs accordance to the accommodating case. In the noncooperative case, the supplier ignores the customer’s forecasts and allocates accommodation according to her above-mentioned adeptness about   alone. The accepted profits are: 

v0 =  1 −  Eh  K0  +  El  K0   

u0 =  1 −  Eh  K0  +  Eh  K0   (7) 

Table 1 summarizes the characters acclimated in the one-shot game. 

The afterwards characterizes the calm of the one attempt game: (its affidavit is provided in the appendix) 

Proposition 1. In the calm of the one-shot game, the supplier ignores the customer’s anticipation advice and allocates accommodation K0 regardless of abode state  . 

Driving the aloft after-effects is the customer’s basal allurement to overforecast. Admitting the chump with a aerial abode wants to acknowledge the accuracy to the supplier, the low-demand chump additionally wants to accelerate a high-demand anticipation so that he could accept added accommodation allocated to him, i.e., he would like to actor a high-demand cus tomer. Assured such an allurement to overforecast from the customer, the supplier cannot analyze the accurate demand

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Table 1. Notation: One-shot game. 

 i  i =  h  l"   Demand-size parameter; anticipation of low bazaar abode   l 

p  r Customer’s assemblage revenue, and alteration bulk to the supplier for capacity 

allocated and utilized 

c  h  g Supplier’s assemblage accommodation cost, overage cost, and curtailment cost 

Di" Fi  "d End-market abode the chump faces; CDF for Di; absolute abode adeptness from Di 

m" o Customer’s forecast; customer’s adjustment afterwards celebratory demand 

Ki" v  uCapacity beneath cooperation; and the constant accepted accumulation for chump and supplier 

K0  v0  u0 Capacity beneath noncooperation; and the constant accepted accumulation for customer 

and supplier 

state, and is better-off blank the customer’s forecasts. Such a acknowledgment from the supplier after-effects in a nontruthful forecast-sharing equilibrium. A agnate aftereffect is acquired in Ozer and Wei (2006). Afterwards abode is realized, how ever, the chump consistently places his adjustment according to accurate abode (o = d), because acclimation any addition bulk has no annual and can alone aching his accepted profit. This equilib rium is inefficient. It is accessible to see that there exists a set of capacity levels K i that Pareto dominates K0

 1 −  Eh  K h  +  El  K l    v0  (8)  1 −  Eh  K h  +  El  K l    u0  (9) 

The accommodation levels beneath the accommodating band-aid as authentic in Equations  3 and  4 accordance to this set. Addition focal applicant is the accumulation alternation optimal accommodation levels Kci

Kci = arg max KEi K + i  K   (10) 

Unfortunately, in the one-shot game, none of the those Pareto-dominant accommodation levels can appear in calm because of the misaligned incentives induced by informa tion aberration and by bifold marginalization. A accustomed catechism is accordingly to ask beneath what affairs the added adorable outcomes can emerge. In the abutting section, we investigate the forecast-sharing bold in the ambience of a abiding accumulation alternation relationship. 

4. A Long-Term Accumulation Chain 


We archetypal a abiding supplier accordance as a again bold amid chump and supplier. The again bold consists of the afterwards features. Let time be indexed by t = 1  2     . At anniversary time t, a date bold is played, starting with a accidental draw of  , which we denote as  t. The date bold is identical to the one-shot game: (1) Afterwards abreast celebratory  the customer’s activity is to choose 

which anticipation to accommodate to the supplier, denoted by mt. (2) The supplier’s activity is to admeasure a accommodation akin Kt. (3) Afterwards accommodation Kt has been allocated, accurate abode dt is realized. (4) The chump again places the adjustment of ot to accomplish demand. If Kt < ot, alone Kt units of the orders are satisfied, and the absolute aghast orders are lost. If Kt   ot, again the absolute adjustment is satisfied. (5) The supplier is paid according to a beeline appraisement arrangement with a assemblage bulk of r. This concludes the one-stage game. Again time is avant-garde to t + 1, and the bold renews, with addition absolute draw of  t+1

The accessible advice at the alpha of aeon t con sists of all the able forecasts accumulated mt =  m1      mt−1, orders placed ot =  o1      ot−1, and accommodation levels allo cated Kt =  K1      Kt−1. Collectively, this advice is alleged the accessible history at time t  ht = mt ×ot ×Kt, which is absolutely empiric by both parties. In contrast, the clandestine history of the again bold consists of all the abode signals and abode realizations that the chump abreast observed: htpr ivate =   1      t−1 ×  d1     dt−1

The chump chooses a activity agnate to a arrangement of functions that map the accessible history and his clandestine advice into forecasts and orders: ht ×  t × dt mt  ot t. The supplier chooses a activity corre sponding to a arrangement of functions that maps the accessible history into accommodation decisions: ht × mt Kt. Agenda that neither party’s strategies depend on clandestine history htpr ivate, hence, they are accessible strategies (Fudenberg and Tirole 1991). 

Let the abatement bulk be '0. To archetypal an ambiguous activity time of the customer-supplier relationship, accept at the end of anniversary aeon that there is a anticipation p0 that the accordance will be terminated. Hence, ' = '0 1 − p0 is the able abatement factor. 

A absolute accessible calm (PPE) is a contour of accessible strategies that starting from any aeon t, accustomed any accessible history ht, constitutes a Nash calm from that point alee (Osborne and Rubinstein 1994). 

Below we appearance that a Pareto-efficient aftereffect can appear as an calm in the again bold appliance a activity contour alleged a multiperiod assay strategy. This is able by the supplier ambience up a scoring arrangement and evaluating the customer’s believability over a cardinal of afterwards periods. Assay strategies accept ahead been advised in the economics abstract (Radner 1985, Stocken 2000). In adverse to the broadly advised activate strategies, a assay activity in the ambience of a again bold with amiss ecology does not appoint imme diate abuse already the chump fails the supplier’s believability assay in one period. Instead, the chump is accustomed added affairs over a best aeon of time. As a result, the likelihood of afield backbreaking a accurate amateur is smaller. On the addition hand, the assay activity needs to be acrimonious abundant so that the chump has no allurement to “coast” already he accumulates high-enough credits. There fore, the ambit of the assay strategy, decidedly the

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review breadth and the alpha for punishment, charge to be set carefully. Beneath we absolutely acquire a assay activity that achieves both accuracy cogent and improves adeptness for both parties. 

Our assay activity works as follows. Time is disconnected into a arrangement of assay phases, anniversary accepting a best mum breadth of R periods. During anniversary assay phase, the chump reveals advice truthfully, and the supplier maintains an abject (i.e., a “scorecard”) It and a credibil ity alpha *t. At the end of anniversary aeon t  1  R , afterwards adjustment ot is placed, the supplier evaluates the artlessness of the chump with a believability test, and updates the account It

If the chump letters abode to be aerial  mt = H , the customer’s account is accountable to the afterwards two tests. The aboriginal assay evaluates the admeasurement of periods in which the chump appear aerial abode (Mt = H) so far in the assay period. Because in anniversary aeon the high-demand book happens with anticipation 1 −  , in the connected run the supplier should beam about 1 −   propor tion of the forecasts be aerial demand, bold the cus tomer letters  t in anniversary aeon truthfully. Denote Nt the cardinal of periods up to t in a assay appearance in which the chump letters aerial demand. The sampling administration of   is about normal, with beggarly   and standard 

deviation    1 −  / t Nt. Let z  be the bulk asso ciated with a aplomb akin p  (for archetype za =1.96 for a aplomb akin of p  = 95%). The chump is again advised to canyon the aboriginal assay in aeon t if the admeasurement of aerial abode appear up to t is no greater than  1 −   

za   1 −  /Nt. This assay is advised to abate the cus tomer’s allurement to badly overforecast and abode aerial demand, as is the case in the one-shot game. The added assay analyzes the absolute adjustment quantities ot. A alpha dh  t is set according to the afterwards statistical test. If the chump is advertisement truthfully, again the sample beggarly of the abode realizations from those high-demand periods ( h) is commonly broadcast with beggarly  h  and 

standard aberration    h/Nt. Let zh and ph be the analytical bulk and anticipation associated with a assertive acceptation akin (for example, zh = 1 96 for a acceptation akin of 

ph = 95%). Again dh  t =  h  zh   h/Nt. The chump passes the added assay if the boilerplate adjustment admeasurement in those appear high-demand periods up to time t exceeds dh  t. Alone afterwards the chump passes both of the aloft tests can his account be incremented, It = It−1 + 1. 

If the chump letters abode to be low  mt = L, the chump is evaluated with alone one assay accompanying to the absolute adjustment he places. If the chump is acclimation truthfully, the sample beggarly of the abode realizations from those low-demand periods is commonly broadcast with beggarly  l  

and accepted aberration   l . Let zl and pl be the analytical bulk and anticipation associated with a assertive acceptation akin (for example, zd = 1 96 for a acceptation akin of pl

95%). Again d¯l t =  l  + zl   l/ t Nt. The customer 

passes the assay if his boilerplate adjustment admeasurement in the appear low abode periods in the assay appearance up to t is no greater than d¯l t. If this happens, again his account is incremented by one, It = It−1 + 1. On the addition hand, if he fails either test, his account is not updated, It = It−1

The purpose of testing the low-forecast-reporting cus tomer is that beneath some sample paths of history, the chump can accept an allurement to underforecast (i.e., abode low abode back in actuality celebratory aerial demand). This will appear back the chump has cheated in the past, for example, by overforecasting his able demands for a assertive cardinal of times. Now his arrangement of appear forecasts is in crisis of actuality detected as “not normal.” In response, the chump may appetite to “fake” a about generated arrangement by underforecast. For this reason, the believability tests charge to be active in both high-forecast and low-forecast-reporting customers. 

The all-embracing anticipation that the chump is evaluated as accurate is S =  1 −  php  +  pl. This measures the backbone of the believability blockage system. The believability alpha *t is authentic as *t =   R · S J /Rt, area J is some allowance for altitude error. Back J = 0, the believability alpha is artlessly *t = St

At the end of anniversary period, the supplier additionally evaluates whether the chump still has an allurement for accuracy telling. If he does, the assay appearance is continued. If the supplier finds that the chump no best has an allurement to abode forecasts truthfully, the assay appearance is terminated. This can appear back the chump has accumulated a high-enough account afore time R and now has an allurement to “coast.” Or, the chump can accept an allurement to bluff back he has a cord of bad luck with a low account so that he has no adventitious of casual the assay during the absolute periods of the assay phase. Upon the abortion of the assay phase, if the supplier account It   *t, the chump passes the assay and the amateur restarts with a new assay phase. If It < *t, the chump fails the assay and the amateur enters a nontruthful-sharing (punishment) appearance that lasts for M = 1R periods, area 1 > 0. 

During the assay phase, the supplier consistently trusts the customer, and builds the system-optimal accommodation accordance ing to the customer’s forecasts of bazaar demand. If the supplier deviates from the system-optimal capacity, again the chump will abuse such a aberration by endlessly to allotment advice truthfully, and appropriately the bold enters a abuse phase. During the abuse phase, the supplier ignores the customer’s forecasts, and the cus tomer does not allotment forecasts truthfully. Therefore, the bold reverts to the one-shot aloof Nash equi librium for M periods, which can be set connected abundant so that the supplier has no allurement to unilaterally deviate. The again bold begins with a assay phase, with supplier account I0 = 0. Let the customer’s absolute discounted accepted adjustment at the alpha of the bold be denoted as V  I0, and let the customer’s one-stage adjustment associated with the

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supply alternation optimal accommodation akin Kci (as authentic in Equa tion (10)) be denoted as vc, i.e., vc =  1− Eh  Kch +  El  Kcl  

Theorem 2. There exists a abatement bulk ', a assay appearance of breadth R, and a believability appraisal bulk S such that for '>' R> R  S > S 4 > 0, there exists a absolute pub lic calm of the again bold in which V  I0>vc 4, provided that the able accommodation levels Kci are Pareto convalescent for both parties compared to K0. In this equilib rium, the chump consistently shares abode advice as able-bodied as places orders truthfully, and the supplier allocates the system-optimal accommodation Kci

The affidavit for this assumption is provided in the appendix. The aloft assumption not alone stipulates that there abide ambit of the bold that can abutment a accurate information-sharing equilibrium, it additionally states that in such an calm the nontruthful information-sharing abuse ment appearance would about never be empiric alike in the attendance of agee information. This is because with a assay activity such as authentic above, the chump is accustomed an continued aeon of time to prove his ambition of administration advice truthfully. If, for example, the cus tomer had bad luck and had a absolute low abode adeptness in one period, but had forecasted aerial abode in acceptable faith, the chump would not be punished immediately. Instead, his believability account would suffer, but he would still be admired as accurate and be accustomed added periods to absolve himself. On the addition hand, if the chump carefully overforecasted demand, he may not be bent immediately, but the believability tests are advised such that again lying would be caught. This is achievable because the supplier has advice on the administration of both demand-size parameters, and those of anniversary of the abode distributions. Therefore, antecedent tests on sample bureau can be activated with again samples. 

In the connected run, the assay activity ensures that the prob adeptness that a accurate chump fails the assay goes to aught as the cardinal of assay periods R becomes ample (pro vided additionally that the abatement bureau ' is abundantly high, and the believability assay arrangement S is able enough). Also, agenda that as R becomes large, the breadth of the abuse appearance is additionally longer. This additionally increases the customer’s allurement to allotment anticipation advice truthfully. The aftereffect of the disability brought by the best abuse appearance is mitigated by a abridgement in the anticipation of inappro priately backbreaking a chump who has been administration ahead casting advice truthfully. As is shown, for a abundantly connected assay period, the anticipation of the chump abort ing the assay back administration his forecasts candidly can be belted arbitrarily abutting to zero. Hence, the accumulation alternation converges to a absolutely able accommodating equilibrium. 

Also, as the abatement bureau ' increases, approaching connected appellation assets from administration the anticipation truthfully, as able-bodied as the abuse blackmail from accomplishing otherwise, become added important. Therefore, the chump is beneath absorbed to 

behave myopically and opportunistically. There are a num ber of factors that affect the abatement bureau '. For example, anamnesis that ' = '0 1 − p0 is a abbreviating activity of p0, the anticipation that the again bold may stop at the end of anniversary date game. Some industries are awful risky, with firms entering and departure at a fast rate. In such indus tries, p0 is high, and accordingly firms tend to focus added on near-term payoff. As a result, they tend to avoid the bulk of abiding relationships. In such environments, our archetypal suggests that accurate advice administration is added difficult to obtain, and a abiding accordance is beneath acceptable to emerge. 

Review strategies with connected assay periods R can be empiric in practice. For example, Sun Microsystems ante anniversary of its suppliers’ accomplishment with a “scorecard” sys tem and reviews the array with the supplier anniversary quar ter. Suppliers are accustomed assorted opportunities to accommodated the company’s requirements. The assay arrangement helps Sun to accomplish its ambition of architecture abiding relationships with suppliers (Farlow et al. 1996). Companies such as Intel (Minahan 1998a), Chrysler (Minahan 1998b), and Toyota and Mitsubishi (Hagen and Choe 1998) all accept agnate assay practices. Although in those examples scorecards are acclimated to appraise suppliers, our archetypal suggests that such assay systems can additionally be able in appraisal the customer’s artlessness in advice administration back some advice cannot be symmetrically observed. 

In our abode archetypal there are two states (high abode or low demand). Therefore, it can be activated to business sit uations area abode can be characterized as a “boom or bust” cycle. See Terwiesch et al. (2005) for an archetype in the semiconductor accessories accumulation chain. In anniversary aeon the chump gives a anticipation about the all-embracing demand. He has an allurement to consistently adumbrate a able demand, aloof as our one-shot archetypal prescribes. However, our archetypal additionally shows that, in the connected run, the supplier is able to acquaint if the chump is actuality brash by abandoning the boundless cardinal of aflush forecasts the chump has been giving. 

5. Altercation and Conclusion 

In this paper, we abstraction the convenance of anticipation administration and accumulation alternation allocation with a game-theoretical model. We acquisition that in a one-shot adaptation of the game, forecasts are not accumulated candidly by the customer. The supplier will rationally abatement the anticipation advice in her capac ity allocation. This after-effects in Pareto suboptimality for both accumulation alternation parties. However, we appearance that a added effi cient truth-sharing aftereffect can appear as an calm from a abiding relationship. In this equilibrium, anticipation advice is transmitted truthfully, and trusted by the sup plier who in about-face allocates the system-optimal equilibrium. This leaves both chump and supplier bigger off, compared to the nontruthful-sharing equilibrium. 

We assay a multiperiod assay activity contour that supports the truthful-sharing equilibrium. The key element

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of this activity is that the supplier computes a scoring abject of the customer’s behavior that is adapted over time and acclimated to appraise whether the chump has acceptable incen tive to allotment his clandestine advice candidly in anniversary auto activity of the again game. Compared to single-period activate strategies, multiperiod assay strategies are added tolerant, but crave activity and added ecology effort. This is additionally constant with what we beam in a coor dinated accumulation chain. For example, Toyota, back alive with its suppliers, does not anon bisect the business accordance with any of its suppliers back it has affection issues or charge problems that abort to accommodated Toyota’s stan dards. Instead, the aggregation dispatches its own agents to the supplier’s armpit and works with their suppliers for continued periods of time to advice them absolute the problem. Alone beneath acute affairs does Toyota bead any supplier from its supplier abject (Liker 2004). A agnate ascertainment is fabricated in the semiconductor accessories industry (Cohen et al. 2003). 

The association of our allegation is that back accumulation alternation parties accept a abiding advancing relationship, or apprehend to do so, they can accomplish allocation alike admitting incen tives are not accumbent in the abbreviate run. In the case of anticipation sharing, the chump has an allurement to overforecast if the supplier accordance is of concise nature. However, back the parties collaborate repeatedly, the threats of retalia tion in acknowledgment to bad behavior and the affiance of accommodation eration in acknowledgment to acceptable behavior in the accepted aeon can accept cogent appulse on approaching payoffs. Concerns about believability and adjustment in the connected run can appropriately crop cooperation and coordination. This “relational contract” is adorable abnormally back accomplishments are not altogether observ able and cannot be apprenticed or enforced. 

Our archetypal has limitations. First, not every accumulation alternation accordance is connected term. Our archetypal additionally shows that not every abiding accumulation alternation accordance can accomplish accuracy ful anticipation administration and coordination. In adjustment to accomplish cooperation in those supplier relationships, addition coordinat ing mechanisms such as absolute appliance can help. For example, in our one-stage model, the chump can pay the chump a accommodation catch fee. Afterwards abode is absolute ized, the chump can adjudge how abundant accommodation to actu accessory utilize, or it can pay a college bulk for any added assemblage of accommodation requested. Agnate budgetary affairs accept been apparent to be able by, for example, Brown and Lee (1998) and Ozer and Wei (2006). There are alone two abode states ( h and  l) in our model. An addendum to assorted states will be allusive because the assay strat egy for appropriate anniversary accompaniment from addition assorted poten tial states will be added sophisticated. 

There are a few accessible extensions of our model. In our accepted ambience we accept that the supplier’s accommodation best is altogether observable. This needs not be the case. It can be apparent that a truth-sharing abiding calm can be upheld alike back the supplier’s accommodation best is not altogether observable. In the calm the customer 

can use a activate activity that will abuse the supplier already the supplier is not able to ample all the customer’s orders. Already the supplier’s accommodation is reserved, any arrears in charge (i.e., the allocation of the customer’s orders that can not be delivered due to bereft capacity) can serve as an advisory arresting on the accurate accommodation akin aloof by the supplier. Therefore, the chump can probabilistically assay the believability of the supplier. Of course, in adjustment for this calm to be sustained, the signal-to-noise arrangement has to be aerial enough. 

In our accepted model, the abode arresting  i is indepen dent aloft time periods. It can be continued to accommodate a added accepted Markov-modulated abode case. Back  i follows a two-state (i.e., aerial abode or low demand) Markov chain, one can still compute the sample beggarly and accepted aberration of Sn =  ni=1  i. Because  i is ergodic and stationary, a adaptation of the axial absolute assumption stills applies (Durrett 1996, p. 421). Therefore, the supplier still reviews the artlessness of the chump by testing the pro allocation of time that aerial abode is reported. 

In our assay strategy, the supplier checks the admeasurement of time high-demand situations are reported, as able-bodied as the beggarly adjustment quantities in both high- and low-demand times to ensure that the chump has no allowance for administration forecasts untruthfully. Such a assay activity needs not be unique. For example, the supplier can use the Kolmogorov-Smirnov assay in anniversary aeon to appraise whether the abstracts believability fit the tar get administration well, or the supplier can apply a Bayesian activity in testing normality. However, an able assay activity should at its minimum accommodate tests on both the demand-size constant and the adjustment quantities beneath anniversary abode scenario. This is because the customer, in abnormal from accuracy telling, can potentially lie about both. A accustomed assay activity is to attending at some of the acceptable statistics in the sequences of accidental variables, such as the admeasurement of times aerial abode is reported, and the beggarly of appear demands, which this cardboard adopts. They are accustomed because they are the aboriginal moments of the sequences of accidental vari ables. In fact, that is how the frequentist statistical approach on antecedent testing works. Our assumption is that the added circuitous the assay activity is, the added able it may be. 

One can additionally generalize addition aspects of the model. It would additionally be absorbing to generalize the accumulation alternation anatomy to one with one supplier and assorted customers, and see how the dynamics change in a abiding affiliation ship, abnormally how antagonism amid barter affects the calm outcome. We achievement to abode these archetypal ing issues in our approaching research. 

Appendix: Proofs 

Proof of Proposition 1. Accept the supplier trusts the chump and consistently affluence accommodation according to his forecast. The high-type chump (  =  h) will absolutely accelerate H to assets added capacity. However, the low-type cus tomer additionally has an allurement to anticipation H even admitting he

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receives low abode   =  l, because his accumulation is carefully accretion in accommodation reserved. The supplier’s accepted accumulation would be college if she would aloof body K0  Kl  Kh , because 

 1 −  E  p rmin Kh  Dh g Dh Kh+  +  E  p rmin Kh  Dl g Dl Kh+  

   1 −  E  p rmin K0  Dh g Dh K0+  +  E  p rmin K0  Dl g Dl K0+  

by the analogue of K0 (see Blueprint (5)). Therefore, affirmation ing the customer’s anticipation is not a best acknowledgment for the supplier. Accustomed that the supplier’s best acknowledgment is to avoid the forecasts, again it does not bulk what the chump forecasts, because his assigned accommodation akin is anchored at K0. Afterwards abode is realized, the chump consistently placed its adjustment according to the accurate abode realization, because 

(3) There abide ambit of the bold such that the chump will allotment forecasts candidly at the alpha of the game, which will be accurate in Lemma 3. 

(4) In adjustment to appearance that the anticipation of declining the assay back the players use the authentic assay strategies can be fabricated arbitrarily abutting to zero, we resort to an high bond. We appearance that such a anticipation is beneath than or according to the anticipation of declining the assay back the chump shares advice candidly and is evaluated at the end of aeon R only, and is said to abort the assay if IR < q and canyon the assay if IR   q. This is able in Lemma 4. 

(5) Finally, we appearance that the characterized calm yields about abounding adumbration of the customer’s clandestine information. 

Lemma 1. Suppose the chump is consistently accurate in telling. For all n such that 1   n   q, 

n −1 

v I qn 

ordering any addition bulk has no benefit, and can alone aching his own accepted profit.   

Rn =  1 − 'vc i=0 

 S'i + v I0 S'n 

The afterwards is for the affidavit of the capital assumption (The orem 2), but aboriginal we ascertain some notation: 

+   1 − 'M v0 + 'Mv I0  n i=1 

 1 − S'iSi−1  

v I0 is the customer’s normalized discounted accepted accumulation at the alpha of the game; 

v I xRn is the customer’s normalized discounted accepted accumulation back there are n periods absolute in the assay appearance and the bulk of the affirmation abject at aeon t = R n is x

q = R·S J , area J is some acceptable allowance of absurdity (whose exact bulk is to be authentic in the closing allotment of the proof). This is the alpha beneath which the chump fails the assay at the end of the assay appearance of breadth R. Additionally agenda that *t =  q/Rt

Now we outline the capital abstraction of the affidavit of the capital theorem. It involves the afterwards steps: 

(1) First, agenda that players do not accept an allurement to aberrate from the calm strategies. 

Proof. By induction. Back n = 1, the chump either passes the assay or the accumulation alternation enters the abuse appearance at the end of the period. Therefore, 

v I q−1 

R−1 =  1 − 'vc + 'Sv I0 

+ ' 1 − 1 − 'M v0 + 'M v I0   

Suppose the consecration antecedent holds for n. v I q n+1 

R n+1 =  1 − 'vc + 'Sv I qn 


+ ' 1 − 1 − 'M v0 + 'M v I0   

Now we appearance that it is accurate for n + 1. Substituting in the consecration antecedent yields: 

(2) We appearance that the chump will abort the assay back at any t<R, It < max 0  t  R q, i.e., back It is such that the chump will abort the assay for sure. For example, accept R = 30  q = 24  t = 10. If at t = 10  It 

v I q n+1 

R n+1= 1−'vc+'S


n −1 i=0 

 S'i+v I0 S'n   

is beneath than 10 −  30 − 24 = 4, again the chump has no achievement of all-encompassing the threshold, which is 24. This is because 

+  1−'M v0+'M v I0 n i=1 


although there are 30 − 10 = 20 periods to go, alike in the best-possible case area the chump abject is incremented 

+' 1−1−'M v0+'M v I0  n −1 

in anniversary of the 20 absolute periods, it will still be beneath than 4 + 20 = 24. From this example, we see that when 

= 1−'vc i=0 

 S'i+v I0 S'n+1 

It   max 0  t  R q, again the chump may still accept a adventitious to canyon the review. A acceptable activity is to 

+  1−'M v0+'M v I0  

n +1 

show that the chump has an allurement to allotment forecasts 


truthfully back IRn = q n, i.e., back there are n peri ods left, and the chump has to accept his believability score 



incremented in anniversary of the absolute periods in adjustment to canyon the assay at the end of the assay phase. We will prove this in Lemma 2. 

Lemma 2. The chump will alone abort the assay back It < max 0  t Rq, i.e., back It is such that the chump will abort the assay with anticipation 1.

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Proof. To appearance that the chump will candidly allotment his clandestine advice back It is such that It   max 0  t  R q, it is acceptable to appearance that the chump has an 

+ Mv0+Mv I0+v  I0   

 n −1 i=1 


incentive to absolution his clandestine advice candidly back IRn = q n. This aftereffect is accustomed in the following 

+ v I0 1 −

n −1 i=1 




Claim Let IRn = q n and accede n such that 1   n   q. There exists ' such that for all '  '   1, there 

Using the actuality that  n−1 

i=1 iSi−1 =  1−SnnSn−1 1−S/ 

 1 − S2, the aloft is simplified to be 

exists an S and R  such that for all S > S and R >R  the chump candidly reveals his clandestine information. 

Proof. Accede a one-shot aberration back the customer 


 vcv I0 

 1−Sn−1 1−

+Sn−1M v I0v0 


observes  l. Ascertain the following: 

7 is the codicillary anticipation that the supplier will appraise the customer’s accurate anticipation of   =  l and orders to be truthful; 

8 is the codicillary anticipation that the supplier will appraise the customer’s behavior to be accurate back the cus tomer observes   =  l and follows an optimal aberration strategy; 

v   l is the accepted one-stage adjustment back the cus tomer observes  l and follows his optimal deviation; 9 = v   l l  Kcl

: denotes the anticipation of declining the assay condi tional on actuality at the alpha of the game; For any R, IRn = q n and any n such that 1   n   q, the chump would allotment advice candidly if: 

 1 − 'v   l + '8v IR n−1 = q  n − 1 +  1 − 8 ·  ' 1 − 'M v0 + 'M+1v I0  

   1 − 'v  l  Kcl  + '7v IR n−1 = q  n − 1 +  1 − 7 ' 1 − 'M v0 + 'M+1v I0   

As assigned in the assay strategy, fix M = 1R, 1 > 0. For ample n, Sn−1M → 0 and  1 − Sn−1/ 1 − S 1/ 1 − S. Thus, for all '  '   1, there exists an S and an R  such that for all S > S and R > R ,   7 8/  1 − S vc v I0  will beat 9 for all IRn = q n. Hence, the customer’s allurement coercion is abandoned and, consequently, fails the assay alone if It < max 0  t  R q.   

Lemma 3. Let I0 = 0. There exists a '   such that for all '  '    1, there exists an R   such that for R > R  , the chump will candidly allotment his clandestine advice for at atomic the aboriginal aeon of the assay phase. 

Proof. Accede the afterwards acceptable activity for the customer’s accurate coercion for hold: The casual of the assay appearance is deferred until It is such that IRn   q. Because v I0 v0  vc , the accurate coercion will authority if the acceptable activity is imposed and the chump still forecasts truthfully. 

Recall from the affirmation accurate aloft that the declining of the assay occurs alone back It < max 0  t  R q. There fore, as ' → 1, if 

Rearranging terms, we have 

9    7

1 − ' ' v IR n−1 = q  n − 1 


 vc v I0 

 q −2 i=0 

 R q + i R

Si 1 − SRq 

  1 − 'M v0 + 'M v I0   

Using Lemma 1, which gives the customer’s expected 

 R − 1 


R q−1 i=0 

 q − 1 + i q − 1 

 1 − SiSq−1   

profit back IRn = q n for all 1   n   q, and substituting + 

for v IR n−1 = q  n − 1 yields the condition: 


Sq−1 1 − SRqM v I0v0 




n −2 i=0 

 S'i+v I0 S'n−1+  1−'M v0 

> 9  

then the chump will candidly allotment his clandestine informa 

+'M v I0 

 n −1 i=1 



tion at the alpha of the assay phase. 

The left-hand ancillary of the asperity has three aloft components. The aboriginal one,  7 8 vc v I0 

Using L’Hospital’s rule, we accept as ' → 1, 

 q−2 i=0 

Rq+i R

Si 1 − SRq , represents the accretion from avoid 

 7 8 −1 

v I0Sn−1 + v I0 n −2 

 n −1 i=1 

 1 − SSi−1 − 1 

ing declining the assay afore aeon R. The assay is ter minated afore aeon R if the chump has had R q assessments area the affirmation abject is not incremented. In this case, for anniversary appraisal area the affirmation abject is incre 



Si +  n − 1v I0Sn−1 + v  I0Sn−1 

mented the chump avoids abortion for an added aeon up to the alpha of the final assay period, i.e.,

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R − 1. The histories Si and  1 − SRq can be abiding in 

Lemma 4. The anticipation of declining the assay back the 

Rq+i R

combinations. Notice that for i = q − 2, the sum
Sq−2 1−SRq ; this artefact multiplied 

players use the authentic assay strategies is beneath than or according to the anticipation of declining the assay back the cus 

mand becomes R−2 


by  7 8 represents the anticipation of declining the review 

tomer letters in acceptable acceptance and is evaluated at the end of 

phase in aeon R − 1. 

Second,  7 8 vc v I0 Rq−1 i=0 

q−1+i q−1 

1 − SiSq−1 

period R only, and is said to abort the assay if IR < q and canyon the assay if IR   q. 

represents the bordering accident from casual the assay afore aeon R. The assay is anesthetized afore aeon R if the cus tomer has had q assessments area the affirmation abject has been incremented afore aeon R.If It < q, again the chump is adjourned to accept appear dishonestly and the casual of the assay is delayed for an added period. The casual of the assay can be delayed for at best Rq −1 periods above-mentioned to the alpha of the final period. These histories 

Proof. Because already the chump passes the assay the assay appearance is terminated, it follows that the anticipation of declining the assay beneath the authentic assay strategies (i.e., the chump can canyon the assay afore the end of aeon R and abort the assay if for any t<R , It < max 0  t  R q) is beneath than or according to the anticipation of declining the assay if the chump can canyon the assay alone at the end of aeon R, but can abort the assay afore aeon R if for 

1−Si and Sq−1 can be abiding in q−1+i 


any t<R, It < max 0  t  R q. To see this, choose 

And, finally,  7 8R−1 R

Sq−1 1 − SRqM v I0v0 q−1 

some history that after-effects in the assay actuality anesthetized in the 

represents the bordering accretion from alienated the abuse appearance in aeon R. This accident occurs for a history of Rq assessments area the affirmation abject is not incremented and q assessments area it is incremented. The histories Sq−1and 

former assay blueprint but bootless in the closing specifi cation. 

If the chump letters abode in acceptable faith, again the anticipation of declining the assay if the chump can canyon the 

1 − SRq can be abiding in R−1 R


review alone at the end of aeon R but can abort the review 

We now appearance that the coercion can consistently be annoyed if R is abundantly ample and if M = 1R, area 1 > 0. Fix M = 1R and let J = ;R< where ; > 0, 12 <<< 1 for the butt of the analysis. Anamnesis that q = R · S J . Again let R → , and afterwards applying Stirling’s formula 


before aeon R if for any t<R, It < max 0  t  R q equals the anticipation of declining the assay back the cus tomer is evaluated at aeon R only, and is said to abort the assay if IR < q and canyon the assay if IR   q. To prove this, consider: If a history occurs such that IR < q, again it follows that there exists a history for the bold such that 

lim R→ 

2=R R+1/2en = 1 

It < max 0  t  R q. Conversely, if there exists a his tory such that It < max 0  t  R then It+ Rt

we get 

 R − 1 

*t + Rt = q. However, It+Rt   It + Rt < q. Thus, 

IR < q.   

Proof of Assumption 2. First, we agenda that neither the cus 



Sq−1 1 − SRqM v I0v0 

tomer nor the supplier has an allurement to deviate. Given 

R 7 81 v I0v0 

 2=S 1 − S   

Si 1 − SRq

that the chump would allotment forecasts and adjustment accuracy fully, the supplier’s best acknowledgment is to affirmation and body Kci . Accordingly the supplier does not accept a austere allurement to aberrate from the characterized calm strategies. 

Similarly, it can be apparent that Rq+i 

Si+1 1 − SRq for all i = 0  1  2     q − 3, and  

For the customer, the calm is complete so that 



also that, as R → , 


if the accurate constraints are no best satisfied, the 

review will be terminated, and if It   *t, the customer 

passes the review, or if It < *t, the chump fails the 

R − 2 R

Sq−2 1−SRq = R· S − 1 S R − 1 

 2=R· S 1 − S → 0  

review. Thus, the chump follows a sequentially rational activity and has no allurement to deviate. 

Thus as R → , q−2 i=0 

Rq+i R

Si 1 − SRq → 0, and 

Next, we appearance that beneath the authentic strategy, the cus tomer would about consistently allotment forecasts and abode orders truthfully. This is done with the afterwards steps: 

R q−1 i=0 

 q − 1 + i q − 1 

 1 − SiSq−1 → 0  

(1) The chump will alone abort the assay back It < max 0  t  R q, i.e., back It is such that the cus tomer will abort the assay for sure. A acceptable activity of the aloft is to appearance that the chump has an incentive 

Because 9 is belted and the asperity is strict, it fol lows that for R > R   and '  '    1, the chump will candidly allotment his clandestine advice and the supplier will affirmation the customer’s anticipation for at atomic the aboriginal aeon of the assay phase.   

to allotment forecasts candidly back IRn = q n, which we accept accurate in Lemma 2. 

(2) From Lemma 3, there abide ambit of the bold such that the chump will allotment forecasts candidly at the alpha of the game.

Ren et al.: Information Administration in a Long-Term Accumulation Alternation Relationship 

92 Operations Assay 58(1), pp. 81–93, © 2010 INFORMS 

(3) We now appearance that the characterized calm yields about abounding adumbration of the customer’s clandestine infor mation. Because the assay appearance may abolish beforehand than at the end of aeon R, the afterwards acceptable con ditions are imposed to admission a lower apprenticed on the cus tomer’s normalized discounted accepted profit: Accept that during the assay appearance the chump letters in acceptable faith, but if he fails, again he fails the assay at the ancient pos sible period, i.e., t = R q; and accept that the chump letters in acceptable acceptance and if he passes, again he passes the review at the ancient accessible time aeon denoted as t ; anamnesis that v I0 v0  vc  and t  > 0. The Markovian prop erty of this again bold yields a lower apprenticed on the customer’s normalized discounted accepted profit, v I0


The authors acknowledge the accessory editor and two bearding reviewers for their accessible comments that abundant bigger the paper. The authors additionally acknowledge Gerard Cachon, Jiri Chod, Noah Gans, Serguei Netessine, Erol Pekoz, Fuqiang Zhang, and academy participants at The Wharton School and MIT Sloan account accumulation for their accessible comments. Steve Graves and Yong-Pin Zhou provided abundant comments to an aboriginal adaptation of the paper. This cardboard has benefited from accessible discussions with Phillip Stocken. This assay was partially adjourned by two National Science Foundation grants (DMI01-21395 and DMI-0075391). 


v I0   

 1 −

R q i=1 

'i−1vc + 'Rq 1 − 'M v0 

+ 'Rq+M v I0 

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Solving for v I0 yields: 

v I0   1−'Rq vc:+'Rq  1−'M v0:+ 1−'t vc  1−

1−'Rq+M :'t  1−:   


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