The Quantity Flexibility Contract and Supplier-Customer Incentives

March, 2015

Paper’s summary

The Quan7ty Flexibility Contract and Supplier-‐Customer Incen7ves (Tsay 1999)

Based on the paper “Tsay, A. 1999. The Quantity Flexibility Contract and Supplier-Customer Incentives. Management Science 45(10) 1339-1358”

Leonardo Laranjeira Gomes PhD Student MIT-‐Zaragoza Interna5onal Logis5cs Program Zaragoza Logis5cs Center

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Contents

1.   Research ques7on 2.   Relevant literature 3.   Assump7ons 4.   Model 5.   Numerical analysis 6.   Conclusions and discussion 7.   Personal opinion

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Contents

1.   Research ques7on 2.  Relevant literature 3.  Assump5ons 4.  Model 5.  Numerical analysis 6.  Conclusions and discussion 7.  Personal opinion

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The paper considers an external manufacturer (EM) that provides a product to a retailer, which in turn serves the end market…

Base scenario: • EM commits resources to produc5on quan55es based on forecasted rather than realized demand • Uncertain market demand: retailer oNen prefers to postpone the purchase commitment • Retailer provides an ini7al point es7mate of its intended purchase to assist the EM’s produc5on quan5ty decision

•  Retailer’s eventual purchase will likely differ from the forecast: •  Demand uncertainty •  Individual preferences towards overproduc5on and underproduc5on

•  A careful EM will adjust for these incen7ves and will incorporate its own economic prospects

…in a base scenario that leads to an efficient outcome for the overall system

Source: Tsay 1999

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Lee et all (1997) described the emergence of QF contracts as a response to supply chain inefficiencies…

…however firms are unwilling to reveal the terms of the trade and liale formal documenta7on existed describing how industrial users arrived at the contracts’ parameters

Source: Tsay 1999

Author Year Company using QF

Lovejoy 1999 Nippon Otis

Lovejoy 1999 Toyota

Ng 1997 Solectron

Faust 1996 HP and Compaq

Farlow et al. 1995 Sun Microsystems

Connors et al. 1995 IBM

Magee and Boodman 1967 Within departments of individual Kirms (e.g. manufacturing and marketing/sales functions)

The QF contract: • The retailer commits to purchase no less than a certain percentage below the forecast • The EM’s guarantee to deliver up to a certain percentage above the retailer’s forecast • Single transfer price per unit

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Tsay studied the supplier-‐customer incen7ves in such sebng and how the quan7ty flexibility (QF) contract can overcome channel inefficiency

Main research ques7on: • How can the quan5ty flexibility (QF) contract be used to promote the achievement of system-‐wide efficiency?

Addi7onal ques7ons: • What are each party’s behavioral incen5ves in an inefficient se\ng?

• What are the parameters of the QF contract? • What are the impacts of the QF contract’s parameters on the economic outcomes for each party involved? • How does the QF contract performs under demand’s informa5on asymmetry? • What are the condi5ons for a coordina5ng QF contract?

Source: Tsay 1999

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Contents

1.  Research ques5on 2.   Relevant literature 3.  Assump5ons 4.  Model 5.  Numerical analysis 6.  Conclusions and discussion 7.  Personal opinion

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Channel miscoordina7on and its addressing approaches have been exposed by several authors, in different fields…

…and Tsay described Iyer and Berger’s (1997) model of quick response (QR) as the most relevant for this par7cular study

Source: Tsay 1999

Author(s) Year(s) Topic/:ield General Idea

Spengler Tirole

1950 1988

Double marginalization

In most cases, a SC composed of independent agents acting in their own best interests will be inneKicient

Tsay et al. 1999 SC contracts Reconsider the nature of the supply contracts along the chain

Whang 1995 The goal in SC contracts

Install rules for materials accountability and/or pricing that will lead to the desired outcome

Methewson and Winter Katz

1984 1989

Economic literature “Vertical restraints”

Jeuland and Shugan Moorthy

1983 1987

Marketing literature “Channel coordination”

Bergen Van Ackere

1992 1993

Pol. Sci. / economics Agency theory

Lee and Whang Chen Iyer and Berger

1997 1997 1997

Operations literature Multiechelon inventory

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Iyer and Berger (1997) modeled the delay of the SC’s commitment to quan7ty in a manufacturer-‐retailer sebng on a QR effort..

Source: Tsay 1999

•  The retailer benefits from procuring under improved informa5on, yet the manufacturer can be made worse off

•  Manufacturer produces to order and its payoff is determined once the retailer orders, regardless of how the uncertain market demand resolves

•  The manufacturer naturally prefers a large retailer order, even if this includes excess amounts of safety stock that never get sold

•  Higher service to the end customer •  Wholesale price increase

•  Volume commitments

•  Manufacturer forces the retailer to buy or pay more than it would with the QR alone

•  Focus on Pareto improvement at the cost of system-‐wide or local op5mality

Manufacturer’s incen.ves: overproduc.on Side-‐agreements to preserve manufacturer’s profit

…showcasing the importance of individual incen7ves in implemen7ng SC reform

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“Rela7onal contracts” (Masten and Crocker 1985, 1991) arises a class of mechanisms to coordinate the disparity of the order and the es7mate…

Source: Tsay 1999

•  Described in the contrac5ng literature of law and economics

•  Acknowledges that informa5on changes over 5me

•  A control structure that preserves the ability to act on new informa5on can be advantageous

•  Formally establishes the rela5onship •  Defers precise decisions on price, quan5ty, and other aspects of the exchange

Background Characteris.cs

…examples of papers that model variants of this rela7onship can be segmented into two general categories: those focused on the buyer’s decision and those focused on both par7es

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Examples of papers describing single-‐node models for “rela7onal contracts”

Source: Tsay 1999

Author(s) Year(s) General Idea

Bassok and Anupidini 1995 Buyer forecasts month-‐by-‐month for a year then revises within speciKied percentage bounds

Anupidini 1997a When cumulative multi-‐period purchases must exceed an speciKied quantity (a form of minimum-‐purchase agreement)

Bassok and Anupidini 1997b Rolling-‐horizon :lexibility contract, similar to the QF structure, for a retailer facing independent and stationary market demand

Eppen and Iyer 1997 Backup agreements: buyer is allowed a quantity in excess of its forecast at no premium, but pays a penalty for any of these units not purchased

Fisher and Raman 1996

Two-‐stage production: initial run covers 20% of the selling season, whose sales inform a second run that covers the rest of the season. An exogenous constraint on second-‐run capacity forces some production to the riskier early commitment.

These allow considera7ons of complex sebngs by focus on only one party, but ignores the supplier’s preferences

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Examples of papers describing two-‐party models for “rela7onal contracts” (most are variants of the newsvendor model)

Source: Tsay 1999

Author(s) Year(s) General Idea

Pasternack 1985

Determines that coordination can be achieved full return at partial refund. The manufacturer can determine the efKicient prices without knowing the market demand distribution . However, requires common information.

Kandel Ha Emmons and Gilbert

1996 1997 1998

Full return at partial refund with price-‐sensitive demand

Donohue 1998

EfKiciency with three-‐prices in a two-‐stage decision model: (1) Kirst commitment on price and quantity; (2) Bayesian update with observed demand before additional order (for a different price). Buyback at a third price.

QF contracts differ from these as it provides flexibility with no explicit penalty for exercise, but uses constraints as a way to mo7vate appropriate behavior.

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The author also evaluate a number of other papers describing buyer-‐suppliers rela7onships in which flexibility plays some role…

Source: Tsay 1999

…and Tsay posi7ons the study on the mechanism of incen7ves and parameters that drive the QF contract, enabling comparison with other SC coordina7on methods

Other examples: •  Parlar and Weng (1997) model independent supply and manufacturing departments under a nonlinear internal transfer pricing arrangement. However, no specific coordina5on mechanism is proposed or evaluated

•  Barnes-‐Schuster et al. (1998) discuss op7ons for supplier capacity as a means of affec5ng flexibility for the buyer

•  Tsay and Lovejoy (1999) examine the QF contract in a mul7-‐period, rolling horizon context. But no op5mal benchmark is available

•  Weng (1997) considers a manufacturer-‐distributor supply chain facing price-‐sensi7ve stochas7c demand. Excess demand is sa5sfied via a second, more costly produc5on run

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Contents

1.  Research ques5on 2.  Relevant literature 3.   Assump7ons 4.  Model 5.  Numerical analysis 6.  Conclusions and discussion 7.  Personal opinion

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Cost’s structure and assump7ons are common knowledge, in a modified newsvendor model

Source: Tsay 1999

•  Cost parameter values are common knowledge and all are exogenous to the model, except c

•  Salvage value is the same to both par5es

Cost structure, per unit Assump.ons

lossgoodwillsvaluesalvageu

tproductionmpricetransferwholesalec

priceretailp

cos /

=

=

=

=

=

p > c > m > 0u < ms ≥ 0

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Chronology of events, nota7on, and informa7on structure are as follows

Source: Tsay 1999

1.  The terms of the supply contract are nego5ated

2.  The retailer states qj 3.  The EM builds Qj, thus determining πEM,j

and πR,j

Note: all decisions up to this point are based on the prior X

4.  μ is observed 5.  The retailer places rj, based on the updated

informa5on X|μ. This is the amount of material available to meet market demand. Any EM surplus is salvaged

6.  Market demand X is revealed, and is filled to the extent possible by the retailer’s stock. Any retailer surplus is salvaged

Decision flow Nota.on

qj = initial purchase order forecastQj = quantity produced by the EMπ EM , j and π R, j = expected profitsX = distribution of market demandµ = signal about market demandrj = retailer 's firm order

Note: Subscripting identiKies the control scheme being considered: j takes values CC, NC, and QF, to denote control by a central planner, a no-‐commitment arrangement, and the QF contract, respectively

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Ra7onality assump7on: both par7es are ra7onal, risk neutral, and an7cipates the op7mal counterpart’s behavior, by backward induc7on…

Source: Tsay 1999

1.   Retailer’s actual purchase is made aher q has been stated, Q has been produced, and μ has been observed. qj has no impact here. G(r|μ) represents retailer’s expected profits at this point

2.   The EM commits to produc7on prior to the forecast update. πEM,j an7cipates the possible outcomes of μ and the retailer’s adjustment

3.   The retailer states qj with knowledge of the EM’s subsequent produc7on response (from 2) and its own purchasing policy (from 1)

rj*(qj,Qj,µ) ≡

argmaxr

s.t.G(r |µ)r ≤Qj

r due to the arrangement

tarrangementhetodueQQqrqQ

tsqQ

j

jjjjjEMQjj

)),,(,,;(

..argmax

)(*

,* µπ≡

qj* ≡ argmaxq{π R, j (rj

*(qj,Qj*(q),µ))}

…so the retailer (the first-‐mover) an7cipates the game outcomes and manipulates its ini7al forecast

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Demand assump7on: EM must commit at a par7cular 7me, no maaer when the retailer’s order becomes firm

Source: Tsay 1999

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Contents

1.  Research ques5on 2.  Relevant literature 3.  Assump5ons 4.   Model

•  Central control (CC) •  Decentralized control with no commitment (NC) and asymmetric informa7on •  Decentralized control with no commitment (NC) and common knowledge •  The quan7ty flexibility (QF) contract •  The efficient quan7ty flexibility (QF) contract

5.  Numerical analysis 6.  Conclusions and discussion 7.  Personal opinion

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Contents




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A centrally-‐controlled SC provides an efficiency benchmark by applying the standard newsvendor problem…

Source: Tsay 1999

… and since there is no intermediate transfer, q, rj ,and c play no role here

Central control •  Manufacture and retail are coordinated by a single firm •  Delivers the greatest possible expected system profit •  Unique op5mal produc5on quan5ty •  Standard newsvendor problem:

Underage cost (p+s-‐m) Overage cost (m-‐u)

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Contents




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NC, with asymmetric informa7on, leads to a game of specula7ons in which the outcome is subop7mal

Source: Tsay 1999

•  EM does not share the retailer’s visibility of the market demand

•  Retailer provides a forecast of intended purchase

•  EM is leh with its own beliefs about the retailer’s purchasing behavior Λq( ), influenced by the forecast

•  Retailer buys in order to:

•  EM produces:

•  A retailer devoid of economic consequences will state large forecasts to induce overproduc5on and postpone decisions

•  A careful EM will an5cipate this, but must s5ll ascertain how to best deflate the exaggerated numbers

•  Retailer has incen5ves to bias Λq( ) by exaggera5ng qNC

•  Λq( ) is low quality, since EM is not privy to retailer’s informa5on

•  EM posi7ons to retailer’s behavior, based on its cri7cal frac7le, as opposed to the system as a whole

•  Different cri7cal frac7les to the EM, retailes, and the system as a whole leads to different op7mal quan77es

NC, asymmetric informa.on Causes of inefficiency

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Contents




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NC, with common knowledge, leads to subop7mal expected profits as well, due to asymmetric incen7ves (i.e. cri7cal frac7les)

Source: Tsay 1999

NC, common knowledge •  Common beliefs on market demand •  Retailer provides a forecast of intended purchase •  Since the forecast does not imply firm commitment, it does not affect demands to EM •  EM solves a newsvendor, as before, only improving the demand parameter

•  Profit alloca5on can be determined by c •  Cri7cal are s7ll divergent among EM, retailer, and the system as a whole

Proposition 1. If the forecast of the retailer’s purchase represent no commitment for either party, then for any c, underproduction occurs relative to the optimal centralized solution (i.e. Q*NC < Q*CC ). Therefore,

expected total system proKit is strictly suboptimal

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Contents




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QF contract {c,(α, ω)}: retailer, for a price c, has purchase flexibility of a certain percentage above and below a previously established forecast

Source: Tsay 1999

The quan7ty flexibility (QF) contract •  Retailer must purchase at least qQF(1+ ω), ω ϵ [0, 1] •  EM guarantees product availability of up to qQF(1+ α), α ϵ [-‐ω, ∞] •  Retailer’s purchase:

•  EM’s produc5on: •  Equilibrium:

Proposition 2. Under the terms of a QF contract, when qQF > 0, the EM produces exactly qQF(1 +α ). If qQF = 0, for any given c the EM will prefer

the NC arrangement.

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The equilibrium solu7on for the retailer’s forecast considers equality of expected cost and benefit for increasing the forecast

Source: Tsay 1999

Proposition 3. Properties of the equilibrium solution when ω < 1: (a) q*QF is strictly positive and Kinite, and may be obtained as the unique

solution to:

•  Retailer’s expected marginal benefit for increasing the forecast

•  G’(q(1+α)|μ)) Retailer’s marginal benefit on product availability

•  Integral takes the expecta5on for all scenarios in which add. unit is desired but not obtained

•  (1+α) mul7plier: unit increase in q affects addi5onal product availability

•  Retailer’s expected marginal cost for increasing the forecast

•  Cost is imposed by the minimum purchase implica5on

LHS RHS

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For the system as a whole, the flexibility parameters (α, ω) can be simplified by a net amount of flexibility (ψ)

Source: Tsay 1999

Proposition 3. Properties of the equilibrium solution when ω < 1:

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Tsay also describes the dynamics of the supply rela7onship for the retailer and the EM with respect to the parameters of the QF contract...

Source: Tsay 1999

Proposition 3. Properties of the equilibrium solution when ω < 1: (c) Comparative statics

q*QF Q*QF π*R,QF π*EM,QF

↑c -‐ -‐ -‐ + or -‐ ↑ω + + + + or -‐ ↑α + or -‐ + + + or -‐

Dynamics of the supply rela7onship •  Higher c means retailer’s higher overage and lower underage cost, decreasing op5mal forecast •  Higher ω means relaxa7on of the minimum purchase, so increasing the forecast makes retailer worse-‐off when demand are low, but beuer-‐off when demand is high (upside availability)

•  Increase in α is undetermined as retailer has incen5ves to decrease forecast (lower minimum purchase) and also to increase (mul5plica5ve effect)

•  EM’s profits are undetermined because its demand is sen55ve to both price and flexibility, since both influence the retailer’s purchase

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...and provides two scenarios as examples that the QF contracts are not necessarily efficient

Source: Tsay 1999

Proposition 4. Properties of extreme forms of the QF contract, for any transfer price c:

(a)  If the retailer is not bound to any minimum purchase commitment (ω=1, or

ψ=∞), overproduction occurs relative to the central-‐control case

(b)  If the retailer must purchase the full amout forecast ((α,ω)=(0,0), or ψ=1), underproduction occurs relative to the central-‐control case

In both cased, total system proKit is strictly suboptimal

•  An upside promise with no minimum purchase commitment

•  Presumably the retailer would prefer this arrangement

•  Without the upside commitment this would revert to the NC case

•  Problem: lack or retailer’s accountability for the forecast

•  Requires the retailer to accept exactly what it forecasts

•  Likely to be preferable to the EM •  Problem: double marginaliza7on

Proposi.on 4.a Proposi.on 4.b

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Contents




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As retailers pay more for flexibility, there exists an unique net flexibility solu7on that coordinates the supply rela7onship in a QF contract ...

Source: Tsay 1999

Assumed condi7ons for system efficiency: i.  Q*

CC must be resident in the model, and ii.  It must be fully accessible to the end customer when market demand occurs

Proposition 5. for any c ϵ (m, p + s):

(a) There exists and unique ψ such that Q*QF(c, ψ) = Q*CC (b) Among such combinations, greater Klexibility (ψ) is associated with a

higher transfer price

… however, there is not a closed-‐form general characteriza7on for the op7mal c, ψ...

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...Yet, under a simplifying assump7on, the solu7on for (c, ψ) can be established

Source: Tsay 1999

•  To preserve efficiency, any increase in α, which encourages lower q*EF, must be couteracted by reducing ω, which commits the retailer to a larger por5on of the q*EF

•  When transfer price is simultaneously adjusted to restore the system’s efficiency, it turns out that the EM ends up claiming more of the system profits

Proposition 6. for the demand model in which σϵ=0:

(a)  System efKiciency will result from a QF contract with total Klexibility ψ ≣(1+α)/(1-‐ω) when the transfer price is

(b)  Any split of the expected profits can be achieved with some efficient QF contract (c)  Among these contracts, increasing the flexibility shiNs profit to the EM

Reitera7on note: even with the necessary condi7on demand’s common beliefs, inefficiencies can result if the individual incen7ves are not aligned!

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Contents

1.  Research ques5on 2.  Relevant literature 3.  Assump5ons 4.  Model 5.   Numerical analysis 6.  Conclusions and discussion 7.  Personal opinion

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Numerical analysis setup

Source: Tsay 1999

•  Simplified model σϵ=0 •  Market demand X is uniform •  Unless stated otherwise {p=15, c=10, m=6, u=3, s=0} •  Demand parameters {m=100 δ=100) and α=0 in all QF contracts

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Juxtaposi7on of control methods depicts the alloca7on of expected profit and how the total compares to what central control could achieve

Source: Tsay 1999

•  NC is inefficient because of underproduc5on

•  Allowing complete cancela5on results in overforecas5ng

•  QF with no flexibility is not the solu5on, although is good for the EM

Comparison of control methods Comments

In the efficient contract, the retailer accepts a 55% purchase commitment in exchange of a price reduc7on of ~7%

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Sensi7vity of the flexibility parameter indicates that retailer profit increases with ω

Source: Tsay 1999

Expected profit and produc.on vs flexibility (c=10) Comments

•  Since α=0, this is only specified by ω

•  LeN-‐to-‐right progression provides the transi5on from full purchase commitment to full cancela5on privileges

This makes concrete the value of the flexibility to a buyer and therefore the willingness to pay for it

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Sensi7vity of the transfer price parameter confirms that while retail profit is always decreasing in c, EM’s profit increases, then decreases...

Source: Tsay 1999

Expected profit and produc.on vs transfer price ((α,ω)=(0, 0.2)) Comments

•  The leN extreme has EM pricing at cost (c=m). This imparts on the retailer the cost structure of the whole channel

•  For the given flexibility parameters, efficiency occurs at p=7.1

…corrobora7ng to the illustra7on of the general tension in the contract nego7a7on due to the duality between pricing and constraints

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An illustra7on on how profits are allocated when the set of efficient contracts is arrayed by ω

Source: Tsay 1999

Expected profit and flexibility in an efficient QF contract Comments

•  Whenever the retailer receives more flexibility, the efficient c also increases to offset any profit gains

Any profit alloca7on is possible

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Along the QF efficient fron7er, there is a Pareto improvement region, where no party can be worse-‐off, compared to NC

Source: Tsay 1999

The QF efficient fron.er and Pareto improvement Comments

•  At L, which is the lowest efficient c, the retailer reaps all gains and the EM is indifferent; the reverse is true at H

•  All these combina5ons represent the retailer’s willingness to accept greater inventory for a price reduc5on

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Efficient QF contracts are dependent on the distribu7on of the demand

Source: Tsay 1999

Expected profit and efficient transfer price vs. demand variability (ω=0.2) Comments

•  As σX increases the efficient c decreases. This is because the retailer finds the installed flexibility to be decreasingly meaningful in the task of matching the market demand

•  A reduc5on in transfer price counteracts this effect, while shiNing profit to the retailer (since the flexibility is unaltered)

Contracts needs to be renego7ated whenever beliefs about demand change

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Contents

1.  Research ques5on 2.  Relevant literature 3.  Assump5ons 4.  Model 5.  Numerical analysis 6.   Conclusions and discussion 7.  Personal opinion

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QF contract takes its place among solu7ons for divergences on inventory ownership and the commitment implied by a forecast

Source: Tsay 1999

Key insights

•  In a decentralized supply rela5onship in which the customer’s forecast does not imply commitment, inefficiency will result in the absence of addi5onal structure

•  Behaviors such as overforecas5ng and decisions based on the local perspec5ve are natural consequences of decentralized control

•  These problems can be at least par5ally remedied by the QF contract, in which the retailer commits to a minimum purchase and the EM guarantees a maximum coverage

•  QF, by itself, does not guarantee efficiency. The correct parameters must be stablished

•  Trade-‐off between flexibility and price: customer commits to minimum purchase in exchange of price reduc5on and supplier offers that price break in exchange for more predictable sales

•  Naturally, the retailer pushes for lower price and greater flexibility

•  The economics of the model indicates that some5mes the EM can concede a more aarac7ve price, when demand is price-‐sensi7ve

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However, the QF contract relies on common beliefs about the demand, which are difficult to achieve

Source: Tsay 1999

Most significant limita7ons

•  The results of the research can only demonstrate efficiency under shared beliefs about the demand

•  These common beliefs are difficult to achieve, even with informa5on sharing systems

•  The issues of coordina5on under informa5on asymmetry remains unresolved

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The concept of QF contracts is simple and has a qualita7ve appeal with coopera7ve flavor

Source: Tsay 1999

Managerial implica7ons

•  QF may be useful when the EM relies heavily on the retailer for guidance about market condi5ons

•  The concept is simple and has a coopera7ve flavor in that each party accepts some of the inventory and stock out burden

•  QF has a qualita7ve appeal in the sense that a single-‐price structure is more poli5cally palatable

•  The single-‐rate pricing reflects a philosophical view of many companies in turbulent demand environments

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The concept of QF contracts is a candidate to extension to supply chains with many players

Source: Tsay 1999

Possible extensions

•  As QF contracts may be effec5ve at mi5ga5ng the retailer’s gaming by auaching economic accountability to the forecasts, it seems to extend naturally to supply chains with more than two players deep, as each link represents another opportunity for informa5on distor5on

•  Coordina5on under informa5on asymmetry

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Contents

1.  Research ques5on 2.  Relevant literature 3.  Assump5ons 4.  Model 5.  Numerical analysis 6.  Conclusions and discussion 7.   Personal opinion

Page - 49 -

Personal opinion

Source: personal opinion

•  Nice concept, simple, and can be useful

•  Paper explains the dynamics of the QF contract parameters

•  Incen5ves and behavior are elegantly clarified

•  Condi5ons for efficiency are described

•  Mo5vates further inves5ga5on

•  A very influen5al paper on QF contracts (the most relevant according to Google Scholar, with 897 cita5ons)

However…

•  Relies on strong assump5ons:

•  Common beliefs about market demand (difficult to achieve)

•  Closed-‐form solu5on with σϵ=0 (not generally observed in the real world)

•  Does not fully explains how to translate it into prac5cal terms

Business

The Quantity Flexibility Contract and Supplier-Customer Incentives