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Designing Supply Contracts: Contract Type and Information Asymmetry Authors: C. Corbett, C. S. Tang Presenter: T.J. Hu

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Contents Introduction Literature Model Supplier's Optimal Supply Contracts Comparisons Numerical Examples Conclusions Future Research

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Introduction

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The Supply Chain Supplier Buyer L(q)L(q)w(q)w(q) p(q)p(q) s cost c C ~ F()

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Supplier's Concerns: The types of contracts Information about the buyer's cost structure

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Three Types of Contracts 1. One-part linear contract: w 2. Two-part linear contract: w, L 3. Two-part nonlinear contract: {w(q), L(q)}

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Six Scenarios

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Questions to Answer: What should supplier do when faced with decreased buyer demand? Value of information about the buyers cost structure Value of more sophisticated contracts Which of the above two is more valuable? When there is no double marginalization?

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Literature 1. Supply Chain Management 2. Economics

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Supply Chain Literature Deriving optimal ordering policies in the context of a given contract Deriving optimal contract parameters given the functional form of that contract Coordination within supply chains, the value of information and various alternative contracting schemes

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Selected Papers Lee, So, and Tang (1998) –Quantify the value of sharing demand information –Demand follows an AR(1) process Bourland, Powell and Pyke (1996), Cachon and Fisher (1997), Gavirneri, Kapuscinski and Tayur (1996) –Benefits of information sharing when demand is i.i.d. Lee and Whang (1996) –Incentive scheme for a multi-echelon supply chain (central planner, but each echelon uses local information only) Corbett (1996, 1998) –Asymmetric information leads to suboptimal outcomes (without central planner)

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Selected Papers (Cont d ) Weng (1995) –Quantifies the value of channel coordination –Quantity discounts alone are not sufficient to achieve coordination Corbett and de Groote (1997) –Compares various coordination schemes for a 2-level SC –Preferences ordering of these schemes for the supplier, buyer and vertically-integrated firm This paper –Quantifying the value of information and the value of more complex contracts

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Economics Literature Vertical contracting –Two successive monopolists –Double marginalization Topics –Comparing total surplus under various schemes –Contract to mitigate the double marginalization issue

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Selected Papers Tirole (1988) : The Theory of Industrial Organization F. Machlup and M. Taber (1960) –Bilateral monopoly, successive monopoly, and vertical integration, Economica, May (1960), 101-119. Gal-Or (1991a,b) –In general, neither franchise fees nor retail price maintenance can achieve the integrated solution under asymmetric info –Equilibrium sometimes achieved with linear pricing and franchise fee contract (two supplier) Bresnahan and Reiss (1985) –Study the ratio of the profit margins under simple wholesale price with full information –How the ratio depends on the convexity of demand function

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Contribution of This Paper Combine two strands of theory –building on the basic bilateral monopoly framework offered in economics –asking the normative and more micro- level questions more typical of supply chain literature –measure the cost of sub-optimality (quantification and insights of the differences between the cases)

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The Model

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The Supply Chain Supplier Buyer L(q)L(q)w(q)w(q) p(q)p(q) s cost c

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Assumptions One supplier and one buyer One product One period contract Deterministic demand Linear price-demand curve q = a - bp a - b (s+ ) 0 F(c)/f (c) is increasing in c

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F/f for Normal Distribution

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Suppliers Problem ( S ) Buyers individual rationality constraint Buyers individual rationality constraint Buyers incentive compatibility constraint Buyers incentive compatibility constraint

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Sequence of Events Supplier offers one of the three types of contracts Buyer (with c) selects the order quantity q or (w(q), L(q)) All sales and financial transactions take place simultaneously

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Revelation Principle ( A3 ) Reformulating the contracts in terms of c, i.e. optimizing over {w(c), L(c)} There is an optimal contract under which the buyer will reveal truthfully.

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Suppliers Optimal Supply Contracts 1. Buyers problems 2. Suppliers problems

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Buyers Problem ( B 1, B 2 ) In B 1, set L=0 In B 2, to buyer, L is independent of q

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Solutions for B 1, B 2

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Comments on the Solutions

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Buyers Problem ( B 3 )

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Solution for B 3 Revelation Principle FOC evaluates at c It tells the supplier how to choose w() and L(). SOC holds in the neighborhood of c.

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Suppliers Problems Optimal Contracts Under Complete Information: Case F1, F2, F3

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Contracts with Full Information

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Case F1 ( S F 1 ) Note: The Supplier knows the buyers optimal order quantity q *

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Solution for S F 1

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Profit and Profit Margins Suppliers profit and profit margin are double those of the buyer!

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More on Profit and Margins is a local measure of the curvature of the demand curve Ref. Bresnahan and Reiss (1985)

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Question: Is the buyers individual rationality constraint satisfied? If not satisfied, as we commented before, the buyer wont order and thus both parties profits are zero!

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Case F2 ( S F 2 )

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Observations With complete info about c, supplier can set the rationality constraint to be binding. He then maximizes the joint profits.

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Solution for S F 2

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Comments on Solutions for S F 2

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Interpretation Its optimal for the supplier to set the whole sale price equal to his marginal cost and use the lump sum side payment to extract all profits from the buyer in excess of his reservation profit level.

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Case F3 ( S F 3 ) Superset of F2 F2 is optimal given full info on c: buyer only gets minimum level Value of addition flexibility is 0 results carry over from F2

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Suppliers Problems Optimal Contracts Under Asymmetric Information: Cases A1, A2, A3

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Contracts with Asymmetric Information

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Case A1 ( S A 1 ) Note: The Supplier knows the form of the buyers optimal order quantity q *

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Solution for S A 1

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Profit and Profit Margins Supplier has incentive to induce the buyer to reveal his true cost c. (???) Supplier has incentive to induce the buyer to reveal his true cost c. (???)

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If not satisfied, the buyer wont order. Question: Is the buyers individual rationality constraint satisfied, i.e.

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Case A2 ( S A 2 )

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Observations For any given w, the supplier will always choose the lowest L that still satisfies the buyers rationality constraint. b (c) is decreasing in c necessary and sufficient to set b ( ) = inf c b (c) b -

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Solution for S A 2

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Remarks If =E(c)=c, case A2 reduces to F2. The information asymmetry means the supplier must now offer a larger side payment (or less franchise fee) than in F2, to meet the worst-case buyers min profit requirements. Effectively, need

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Question: When and what if the expected suppliers profit is zero?

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Case A3 ( S A 3 ) Using buyers optimal order quantity q * and FOC from B 3

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Eulers Equation: Necessary Conditions

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Constrained Problems: Lagrangian

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Solution for S A 3 Based on our assumption, the optimal w is increasing in, whereas in earlier cases, it is decreasing in or E[c]. From FOC, L is also increasing in.

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Buyers Tradeoff Accepting a higher lump sum payment and a higher unit whole sale price versus Accepting a lower lump sum payment and a lower unit whole sale price.

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Special Case A3: Uniform Prior

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Special Case A3 (Cont d ) The unit whole sale price can be interpreted as the average of a constant part and a part decreasing in q, illustrating how w decreases with quantity. Compare: p=a/b - q/b

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Comparisons

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The Impact of Buyers Cost on the Suppliers Profit Margin Buyers cost c Buyers profit margin m b Buyer orders less Suppliers profit How should the supplier respond?

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Suppliers Response In case F1, A1, A2: –sacrifices margin for volume In F2 and F3: –insensitive In A3: –sacrifices volume for margin

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Effective Wholesale Price More precisely, one should take the side payment into account and evaluate the effective unit wholesale price as follows:

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The Value of Info to the Supplier The value of information is (significantly) greater when the supplier has the flexibility to offer two- part contracts.

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The Value to the Supplier of Offering Side Payments As demand becomes more price-sensitive, the absolute penalty from using only wholesale price without side payments decreases. The value of contracting flexibility is greater under full information.

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Value of Information v.s. Value of Contracting Flexibility Value of information increases with b, while value of contracting flexibility decreases with b. Therefore, In more price-sensitive environments, supplier should focus more on obtaining info about the buyers costs.

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Value of Info v.s. Value of Contracting Flexibility (Cont d ) F1 F2 A1 A2

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Numerical Examples

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Conclusions

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Conclusions Under full information, a supplier will decrease his wholesale price in reaction to a buyer cost increase, maintaining the volume while sacrificing margin.

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Conclusions (Cont d ) Under asymmetric information, however, the supplier may do the opposite: increase average wholesale price, thus maintaining margin while sacrificing volume.

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Conclusions (Cont dd ) The value to the supplier of obtaining better information about the buyers cost structure increases with the variance of the suppliers prior distribution about that cost parameter and with price-sensitivity of demand.

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Conclusions (Cont ddd ) The value of better information is greater when the supplier can offer two-part contracts rather than only one-part contracts, and The value of being able to offer two- part contracts rather than one-part contracts is decreasing in price- sensitivity b.

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Future Research

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…. In many contracting situations, the supplier starts in case A1: –offering a simple linear wholesale price –with no side payment –without knowing the buyers cost structure

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Questions to Answer: When should the supplier focus on obtaining better information about the buyers cost structure? When should he offer more sophisticated contracts? How would the results change if we introduce stochastic price-sensitive demand? What changes if the the supplier cannot observe the price-sensitivity parameter b?

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Designing Supply Contracts: Contract Type and Information Asymmetry Authors: C. Corbett, C. S. Tang Presenter: T.J. Hu

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