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1、Auctioning supply contracts with uncertain demandCuihong LiGraduate School of Industrial AdministrationCarnegie Mellon University5000 Forbes AvenuePittsburgh,PA 15213cuihongandrew.cmu.eduAnupriya AnkolekarSchool of Computer ScienceCarnegie Mellon Univerity5000 Forbes AvenuePittsburgh,PA 15213anupriy
2、acs.cmu.eduAlan Scheller-WolfGraduate School of Industrial AdministrationCarnegie Mellon University5000 Forbes Avenueawolfandrew.cmu.eduKatia SycaraRobotics InstituteCarnegie Mellon University5000 Forbes AvenuePittsburgh,PA 15213katiacs.cmu.eduAbstractDesign of the contract form,together with the ne
3、gotiation mechanism and strategy,comprise the core decisions in an e-contracting process.In a business-to-business scenarioa buyer(e.g.,a retailer)usually needs to sign a contract with a supplier(e.g.,a man-ufacturer)to satisfy a demand that is uncertain at the time of contracting.The buyerwould lik
4、e to have ordering flexibility to respond to the uncertain demand realization.But the supply that can be provided may be constrained by the capacity investmentof the supplier,which has to be made in advance.The capacity of a supplier may ei-ther be observable and hence contractable,or unobservable a
5、nd hence not enforcable bya contract.We propose two contract forms,an option contract for the situation withobservable capacity,and a wholesale price contract with a franchise fee(WF)for thesituation with unobservable capacity.In both contracts the buyer places her final orderafter the demand is kno
6、wn.In an option contract the buyer first pays a premium fee forreserving a certain capacity from the supplier in advance,and then an exercise fee foreach unit that is ordered.In a WF contract the supplier charges a wholesale price foreach unit ordered by the buyer,but pays a fixed franchise fee to t
7、he buyer.We presentoptimal auction mechanisms in different protocols for the buyer to negotiate an optioncontract or a WF contract with competing suppliers.Both contracts generate higher util-ity for the buyer than the contract in which the buyer procures in advance.Our resultsshow that the optimal
8、auctions for these two contracts have the same outcome.We alsodiscuss the implementation of e-contracting based on our contract auction mechanismswith software agent technologies.11IntroductionThe rapid development of computer and communication technologies has accelerated thebusiness processes from
9、 labor services to electronic(semi-)automated processes 13.Con-tracting is one of the important business processes that has recently received much attentionin this trend toward electronic transactions.E-contracting aims to automate the process ofcreating,negotiating,closing and monitoring the perfor
10、mance of contracts 2.The properdesign of the contract,and the negotiation mechanism and strategy,depends on the specificbusiness situation,and is the core of the decisions in the e-contracting process.Contracting in a business-to-consumer(B2C)and in a business-to-business(B2B)scenarioare different.I
11、n a B2C scenario,for example of the auctions on eBay,the items to exchangeare predefined in the quantity and other attributes.A contract usually only needs to specifya one-shot exchange condition,for example,the price.A standard contract form can thusexist,and the negotiation is simple,because there
12、 are few attributes,usually only the price,to negotiate.But in a business-to-business(B2B)world the contracting parties are usuallyinvolved in a relationship over an extended horizon.The service/good to negotiate andcontract may be configurable,and hence the contract can be highly unstructured and i
13、nvolvemany attributes,such as the price,delivery time,quantity,etc.This negotiation is morecomplicated than in a B2C scenario because multiple attributes are involved,and sometimeseven the contract form can be an object of negotiation.Moreover,the goal of B2B contractingis not only to ensure a prope
14、r division of profits,but also to create more profit,by coordinatingand enforcing the behaviors of both parties.Design of the contract form and negotiationmechanism is thus especially important in a B2B scenario,to achieve coordination and anefficient win-win situation for both parties.Consider a bu
15、yer(retailer)that wants to sign a contract with a supplier(manufacturer)tosatisfy the demand in a coming selling season.The buyer may not know the exact demandin the season when she signs the contract,as she has to contract with a supplier well inadvance so that the latter party can prepare,for exam
16、ple,by procuring components andraw materials from her upstream supplier.This capacity set-up may require long lead time,leaving no opportunity for the supplier to expand the capacity during the season:the capacityinvestment of the supplier constrains the supply.But while the supplier does not want t
17、owaste money on excess capacity,the buyer does not want capacity shortages.To ensure a gooddemand satisfaction level the buyer thus has to provide incentives for the supplier to investin sufficient capacity.There are different ways to provide this incentive.One straightforwardway is for the buyer to
18、 fix the quantity that she is going to buy.This is equivalent to makingadvanced procurement,leaving no ordering flexibility to counter the demand uncertainty.Another way to provide incentives for capacity investment,while retaining ordering flexibility,is to complete the procurement in two stages.In
19、 the first stage the buyer reserves capacityand in the second stage the buyer purchases the product based on the realized demand.Thisprocess can be regulated by an option contract.With an option contract the buyer paysthe supplier a premium fee for the right to buy a certain amount of the product.Af
20、ter the2demand is observed,the buyer can place orders for the product in an amount up to the numberof options,paying an exercise fee for each unit that is ordered.An option contract allowsrisk sharing,and hence induces better coordination,creating a win-win situation between theparties.The buyer wil
21、l order more on average than she would under a contract in which shehas to perform all the procurement before the demand is known,and the supplier will investmore in capacity than she would without contracting upon capacity reservation.With an option contract the buyer must be able to observe and ve
22、rify the capacity preparedby the supplier.If the capacity is not observable,the capacity reservation cannot regulate thecapacity investment of the supplier.In this situation the incentive for capacity investmentonly relies on the exercise fee,which is equivalent to a wholesale price.In this case pay
23、ing apremium fee makes no sense,instead a franchise fee,paid by the supplier,that is independentof the ordered quantity can ensure better profit distribution between the two parties.Wecall this contract a wholesale price contract with a franchise fee(WF).Typically a buyer does not know the efficienc
24、y,or the production cost,of a supplier.Whenseveral suppliers are possible candidates to provide the product,competitive bidding is anefficient mechanism for the buyer to discover the most competent supplier and negotiate acontract.This may take place in a multi-attribute auction that involves all th
25、e negotiableterms in the contract,for example the premium fee,exercise fee and capacity in an optioncontract,and the wholesale price and the franchise fee in a WF contract.There are twomain classes of protocols for such multi-attribute auctions:The first class is auctions with amenu of contracts,and
26、 the second class is auctions with a scoring rule.In the first class theauctioneer,the buyer,announces a set of contract along with the preference order between thecontracts.The suppliers bid by choosing a contract,and the one who bids the highest rankedcontract is the winner.In the second class the
27、 auctioneer announces a scoring function.Thesuppliers bid by submitting contracts,and the winner is decided by the scoring rule.In this paper we present optimal auction mechanisms in different protocols for both an optioncontract and a WF contract,when the cost of a supplier is unknown to the buyer.
28、We alsodiscuss the implementation and automation of the contract auction mechanisms with softwareagent technologies.Although one would expect the buyer to lose certain advantages whena suppliers capacity is unobservable,surprisingly we show that by appropriately designingthe contract form and auctio
29、n mechanism,the buyer can actually achieve the same optimalexpected utility with unobservable capacity as with observable capacity.In both situations,the ordering flexibility in an option contract or a WF contract results in higher utility forthe buyer than pre-specifying a fixed ordering quantity.T
30、he rest of the paper is organized as follows:We review the related work in Section 2.Section 3 sets up the problem,and provides the framework for auction mechanism design.We present the optimal auction mechanisms for an option contract in Section 4,and for a WFcontract in Section 5.The implementatio
31、n and automation of the supply contract auctionswith software agents is discussed in Section 6.32Related workIn supply chain management design of contracts has been an active subject aimed at reconcil-ing conflicts and achieve better coordination between parties:3 provides a good introductionand sur
32、vey on this work.It provides the analysis of the optimal option contract and wholesaleprice contract(without a franchise fee)between a buyer and a supplier when the demandforecast is private information of the buyer,but the cost of the supplier is known by thebuyer.The wholesale price contract resul
33、ts in less profit for the buyer when capacity is un-observable,as compared to the option contract when capacity is observable.In our paperwe study auctions for supply contracts when there are multiple competing suppliers and thecosts of suppliers are unknown.The wholesale price contract,by introduci
34、ng a franchise fee,actually results in the same optimal outcome as an option contract.Another related work,7,investigates the role of options in a buyer-supplier system,illustrating how they provideflexibility and achieve channel coordination.That work is based on complete information-each party kno
35、ws the others cost or revenue.Auctions have been considered in procurement to discover the most competent supplier,thuscutting cost.The auction mechanism for a buyer to procure from one of multiple competingsuppliers is studied in 6 and 5.The item to auction is a supply contract with two attributes:
36、the product quantity and payment.In our paper we study the auction design for a supplycontract in which the ordering quantity is not specified but determined afterwards,basedon the realized demand.Under such demand uncertainty the buyer achieves higher profitwith an option contract or a WF contract
37、than in a contract with a pre-specified quantity.Indirect multi-attribute auction mechanisms are studied in 4,which proposes a scoring rulebased on which first-score and second-score sealed-bid auctions implement the optimal auctionmechanism.The two attributes in this paper are the price and quality
38、(which can also beinterpreted as the quantity).The design of the scoring rule in our paper is inspired by 4,but our auctions are based on different contracts,using an English auction protocol.Englishauction design for multi-attribute items is considered in 9,8,10.The utility function of thebuyer and
39、 the scoring rule are both linear functions of the attributes.Based on this linearfunctional form the optimal weights of the attributes in the scoring rule are proposed,andthe strategies of the bidders are analyzed.The mechanism is only optimal among Englishauctions with linear scoring functions,not
40、 with general scoring functions as we allow.In recent years there has been growing research interest in designing and implementing au-tomated electronic trading systems with software agents.The Trading Agent Competition(TAC)in Supply Chain Management 1 promotes and encourages the development of inte
41、lli-gent software agents capable of buying or selling products/materials on behalf of a company.The competition is based on a B2B situation,and the internal operations of the companiesare integrated into bidding decisions 17.These exchanges are based on a one-shot rela-tionship:the contracts specify
42、 the ordering quantities and leave no purchasing flexibility tocounter demand uncertainty.Finally,20 studies auction mechanism design for supply chainformation to achieve global efficiency.Again the auctions are based on known demand.43Definition of the modelIn this section we shall first describe t
43、he notations and the problem setting,then introducethe auction mechanism design framework.The buyer has uncertain demand d of a productwith probability distribution and density functions G(d)and g(d).DefineH()=1 H()for a general probability distribution function H().The buyer sources the product fro
44、m asupplier with a supply contract.The lead-time for production is zero.But before production(and after contracting)the supplier has to invest in capacity,which constrains the amountof supply.When the capacity is x,the expected satisfied demand is S(x),where S(x)=Exmind,x=x E(x d)+with the derivativ
45、e S0(x)=G(x).The buyer sells the product to consumers at a fixed market price r that is exogenouslygiven.There are n suppliers who compete for the supply contract.Each suppliers costfunction is composed of two parts:the capacity investment cost and the production cost.For each unit of capacity,which
46、 produces one product,the cost k is fixed and identicalfor all suppliers.The cost is known by the buyer and the suppliers.The unit productioncost c c,c depends on a suppliers efficiency and is private information of the supplier.Following the tradition in economics the unit production cost is also c
47、alled the type of asupplier.Within the prior knowledge of the buyer,the production cost of each supplierfollows an independent and identical probability distribution F(c),with the density functionf(c).The probability density of the minimum type among the n suppliers is denoted byf(1)(c)=n(1 F(c)n1f(
48、c).We assume that F(c)/f(c)is a non-decreasing function of c1.Let J(c)=c+F(c)/f(c):J(c)is called the virtual type of a supplier.In addition we assumethat the revenue r is big enough so that r J(c)k.2Generally an auction mechanism(B,)has the following components:a set of possiblemessages(or“bids”)Bif
49、or each bidder i that specifies the bidding rule;a winner determi-nation rule(or“allocation rule”):B P that determines the probability Pithat a bidderi will win a contract,based on the messages b submitted by all bidders;a contracting rule specifies,again as a function of all the messages b,the cont
50、ract i(b)T that will beawarded to each bidder i 12.An optimal auction mechanism is an auction mechanism thatbrings the best expected utility to the buyer among all auction mechanisms.A mechanism isindividually rational(IR)if the expected utility of a player in this mechanism is non-negative.IR is a