Compound mechanism design in multi-attribute and multi...

Scientia Iranica E (2016) 23(3), 1384{1398

Sharif University of TechnologyScientia Iranica

Transactions E: Industrial Engineeringwww.scientiairanica.com

Compound mechanism design in multi-attribute andmulti-source procurement of electricity coal

C.J. Raoa;c;1;�, J.J. Zhengb, Z. Hua and M. Gohc;d

a. Institute of Systems Engineering, Huazhong University of Science and Technology, Wuhan 430074, P.R. China.b. School of Economic and Management, Wuhan University, Wuhan 430072, P.R. China.c. The Logistics Institute-Asia Paci�c, National University of Singapore, Singapore.d. School of Business IT and Logistics, RMIT University, Australia.

Received 13 September 2014; received in revised form 12 November 2014; accepted 4 August 2015

KEYWORDSElectricity coalprocurement;Multi-attributeand multi-sourceprocurement;Compoundmechanism;Multi-attributeauction;Negotiationmechanism.

Abstract. In this paper, the decision making problem of electricity coal procurementin power industry is investigated and a two-stage compound mechanism based on auctionand negotiation is designed for multi-attribute and multi-source procurement of electricitycoal. In the �rst stage of this compound mechanism, a multi-attribute auction mechanism ofelectricity coal is designed. Concretely, the buyer's utility function and the supplier's utilityfunction are de�ned, and the scoring rules and bidding rules are given. Moreover, aimingat maximizing the buyer's expected utility, an optimization model of selecting winnersin multi-attribute auction of electricity coal is established; then, the suppliers' optimalbidding strategies are discussed and the feasibility of auction mechanism is proved. Basedon the winners' scheme and corresponding pre-allocation results of electricity coal supplyin the auction stage, a negotiation mechanism, which can further improve the allocatione�ciency and optimize the attribute combination, is designed in the second stage of thiscompound mechanism and the bidding e�ciency is calculated by using the method ofData Envelopment Analysis (DEA) for each winner. Finally, the speci�c implementationsteps are given to show how to apply this two-stage compound mechanism in the actualprocurement of electricity coal.© 2016 Sharif University of Technology. All rights reserved.

1. Introduction

Electric power industry is an important part of the en-ergy industry and it is one of the most important basicindustries to support and promote the development ofsocial economy. By the limitation of the structure ofenergy resources, coal is the main fuel for electricitypower and the degree of dependence on electricity coalis more than 70% in China and more than 50% in theworld [1,2].

1. Present address: School of Science, Wuhan University ofTechnology, Wuhan 430070, P.R. China.

*. Corresponding author.E-mail address: [email protected] (C.J. Rao)

In thermal power generation, the procurement ofelectricity coal is the basis of electric power production.By implementing e�ective procurement strategies ofelectricity coal, the power generation enterprises willestablish a continuously stable mechanism of fuel sup-ply. It is of great signi�cance to guarantee the safetyin production, reduce costs, increase revenue, andenhance the comprehensive competitiveness of enter-prises. Like the country's basic industries, the electricpower production is continuous production with thecharacteristics of security and stability, which deter-mine that the electricity supply must be sustained,balanced, and stable and the quality of electricitycoal (calori�c value, moisture, ash, volatile matter,ash melting point, and sulfur coal classi�cation) must

C.J. Rao et al./Scientia Iranica, Transactions E: Industrial Engineering 23 (2016) 1384{1398 1385

comply with the requirements of the boiler and reachthe environmental protection standard.

Electricity coal procurement involves a widerange. It not only relates to the coal mine production,but also relates to railway transportation, highwaytransportation, and waterway transportation. In orderto guarantee both quality and quantity to meet thepower requirements of production and to gain moreeconomic bene�ts, the power generation enterprisesmust consider electricity procurement strategy un-der the multi-attribute conditions like price, quality,quantity, supplier's transport capacity, credibility, andso on. In addition, the demand for electricity coalin thermal power generation is great and the powergeneration enterprises need many di�erent kinds ofelectricity coal; therefore, considering quantity andvariety, the supply by a single supplier is limited. Itis often di�cult to meet the needs of buyers within aspeci�ed time. For this reason, the buyer can selectmultiple suppliers to supply the electricity coal at thesame time. Therefore, the electricity coal procurementcan be regarded as a kind of multi-attribute and multi-source procurement.

In the procurement management of electricitycoal, supplier evaluation and selection is a core prob-lem [3]. Scienti�c and rational selection of suppliers cannot only reduce the cost and risk of procurement andimprove the product quality, but also enhance the mar-ket competitiveness of the supply chain. The suppliers'declaration information in the selection of suppliersis a kind of private and asymmetry information inessence. The authenticity of information is di�cultto guarantee; therefore, it may lead to an ine�cientallocation result, and it is di�cult to achieve e�ectiveallocation of electricity coal. Based on this background,in order to reduce the procurement cost, optimizethe procurement channels of coal, and improve theelectricity coal quality, how to design reasonable and ef-fective multi-attribute and multi-source mechanism forelectricity coal procurement is an important researchtopic in the procurement management of electricitycoal.

Electricity coal is a kind of rare resource with thecharacters of continuity, homogeneity, and divisibility(`divisible goods' means that one unit of goods can bedivided into more arbitrary small units; for example,emission rights, stocks, treasury bills, and spectrum areall divisible goods. `Indivisible goods' means that eachunit of goods is independent, e.g. an antique vase, anantique painting, a procurement contract, a �sh, a bot-tle of wine, and so on) and electricity coal procurementis a kind of multi-attribute and multi-source procure-ment; thus, we can reference the thought and methodof multi-attribute auction to design an incentive multi-attribute and multi-source procurement mechanism.In a multi-attribute auction of electricity coal, the

buyer will select the winning suppliers according tothe supplier's bidding and the corresponding methodof winner determining and then give the pre-allocationresults of electricity coal supply in this auction stage.In order to reduce the risk of coal procurement, it isnecessary to make further negotiation with suppliersfor the buyer before signing the procurement contract.Negotiation is an important and inevitable phase ofconsultation. In the negotiation phase, the winnerwill negotiate with buyers about all attribute valuesand then a new protocol will be produced under thecondition that the buyer and suppliers' utilities arenot decreased and the allowed supply quantity for eachwinner is not decreased. Therefore, this new allocationresult can further improve the allocation e�ciency ofprocurement.

Multi-attribute auction theory provides the sup-port for the implementation of valid negotiation inmulti-attribute and multi-source procurement by com-bining the decision analysis tools and auction mech-anism [4-7]. Multi-attribute auction is an auctionmode which considers multiple attributes in the trans-action between buyers and sellers [8-14] and is alsonegotiating in price and other attributes. With therapid development of procurement economy and elec-tronic commerce, especially wide application of onlineprocurement, the research on multi-attribute auctionhas gradually become one of the most active �eldsin auction theory in recent years. There are manysuccessful cases and theoretical results in the researchon multi-attribute auction, but the multi-attributeauction with the characters of continuity, homogeneity,and divisibility has some new problems for furtherresearch in the theory [13,15,16], e.g. the problem ofdetermining the winner, the problem of equilibrium ex-cursion (multiple equilibrium points), and the incentivestrategy design problem of ideal equilibrium.

Multi-attribute auction draws wide attention bythe scholars because of its characteristics of competitivenegotiations and its advantages such as high e�ciencyand time saving. In recent years, the multi-attributeauction has become quite active in the �eld of auctionstudy. Practice has proved that multi-attribute auc-tion is a short-term and e�cient procurement mecha-nism [5,6,11,17,18]. Bichler [4] de�ned multi-attributeauctions as a class of market mechanisms, which enableautomated negotiation on multiple attributes (such asdelivery time, quantity, quality, and credibility) of adeal.

Thiel [14] pioneered the multi-attribute auctiontheory and he was the �rst to discuss the multi-attribute auction in detail. He showed that theproblem of multi-attribute procurement can eventuallybe simpli�ed to a single-attribute and private-valueauction model, and the problem of designing optimalmultidimensional auctions will be equivalent to the

1386 C.J. Rao et al./Scientia Iranica, Transactions E: Industrial Engineering 23 (2016) 1384{1398

design of unidimensional auctions. However, in hispaper, the hypothesis of the bidder's goal to maximizethe utilities of buyers does not meet reality. In additionto Thiel, Che and Branco are also the pioneers in multi-attribute auction research. Che [5] provided a thoroughanalysis of the design of multi-attribute auctions andderived a two-dimensional version of the revenue equiv-alence theorem. Branco [8] extended Che's work. Hisanalysis was based on Che's independent cost modeland derived an optimal auction mechanism for thecase when the bidding �rms' costs were correlated.Unlike Che's independent cost model, the optimalauction mechanism cannot achieve the optimal e�ectthrough the auction process and the buyer must taketwo-stage mechanism. Branco also proved that boththe two-stage �rst price auction and two-stage secondprice auction are the optimal auction mechanisms.The works of Che and Branco were among the �rstconsidering multi-dimensional auctions. But both werestudying auction design only in a context with twoissues, i.e. price and quality. Teich [18] dividedthe multi-attribute into two stages in the relevantliterature, i.e. good attributes and supplier attributes,and pointed out that the combination multi-attributeprocurement had more realistic meaning and he made ita further research direction. David et al. [19] discussedthe three-attribute procurement auction model basedon the background of international logistics market andchose the concrete linear scoring function to determinethe winner.

Later, David et al. [20] continued to extend theirresearch work; they generalized the tender attribute toany numbers and used the quasi linear score functionto determine the winner. This set of studies by Davidet al. followed Che and Branco's research thought andit supposed that the costs of the bidders were indepen-dent from each other. The improvement of their workis that there is no limit to the number of bid attributesand it can be any number. At the same time, the set ofstudies by David et al. introduced the English auctioninto the multi-attribute auction �eld and proposedthe orders of full information disclosure auction andEnglish auction, which enriched the theory of multi-attribute auctions. However, there are also severaldisadvantages for the work of David et al. Firstly,the bidder's choice on quality is independent of price,which does not meet reality. Secondly, the assumptionof cost parameters being independent of each other isunreasonable. Thirdly, from the perspective of buyers,the choice, by which the optimal auction comes downto optimal weighted score function, cannot consider thewhole social welfare. Finally, when choosing winners,David et al. adopt simple weighted score function form.

Considering the insu�ciency in the study ofDavid et al., Jin and Shi [21] presented an increasingbidding multi-attribute auction. The study showed

that this auction mechanism improved the work ofDavid and it could replace the previous ascendingbid multi-attribute auctions. Wang [22] discussed theproblem of N bidders who compete with a franchisedistribution with the bidding consisting of quality andprice and presented the optimal bidding competitionmechanism from the viewpoint of maximizing socialexpectations of welfare. Huang et al. [23] supposedthat the bidding consisted of price and quality andestablished an optimization model of dynamic multi-attribute procurement auction mechanism. Then,Huang et al. [24] discussed the design of a hybridmechanism for e-procurement, which implemented amulti-attribute combinatorial auction followed by abargaining process to achieve desirable procurementtransaction outcomes. Sun and Feng [25] presented amore realistic demand that improved multi-attributeauction model based on the form of simple weightedscore function in the existing multi-attribute auctionmodel. Pla et al. [26] presented a new Vickrey-basedreverse multi-attribute auction mechanism, which tookthe di�erent types of attributes involved in the auctioninto account and allowed the auction customization inorder to suit the auctioneer needs. Wang and Liu [27]proposed a nonlinear scoring rule, which transformedmultiple attributes of a bid into comparable dimension-less ones in practical multi-attribute auctions. Theyfound that as the number of bidders increased, theequilibrium quality improved, whereas the equilibriumprice decreased.

In recent years, scholars have focused on multi-attribute auction theory combined with practice re-search. Perrone et al. [28] designed engineering ser-vices procurement mechanism of new product develop-ment in the automation environment based on multi-attribute auction theory and used numerical experi-ments to simulate the purchase process. Strecker [29]studied information superiority of the multi-attributeauction from the viewpoint of auction e�ciency in thetwo aspects of theory and laboratory experiment. Heconcluded that the more the information disclosure,the higher e�ciency the auction had. Karakaya andKoksalan [30] proposed an interactive multi-attributereverse auction method for the single-good auction anddesigned the experiment that veri�ed its feasibilityand rationality. Liu et al. [31] studied multi-attributeprocurement auction mechanism with the supplierunder risk aversion and focused on in-depth study ofthe number of suppliers and risk attitude e�ects on theequilibrium price. Ray et al. [32] conducted web-basedexperiments to validate this theoretical observationin multi-attribute reverse auctions. They comparedincentive oriented and standard multi-attribute reverseauctions and demonstrated that the results in the lab-oratory setting corroborated the theoretical �ndings.In addition, there are some studies carried out on the


bene�cial discussion from the perspective of suppli-ers bidding composite auxiliary decision-making toolsand on realization of the multiple-attribute decisionmaking evaluation software. For example, Jain etal. [33] considered the major internalization methodsin di�erent contexts and proposed the multi-stageauction mechanism analyzing two-way competitions, aBertrand and Cournot competition where prices perunit and per quantity are two underlying parametersin a utility analysis. Yang et al. [34] constructeda linear programming model to infer the preferencemodel(s) of the auctioneer so that the estimationswere as consistent as possible with the given preferencestatements in multi-attribute electronic procurementauctions. Furthermore, they presented a method toselect a representative preference model from the setof compatible ones. These are all the important andvaluable research results in multi-attribute auctions inthe past few years. But the auction goods mentioned inmost of the studies are a single product or indivisiblemultiple goods and the bid winner is only one. Theresearch on the multi-attribute auctions for divisiblegoods, which its aims are the characteristics of homo-geneity and divisibility, is very little.

In recent years, the amount of studies on nego-tiation has been very rich, but most of them considerthe properties and implementation conditions of thebilateral negotiation mechanism from the angle ofeconomics. Many studies on the mechanism designput the possibility of ex-post bargaining as constraintcondition into the prior-mechanism or contract designand then prove robustness of the mechanism afternegotiations. In the literature on bargaining, thereis no research on combination of goods or bargainingfor multiple goods. Most of them concentrate on theprice argument for a single good for the bargainingparties [35,36]; for example, Cramton [36] studiedthe negotiation strategy with time-delay under thecondition of bilateral information asymmetry. It isof great signi�cance for the follow-up study. Wang etal. [37] proposed the concept of Bargaining Track Chartin order to solve the bargaining problems of centralizedprocurement in the environment of e-commerce. ThisBargaining Track Chart recorded the negotiation op-ponent's historical data and provided a reference forthe current negotiation.

On the combination of auction and negotiation,Branco [8] considered a compound mechanism basedon auction and negotiation for the single-good procure-ment under the assumption that all cost functions ofbidders were related. He only analyzed the propertiesof the corresponding optimal mechanism and did notdiscuss the equilibrium in the stages of negotiation orbargaining. Wang [38] also discussed the combinationof auction and negotiation for a single-good procure-ment, but he did not get the equilibrium strategy

because of the complexity of the model. He onlydiscussed the existence and some properties of equi-librium strategies. Subsequently, Huang and Chen [39]investigated a combined auction-bargaining model in asetting where a buyer procured a good/service fromone of the multiple competing sellers with invisiblee�ort. The two-stage procurement model is a sequen-tial mechanism consisting of an auction phase followedby a possible bargaining phase. They also presentedthe criteria according to which the procurer decidedwhether to bargain or keep the contact in auctionstage. Chen and Tseng [40] also designed the mixedprocurement mechanism based on combination of auc-tion and negotiation. A common point of these studiesis that the auction object is a single unit of goods or acombination of multiple di�erent heterogeneous goods.Practice shows that in many transactions of multi-objects, to study the sequential mechanism consistingof an auction phase followed by possible negotiationis very important. This paper just tries to do themechanism design work in this aspect. Later, Kerstenet al. [41] presented a theory of concessions whichcould be applied to both auctions and negotiationsand provided experimental veri�cation of the theory.The theory-based assessment of concession-making inmulti-attribute auctions and multi-issue multi-bilateralnegotiations makes their comparison possible.

In a study on electricity coal procurement, Shiro-maru et al. [42] used fuzzy satisfaction methods to dealwith the fuzzy information on procurement objective ofcoal-�red power generation enterprises and solved thesupplier selection problem of electricity coal by usingthe genetic algorithm. Lai and Yang [43] analyzed theNash equilibrium problem for the power supply chainand presented a multi-layer optimization procurementmodel to make a joint decision for the suppliers and thepower generation enterprises. Liu and Nagurney [44]proposed a network model of power supply chaincoal and explained how the change of electric powerdemand would a�ect the electricity and electricitycoal market. Dai et al. [45] proposed an electricitysupply chain coordination model based on quantitydiscount contract. Liu [46] established a coordinationdecision model of procurement management for thepower supply chain alliance in the environment of BIC.Yan [47] gave a possible solution for the supply chainprocurement coordination under the condition of inter-net e-commerce; also, he established an experimentalplatform of E-commerce coordinate system. Zhao andQi [48] analyzed the performance and the source ofcooperative conict for the coal supply chain and thenproposed a cooperative conict model for the coal sup-ply chain. From the existing studies in the literature,most of them o�er the procurement mechanisms andmethods based on the classical decision theory. Inpractical procurement, these procurement mechanisms


and methods are di�cult to use for motivating thesuppliers to o�er the real information. They maylead to an ine�cient allocation result and it is di�cultto achieve e�ective allocation of electricity coal. Tosolve this problem, we can directly aim at providingthe characteristics of continuity, homogeneity, anddivisibility for the electricity coal and design incentivemulti-attribute and multi-source mechanism for elec-tricity coal procurement combined with multi-attributeauction theory and negotiation theory.

This paper studies the decision making prob-lem of multi-attribute and multi-source procurementfor electricity coal in power industry and presentsa two-stage compound mechanism based on auctionand negotiation by considering multiple attributes likeprice, electricity coal quality (calori�c value, moisture,ash, volatile matter, ash melting point, and sulfurcoal classi�cation), quantity, delivery time, suppliertransport capacity, credibility, and so on. This studycan provide theoretical basis and decision referencefor the relevant enterprises to implement scienti�cmanagement of electricity coal procurement and hasimportant theoretical signi�cance and academic valueto the improvement and development of the designand optimization of multi-object auction mechanism;it also has the important application value to promotethe combination of auction theory and a kind of realeconomic activity like supply chain management, e-commerce, and so on.

2. Problem description

Suppose that a buyer in a power generation enterprisewants to purchase Q0 tons of electricity coal to use itin generating electricity. Now, n(n � 2) risk neutralsuppliers participate in the supply competition. Theset of suppliers is denoted by N = f1; 2; � � � ; ng. Inthe procurement management of electricity coal, thebuyer will consider multiple attributes, i.e. price,quantity, quality (including calori�c value, moisture,ash, volatile matter, ash melting point, and sulfur coalclassi�cation), and delivery time, where the six qualityattributes must satisfy the relative national standardGB/T7562-2010 [49]. The meanings of the qualityattributes are described as follows:

p The price of electricity coal per ton ($/ton);q The supply quantity (ton);

T The delivery time (day) which reects the trans-port capacity of suppliers; short delivery timerepresents high transport ability;

A1 Calori�c value (MJ/kg) which is an importantbasis for boiler design. In practice, the calori�cvalue of coal must meet the requirements of boilerdesign. The calori�c value is generally divided into

�ve grades: > 24; 21:01 � 24; 17:01 � 21; 15:51 �17; > 12;

A2 Volatile matter (%) which is the core index todistinguish the combustion characteristic for steamcoal. The higher the value of the volatile matter,the easier on �re the electricity coal is. Accordingto the requirements of boiler design in the powerplant, the change of the coal volatile mattershould not be too large; otherwise, it will a�ectthe normal operation of the boiler. The volatilematter is generally divided into �ve grades: 6:5 �10; 10:01 � 20; 20:01 � 28; > 28; > 37, and also thecorresponding calori�c value has the limits, whichare > 24; 21:01 � 24; 17:01 � 21; 15:51 � 17; > 12,respectively;

A3 Ash melting point (�C). Generally, the temper-ature of ame kernel in pulverized coal furnacehearth is more than 1500�C. In such a hightemperature, coal ash mostly shows softening or

uid states. The ash melting point is generallydivided into four grades: > 1150 � 1250; 1260 �1350; 1360 � 1450; > 1450;

A4 Ash (%). Ash content can reduce the speed of

ame propagation, delay the ignition time, causecombustion instability, and reduce the furnacetemperature. Ash is generally divided into threegrades: � 20; 20 � 30; 30 � 40;

A5 Moisture (%), which is one of the harmful sub-stances in the combustion process which can ab-sorb a great deal of heat in the combustion process;its impact on the combustion is much bigger thanash. Moisture is generally divided into four grades:� 8; 8:1 � 12; 12:1 � 20; > 20;

A6 Sulfur coal classi�cation (%). Sulfur is a harmfulimpurity in coal. It has no e�ect on the combustionitself, but if its content is too high, the equipmentcorrosion and environment pollution will be quiteserious. The sulfur content in burning coal cannotbe too high and the general requirement cannotbe more than 2.5%. Sulfur coal classi�cation isgenerally divided into four grades: � 0:5; 0:51 �1; 1:01 � 2; 2:01 � 3.

For the above nine attributes, we denote the val-ues of attributes P; q; T;A1; A2; � � � ; A6 by pi; qi; ti;ai1; ai2; � � � ; ai6(i = 1; 2; � � � ; n), respectively.

In the practical procurement, the buyer can selectmultiple suppliers to supply electricity coal in a certainprocurement. At the beginning of the procurement,the buyer will announce some standards and rules asfollows:

1. For six quality attributes (including calori�c value,moisture, ash, volatile matter, ash melting point,


and sulfur coal classi�cation), the quality levelshould not be lower than the given reserve valuesa = (a1; a2; � � � ; a6). The detailed values can bedetermined by the quality standards of the relativenational standard GB/T7562-2010;

2. The submitted price given by the suppliers shouldnot be more than the reserve price �p, i.e. pi � �p;

3. Each supplier's delivery time cannot exceed theprescribed time limit, i.e. it must satisfy ti � �t,where �t is the longest delivery time;

4. To look for more partners and establish moreextensive cooperation, and to let more suppliershave the chance to supply electricity coal, the buyerwill limit the suppliers' maximum supply quantities,i.e. qi � �q, i = 1; 2; � � � ; n, where �q is the limitativemaximum supply quantity for all suppliers.

All the suppliers' submitted information must satisfythe above standards and rules. Otherwise, the supplierswill be eliminated in the competition.

In addition, the buyer will consider the credibilityof suppliers. Reliable information of this attributecan be collected through visits, market research, andother ways. The result of this attribute can beregarded as the prerequisite for supplier selection. Thesuppliers with bad credibility have no competition'squali�cations and will be eliminated �rst.

According to above basic information, the buyerwill select several winners between n suppliers ofelectricity coal and all winners should supply Q0 tons ofelectricity coal, which satis�es the given quality stan-dards and other rules to the buyer within a speci�edtime.

3. Two-stage compound mechanism forelectricity coal procurement

Considering the fact that electricity coal is a kind ofgoods with the characteristics of continuity, homo-geneity, and divisibility, we will design a two-stagecompound mechanism for multi-attribute and multi-source procurement of electricity coal. The �rst stageis multi-attribute auction stage. In this stage, thebuyer will determine winners among all suppliers andgive pre-allocated results according to the suppliers'bidding and the corresponding method of determiningwinners. The second stage is the negotiation stage. Inthis stage, the buyer will negotiate with each winneron all attribute values and then a new protocol willbe produced to improve the allocation e�ciency ofprocurement. We will present these two stages ofcompound mechanism, respectively.

3.1. The �rst stage: multi-attribute auctionmechanism

In the multi-attribute procurement auction of electric-

ity coal, the buyer is an auctioneer and the suppliers arebidders. The entire procurement process can be seenas a game process between the buyer and suppliers.In this process, the auctioneer is the game's leaderwho will design optimal bidding rules and scoring rulesto maximize his own utility. As the game's followers,the bidders will select their optimal bidding strategiesto achieve their goals of utility maximization basedon the bidding rules and scoring rules given by thebuyer. Now, we design a multi-attribute procurementauction mechanism of electricity coal. The main ideaof mechanism design is as follows. At the beginning ofthe auction, the buyer in a power generation enterprisewill announce the basic requirement and the scoringrules for electricity coal procurement to all suppliers.Then, every supplier submits a sealed bid with theform (pi; qi; ti; ai1; ai2; � � � ; ai6). Within the auction,every supplier has only one chance to submit the bid.When all suppliers submit their bids, the buyer willanalyze the statistic data according to the suppliers'bids and then publish the scores and rank order in time.The buyer will select winners among all suppliers byaiming at maximizing his expected utility and allocatethe allowable supply quantities of electricity coal towinners.

3.1.1. The utility functions of buyer and suppliersNow, we de�ne the utility functions of buyer andsuppliers in the multi-attribute procurement auctionof electricity coal.

For the suppliers, the cost of supplying one unitof electricity coal consists of two parts. The �rst oneis the production cost to produce the electricity coalwith quality values ai1; ai2; � � � ; ai6. It is denoted byCi(ai1; ai2; � � � ; ai6). The second one is transportationcost. Let the transportation cost be the functionof delivery time ti, denoted by ci(ti), where ci(ti)is increasing in type ti. (In fact, here, we supposethat the delivery time ti includes production time andtransportation time. Further, let the production timeand the transportation cost per unit time be invariable;then, the longer the transportation time, the longer thedelivery time ti and the higher the transportation costwill be. Thus, here, we suppose that transportationcost ci(ti) is increasing in delivery time ti.) Then, thetotal cost of one unit of electricity coal can be expressedas:

Csi = Ci(ai1; ai2; � � � ; ai6) + ci(ti):For six quality attributes, calori�c value (A1), volatilematter (A2), and ash melting point (A3) are the bene�ttype attributes, which means the greater their values,the higher the quality of electricity coal is. Thismakes the supplier's cost higher, but the buyer's utilitygreater. Moreover, ash (A4), moisture (A5), and sulfurcoal classi�cation (A6) are three cost type attributes,


which means the smaller their values, the higher thequality of electricity coal is. This also makes thesupplier's cost higher and the buyer's utility greater.For these tree cost type attributes, we denote ai4 as theinverse of ash, ai5 as the inverse of moisture, and ai6 asthe inverse of sulfur coal classi�cation in order to obtaina positive relation between the quality attributes ai4,ai5, ai6, and the production cost.

Let the supplier i's (i 2 N) cost functionCi(ai1; ai2; � � � ; ai6) be additive across six quality at-tributes and cij(aij) be the supplier i's cost functionwhen the value of the j's (j = 1; 2; � � � ; 6) qualityattribute is aij . Then, the utility of supplier i, whowill supply the buyer with qi units of electricity coalwith the unit price pi, can be expressed as:

Usi(pi; qi; ti; ai1; ai2; � � � ; ai6) = qi[pi � Csi]

= qi

24pi � 6Xj=1

cij(aij)� ci(ti)35 :

It is obvious that the supplier i's total utility increaseswith the increase in the bid price pi, and decreaseswith the increase in the value aij of attribute Aj(j =1; 2; � � � ; 6).

To simplify the analysis, here we set:

cij(aij)=kjaij ; j=1; 2; � � � ; 6; i=1; 2; � � � ; n;ci(ti) = hti; i = 1; 2; � � � ; n;

where kj is the quality attribute coe�cient of the jthattribute Aj and the same for all suppliers; and h isthe transportation cost coe�cient of unit time and alsothe same to all suppliers. Then, the utility function ofsupplier i can be rewritten as:

Usi(pi; qi; ti; ai1; ai2; � � � ; ai6) = qi[pi � Csi]

= qi

0@pi � 6Xj=1

kjaij � hti1A :

For the buyer, we suppose that the buyer's utility func-tion is additive across quality attributes A1; A2; � � � ; A6and ti; the buyer's revenue function is denoted byuij(aij) on the j's (j = 1; 2; � � � ; 6) quality attributevalue aij and the buyer's revenue function on deliverytime ti is denoted by ui(ti); then, when the supplier isupplies the buyer with qi units of electricity coal withthe unit price pi, the buyer's total revenue can beexpressed as:

Ubi(pi; qi; ti; ai1; ai2; � � � ; ai6)

= qi

24 6Xj=1

uij(aij) + ui(ti)� pi35 ;

where uij(aij) is the revenue function on attributeAj(j = 1; 2; � � � ; 6) and uij(aij) is increasing, concave,and twice continuously di�erentiable in aij . ui(ti) isdecreasing in ti. This is because the delivery time ti isa cost type attribute for the buyer. A longer deliverytime ti will bring smaller utility to the buyer.

To simplify the analysis, here we set:

uij(aij)=wj(aij)13 ; j=1; 2; � � � ; 6; i=1; 2; � � � ; n;

ui(ti) =w7ti; i = 1; 2; � � � ; n;

where w1; w2; � � � ; w7 are the weights given by thebuyer for six quality attributes and delivery time ti,which means the buyer's preference to all attributes,and wk satis�es the condition

P7k=1 wk = 1. When the

supplier i submits the bid (pi; qi; ti; ai1; ai2; � � � ; ai6),the buyer's total utility from the supplier i can beexpressed as:

Ubi(pi; qi; ti; ai1; ai2; � � � ; ai6)

= qi

24 6Xj=1

wj(aij)13 +

w7ti� pi

35 :3.1.2. The scoring rules and bidding rules1. The scoring rules for suppliers. The scoring rule

(or score function) is the function which is used toselect the optimal bid. The buyer will announcethis scoring rule to all suppliers at the beginning ofthe procurement auction. Because the scoring ruleis given by the buyer, the buyer can design a scoringrule from his total utility function:

Ubi = qi

24 6Xj=1

wj(aij)13 +

w7ti� pi

35 :In order to achieve the goal of maximizing utility,and to induce suppliers to announce their actualcosts truthfully, the buyer can de�ne the scoringfunction as follows:

si =6Xj=1

wj(aij)13 +

w7ti� pi:

Obviously, the score si is increasing in the value ofaij , and decreasing in the price pi and the deliverytime ti; also, the income of unit electricity coalincreases with increase in the score si. Thus, thebuyer will choose the suppliers whose scores arehigher as the winners.

2. Bidding rules. In the auction, every supplier hasonly one opportunity to submit the bid. By Sec-tion 2, every supplier's sealed bid must satisfy some


basic access rules; for example, the quality levelshould not be less than the given reserves valuesa = (a1; a2; � � � ; a6), the submitted price givenby suppliers should not exceed the reserve pricep, each supplier's delivery time cannot exceed aprescribed time limit �t, the suppliers' maximumsupply quantities must satisfy qi � �q, and so on.All suppliers' submitted bids must satisfy thesestandards and rules or they will be eliminated inthe auction.

3. Prepaid rules. The prepaid rules after the auctionand before the beginning of negotiation are asfollows. Each winning supplier must provide thepromised quality level of the electricity coal to thebuyer within the delivery time given in his bid.His received payment is di�erent from the uniformprice auction and discriminatory price auction. Ifthe buyer chooses the discriminatory price auction,then the market clearing price is the unit pricein the bid submitted by each winner. If thebuyer chooses the uniform price auction, the marketclearing price will be discussed in the latter section.

3.1.3. The optimization model of supplier selectionConsidering that the demand of electricity coal in ther-mal power generation is great and the power generationenterprises need many di�erent kinds of electricity coal,the supply of a single supplier is limited consideringquantity and variety; also, it is often di�cult to meetthe needs of buyer within the given time. Thus, thebuyer can select multiple suppliers to supply electricitycoal at the same time, i.e. the �nal winner is not onlyone and can be one or more. Next, we establishedthe optimization model of supplier selection for multi-attribute and multi-source procurement of electricitycoal.

In multi-attribute auction of electricity coal, thebuyer will announce the basic requirement and thescoring rules for the procurement of electricity coalto all suppliers; then, n suppliers will submit thebids (pi; qi; ti; ai1; ai2; � � � ; ai6), i = 1; 2; � � � ; n, to thebuyer. The task of the buyer is to design a supplierselection method to select winners and then determinethe allowable supply quantity q�i for each winner.

For the buyer, his goal is to maximize the utility,i.e.:

maxUb=nXi=1

q�i

24 6Xj=1

wj(aij)13 +

w7ti�pi

35= nXi=1

q�i si:

To achieve this goal, the following conditions must besatis�ed:

1. The limitation of the allowable supply quantity.The sum of the allowable supply quantities for all

winners is Q0, i.e.:nXi=1

q�i = Q0;

where the allowable supply quantity q�i must satisfyqi � �q.

2. Based on the bid (pi; qi; ai1; ai2; � � � ; aim), i =1; 2; � � � ; n, the buyer's utility and the suppliers'utility must be non-negative, i.e.:

Ubi = qi

24 6Xj=1

wj(aij)13 +

w7ti

35 � 0;i = 1; 2; � � � ; n;

Usi = qi

0@pi � 6Xj=1

kjaij � hti1A � 0;

i = 1; 2; � � � ; n:Based on the above analysis, the optimizationmodel of selecting winners in multi-attribute auc-tion of electricity coal can be expressed as:

maxUb =nXi=1

q�i si;

s.t.

(M1)

8>>>>>>>>>:nPi=1

q�i = Q00 � q�i � qi � �q; i = 1; 2; � � � ; nusi � 0; i = 1; 2; � � � ; nubi � 0; i = 1; 2; � � � ; n

Obviously, after all suppliers submit their bids,(pi; qi; ti; ai1; ai2; � � � ; ai6) are all known numbers. Bysolving model M1, the allowable supply quantity q�i canbe obtained. When q�i > 0, the corresponding supplieri is a winner. When q�i = 0, the corresponding supplieri loses his bid.

3.1.4. Equilibrium analysisNow, we analyze the equilibrium for the above multi-attribute procurement auction of electricity coal. Theequilibrium price under a uniform price auction is givenin the following Proposition 1.

Proposition 1. Suppose that the multi-attributeprocurement auction of electricity coal is under auniform price, i.e. all suppliers supply electricity coalto the buyer with a uniform price. Let the minimumvalue and maximum value of bid price submitted by allsuppliers be L = min

ipi and H = max

ipi, respectively;

then, the equilibrium price is p� = L = minipi.


Proof. By the above analysis, in a uniform priceauction, the total revenue can be rewritten as:

Ub =nXi=1

qi

0@ 6Xj=1

wj(aij)13 +

w7ti� p1A

=nXi=1

24qi 6Xj=1

wj(aij)13 +

w7ti

35� p nXi=1

qi

=nXi=1

24qi 6Xj=1

wj(aij)13 +

w7ti

35� pQ0:We set:

nXi=1

24qi 6Xj=1

wj(aij)13 +

w7ti

35 = A1; pQ0 = A2;then, we have U = A1 + A2. Obviously, Ub is onlyrelevant to A2 and decreasing in price p. By theconstraint condition min pi

i� p � max pi

i, we can

obtain the equilibrium price as p� = min pii

, which can

realize the total revenue maximization of the buyer. �In the practical auction of electricity coal, if the

buyer's actual utility function:

si =6Xj=1

wj(aij)13 +

w7ti� pi;

is taken as scoring rule, then the total utility of buyerand suppliers (system's total welfare) is:

U =Ub + Us =nXi=1

24qi0@ 6Xj=1

wj(aij)13 +

w7ti�pi

1A35+

nXi=1

24qi0@pi � 6Xj=1

kjaij � hti1A35

=nXi=1

qi

0@ 6Xj=1

wj(aij)13 +

w7ti

1A�

nXi=1

qi

0@ 6Xj=1

kjaij � hti1A ; (1)

which means when the suppliers realize the maximiza-tion total revenue, the system's total welfare U ismaximal and is not relevant to the transaction priceof the auction. Based on this precondition, in theequilibrium, the optimal values of quality attribute anddelivery time are given as follows.

Proposition 2. In the uniform price auction ofelectricity coal, the optimal values of quality attributeand delivery time in the equilibrium are:

a�ij =�

3kiwi

�� 32and t�i =

�hw7

�� 12;

respectively.

Proof. From Eq. (1), the optimal values of qualitya�ij , which maximize the system's total welfare, mustsatisfy the following condition:

@U@aij

��a�ij

=@@aij

nXi=1

qi

0@ 6Xj=1

wj(aij)13 +

w7ti

1A�

nXi=1

qi

0@ 6Xj=1

kjaij � hti1A��

a�ij

= 0:

By simplifying it, we have:�13qiwi(aij)�

23 � qiki

��a�ij

= 0:

Solving this equation, we obtain:

a�ij =�

3kiwi

�� 32:

Moreover, the optimal values of delivery time t�i mustsatisfy:

@U@ti

��t�i

=@@ti

nXi=1

qi

0@ 6Xj=1

wj(aij)13 +

w7ti

1A�

nXi=1

qi

0@ 6Xj=1

kjaij � hti1A��

t�i

= 0:

Then, we have [�qiw7(ti)�2 + qih]jt�i = 0. Solving it,we obtain t�i = ( hw7 )

� 12 . �3.1.5. Feasibility analysis of auction mechanismBased on the above allocation rules, payment rules, andscoring rules given by the buyer, now we prove thatour multi-attribute auction mechanism is a feasiblemechanism. We give a relative conclusion in Proposi-tion 3, which can show that our multi-attribute auctionmechanism is a feasible mechanism.

Proposition 3. For the above auction mechanism,the higher the score of supplier i, the greater theproportion of the allowable supply quantity q�i ofsupplier i and the supply quantity qi submitted bysupplier i in his bid are, which means the supplier ihas the priority to get the supply right of electricitycoal.


Proof. For n suppliers, we suppose that their scoressatisfy s1 � s2 � � � � � sn. By the constraint conditionnPi=1

q�i = Q0 in model M1, we have q�1 = Q0 �nPi=2

q�i .Thus, the total revenue of the buyer is:

Ub =nXi=1

q�i si= Q0�

nXi=2

q�i

!s1+

nXi=2

q�i si=Q0s1

�[(s1�s2)q�2 +(s1�s3)q�3 +� � �+(s1�sn)q�n]:Since s1 � s2 � � � � � sn, we have:s1 � s2 � 0; s1 � s3 � 0; � � � ; s1 � sn � 0:

Moreover, Q0s1, s1 � si and q�i , i = 2; 3; � � � ; n areall constant, and

nPi=1

q�i = Q0, so we conclude thatthe smaller the values of q�2 ; q�3 ; � � � ; q�n, the greater thevalue of Ub is, which means when s1 � s2 � � � � � sn,if the value of q�1 reaches a maximum value, then thevalue of Ub will reach the maximum value. Togetherwith 0 � q�1 � q1 � �q, we have q�1 = q1, which meansthe allowable supply quantity q�1 of supplier 1 is equalto the supply quantity qi submitted by supplier 1 inhis bid. By the same method, we have the followingconclusions.

When s2 � � � � � sn, the value of Ub increaseswith the increase in the value of q�2 . Thus, if q2 �Q0 � q1, then we have q�2 = q2, and if q2 > Q0 � q1,then q�2 = Q0�q1q2 Q0, and q

�3 = � � � = q�n = 0. Similarly,

for any q�k, k = 3; 4; � � � ; n:

if qk � Q0 �k�1Xi=1

qi; then q�k = qk;

and:

if qk > Q0 �k�1Xi=1

qi; then q�k =Q0 � k�1P

i=1qi

qkQ0

and:

q�k+1 = q�k+2 = � � � = q�n = 0:From the above analysis, we can conclude that the

higher the score of supplier i, the greater the proportionof the allowable supply quantity q�i of supplier i and thesupply quantity qi submitted by supplier i in his bidare. �

From the proof process of Proposition 3, we candirectly obtain the solution of the optimization model(M1); i.e. let the suppliers' scores be s1 � s2 � � � � �sn, then the solutions of the optimization model (M1)are as follows:

(i) If q1 < Q0, then q�1 = Q0 and q�2 = q�3 = � � � =q�n = 0;

(ii) If q1 < Q0 and q2 � Q0 � q1, then q�2 = q2 andq�3 = � � � = q�n = 0;

(iii) If q1 < Q0 and q2 > Q0 � q1, then q�2 = Q0�q1q2 Q0and q�3 = � � � = q�n = 0;

(iv) For any k = 3; 4; � � � ; n, if qk � Q0 � k�1Pi=1

qi, then

q�k = qk and q�k+1 = q�k+2 = � � � = q�n = 0;(v) For any k = 3; 4; � � � ; n, if qk > Q0 � k�1P

i=1qi, then

q�k =Q0�

k�1Pi=1

qi

qk Q0 and q�k+1 = q�k+2 = � � �=q�n = 0.

By the given score function, si =6Pj=1

wj(aij)13 +

w7ti � pi, the score of supplier i is determined by two

kinds of factors. The �rst kind is quantity attributesand delivery time; the score of supplier i increaseswith increase in the values of quantity attributes anddelivery time. The other kind is price attribute; thescore increases with decrease in the bid price.

According to the conclusion of Proposition 2, thevalues of optimal quantity attributes are invariant.Thus, every supplier only needs to consider how tochoose the optimal price in his bidding. For thesupplier i, his bid price must satisfy the condition thatthe price of electricity coal per ton, pi, is equal to orgreater than the cost of electricity coal per ton, Csi.Together with the conclusion of Proposition 3, we knowthat the greater the score of supplier i, the higher thechance of winning is and the greater the proportion ofthe allowable supply quantity q�i of supplier i and thesupply quantity qi submitted by supplier i in his bidare. Moreover, the score function, si, is decreasing inprice, pi; therefore, each supplier's bid price will beclose to his true cost.

When the price of electricity coal per ton pi is lessthan the cost of electricity coal per ton Csi, the score siincreases and supplier i gets more opportunities to winthe bid, but his utility is negative. Thus, the rationalsupplier will not submit his bid to the buyer.

From the above analysis and discussion, themulti-attribute auction mechanism of electricity coalprocurement in this paper is a feasible mechanism,i.e. it satis�es the incentive compatibility conditionand individual rationality condition. Thus, we canuse this multi-attribute auction mechanism to procureelectricity coal. In the practical auction, the buyer mayannounce the method of selecting winners describedby model M1 to all suppliers at the beginning of theauction. It will induce suppliers to submit their bidprices close to their true costs to improve their scoresand get more chances to win the bid.


3.2. The second stage: negotiation mechanismBased on the winners' scheme and corresponding pre-allocation results of electricity coal supply in theauction stage, we further design a negotiation mech-anism which can improve the allocation e�ciency andoptimize the attribute combination in this section.

In the stage of negotiation, the premise conditionof negotiation is that the utilities of the buyer and win-ners are not decreased and the allowed supply quantityfor each winner is not decreased. Therefore, the resultof negotiation is that values of some attributes mustincrease decrease and other values of some attributesdecrease increase. Finally, the buyer and winners get anew equilibrium point (p0i; q0i; t0i; a0i1; a0i2; � � � ; a0i6); thisis called a new protocol, which is the base for the�nal payment. But this new protocol cannot be solveddirectly and it is found by the method of negotiationbetween the buyer and winners.

Without loss of generality, here, we take threeattributes (xi1; xi2; xi3) as an example. Figure 1describes a surface plot of equal utility for the buyerand winners, where � denotes the surface plot of equalutility for the winner i and u denotes the surface plotof equal utility for the buyer; then, the intersectionof � and u is the negotiation set. Any point on thesurface plot of equal utility � for the winner i cansatisfy the buyer's utility value u and any point onthe surface plot of equal utility u for the buyer can alsosatisfy the winner i's utility value �. For the buyer,his satisfactory attribute combination is (x�i1; x�i2; x�i3),which is shown as point B in Figure 1. This pointis unknown for the winners. Thus, in the processof negotiation, the buyer will induce the winners tochange their attribute combination (x0i1; x0i2; x0i3) in thenegotiation set. The initial point (current situation

Figure 1. The surface plot of equal utility for the buyerand winners.

point) is denoted as point A. When the attribute com-bination (x0i1; x0i2; x0i3) changes to point B, which is theonly satisfactory attribute combination (x�i1; x�i2; x�i3) ofthe buyer, the negotiation is over and point B is the newprotocol.

In the negotiation, the winners will negotiatewith buyer on all attribute values and then a newprotocol will be produced under the condition thatutilities of the buyer and suppliers are not decreasedand the allowed supply quantity for each winner isnot decreased. The new protocol can be determinedaccording to the bidding e�ciency of the winners.Here, the bidding e�ciency is de�ned as follows:

De�nition 1. If the following two conditions aresatis�ed, then we declare that a winner's bidding has100% bidding e�ciency.

(i) To get the existing allowable supply quantity andutility, at least one attribute value of a winneris not reduced in multiple attribute values of hisbidding, unless he increases the other attributevalues at the same time;

(ii) Under the condition that all the existing attributevalues are unchanged, the winner's allowable sup-ply quantity and utility cannot be increased.

De�nition 2. If a winner's bidding has 100% biddinge�ciency, then his bidding is called an e�ective bidding.

In the practical application, the bidding e�ciencycan be calculated by using the method of Data En-velopment Analysis (DEA) [50,51] for each winner.Concretely, for the winner i, we can regard the valuesof price, quantity, quality (calori�c value, moisture,ash, volatile matter, ash melting point, and sulfur coalclassi�cation ), and the delivery time in winner i's bidas the input indicators and regard the values of winneri's allowed supply quantity and the utilities of the buyerand the winner i as the output indicators; then, weuse the method of DEA to calculate the winner i'sbidding e�ciency. On the basis of this result, the buyerwill negotiate with each winner on all attribute valuesand then a new protocol will be produced under thecondition that all values of output indicators are notdecreased.

4. The basic implementation steps of thetwo-stage compound mechanism

Based on the analysis and discussion in Sections 2and 3, now, we give the speci�c implementation steps toshow how to apply the two-stage compound mechanismin the actual procurement of electricity coal.

- Step 1: At the beginning of the procurement, thebuyer announces some standards and rules including


the score rule:

si =6Xj=1

wj(aij)13 +

w7ti� pi;

the reserve price of electricity coal per ton �p, thereserve values of quality a = (a1; a2; � � � ; a6), thesupplier's delivery time ti � T (where T is aprescribed time limit), and the limitative maximumsupply quantity �q;

- Step 2: Every supplier submits a sealed bid withthe form (pi; qi; ti; ai1; ai2; � � � ; ai6) based on thestandards and rules given by the buyer. Everysupplier has only one chance to submit the bid;

- Step 3: After all suppliers submit their bids,the bidding data pi; qi; ti; ai1; ai2; � � � ; ai6, i =1; 2; � � � ; n, and the values of Q0, wj , and �q givenby the buyer are substituted into the model M1. Byusing the Lingo software to solve M1, we can obtainthe allowable supply quantity q�i for all suppliers.When q�i > 0, the corresponding supplier i winsthe bid and becomes a winner. When q�i = 0, thecorresponding supplier i loses his bid. The prepaidrules are as follows. The winner i must provide hispromised quality level of the electricity coal to thebuyer within the delivery time given in his bid. Hisreceived payment is di�erent from the uniform priceauction and discriminatory price auction. If thebuyer chooses a discriminatory price auction, thenthe market clearing price is the unit price pi in thewinner i's bid and winner i obtains the allowablesupply quantity q�i and gets the total payment piq�i .If the buyer chooses a uniform price auction, then themarket clearing price is p� = min

ipi, which means

the winner i will supply the buyer with the electricitycoal with price p� = min

ipi and quantity q�i ;

- Step 4: Based on the winners' scheme and cor-responding pre-allocation results of electricity coalsupply in the auction stage, the buyer and allwinners enter the negotiation stage. The premisecondition of negotiation is that utilities of the buyerand winners are not decreased and the allowedsupply quantity for each winner is not decreased.The result of negotiation is that the values ofsome attributes increase/decrease and other valuesof some attributes decrease/increase and at last, thebuyer and each winner get a new protocol point(p0i; q0i; t0i; a0i1; a0i2; � � � ; a0i6). The solving process ofthis new protocol point is as follows. For the winneri, the values of price, quantity, quality (calori�cvalue, moisture, ash, volatile matter, ash meltingpoint, and sulfur coal classi�cation), and the deliverytime in winner i's bid are regarded as the inputindicators and the values of winner i's allowed supply

quantity and the utilities of the buyer and the winneri are regarded as the output indicators; then, themethod of DEA is used to calculate the winner i'sbidding e�ciency. Based on this result, the buyerwill negotiate with each winner on all attribute val-ues and then a new protocol will be produced underthe condition that all values of output indicators arenot decreased. The buyer will pay for each winneraccording to the new protocol.

5. Conclusions

Focusing on the decision making problem of multi-attribute and multi-source procurement of electricitycoal in power industry, this paper designed a two-stage compound mechanism based on auction andnegotiation. Compared with the existing procurementmechanisms of electricity coal, the contribution of thispaper is as follows:

1. The existing procurement mechanisms of electricitycoal are usually the methods based on the classicaldecision theory. It is di�cult to motivate thesuppliers to declare their real information in actualprocurement, which may lead to an ine�cient allo-cation result and it would be di�cult to achieve ef-fective allocation of electricity coal. Considering thefact that electricity coal is a kind of rare resourcewith the characters of continuity, homogeneity, anddivisibility, this paper designs an incentive multi-attribute and multi-source procurement mechanismfor electricity coal procurement based on multi-attribute auction theory and negotiation theory.This new procurement mechanism can induce thesuppliers to announce their actual costs truthfullyand improve the social allocation e�ciency of elec-tricity coal;

2. Considering the fact that demand of electricity coalin thermal power generation is great and the powergeneration enterprises need many di�erent kinds ofelectricity coal, the supply of a single supplier islimited with regard to quantity and variety and it isoften di�cult to meet the needs of buyers within thespeci�ed time. This paper regarded electricity coalprocurement as a kind of multi-attribute and multi-source procurement, which means the buyer couldselect multiple suppliers to supply the electricitycoal at the same time. This paper e�ectivelyimproves the method when the winner (the winningbidder) is unique, like in the existing literature.Also, the winner of the multi-attribute and multi-source procurement mechanism presented in thispaper is not unique and can be one or more, andeach winner can supply the buyer with multiple-quantity electricity coal;

3. For realizing the procurement operations with


higher e�ciency, this paper further introduced ne-gotiation mechanism into the multi-attribute auc-tion mechanism and then designed a two-stagecompound mechanism based on auction and ne-gotiation. The prominent characteristics and themain di�erence from the previous research onthis two-stage compound mechanism are that thismechanism considers the quality competition inmulti-attribute and multi-source procurement ofelectricity coal and pays attention to the privateinformation disclosed to the buyer and the sup-pliers. In the multi-attribute auction stage, thebuyer will determine the winner among all suppliersand give the pre-allocated results according to thesuppliers' bidding. In the negotiation stage, anew protocol will be produced under the conditionthat the utilities of the buyer and suppliers arenot decreased and the allowed supply quantity foreach winner is not decreased; thus, the allocatione�ciency of procurement can further improve.

Moreover, for the two-stage compound mechanismpresented in this paper, one important topic is thatwhether there are multiple equilibrium in it? If theequilibrium is not unique, then how to direct theauction to a desired equilibrium state? This is aresearch focus in our future work. In addition, anotherfuture work is that we intend to design an interactivemulti-attribute and multi-source e-procurement systemof electricity coal based on the two-stage compoundmechanism in this paper.

Acknowledgements

This work was supported by the National Natural Sci-ence Foundation of China (Nos. 71540027, 71201064,71371147, 61403288), the Natural Science Foundationof Hubei Province, China (No. 2014CFC1096), and the2014 Key Project of Hubei Provincial Department ofEducation, China (No. D20142903).

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Biographies

Congjun Rao was born in Huanggang, China, in1979. He received an MS degree from Wuhan Uni-versity of Technology, China, in 2006, and receivedhis PhD degree from Huazhong University of Scienceand Technology, China, in 2011. His research interestsinclude supply chain management, auction theory, anddecision theory and method.

Junjun Zheng was born in Songzi City in HubeiProvince, China, in 1966. She received her MS and

PhD degrees from Wuhan University in 1998 and 2006,respectively. She is currently a Professor in WuhanUniversity. Her current research interests includeauction theory and management decision.

Zhuo Hu received his PhD degree from HuazhongUniversity of Science and Technology, China, in 2012,and is now a postdoctoral fellow in the School of PublicAdministration at Huazhong University of Science andTechnology. His research interests include supply chainmanagement and decision making theory and method.

Mark Goh holds a PhD degree from the University ofAdelaide. In the National University of Singapore, heholds the appointments of Director (Industry Research)at the Logistics Institute-Asia Paci�c, a joint venturewith Georgia Tech, USA, and Principal Researcherat the Centre for Transportation Research. Also,he was a Program Director of the Penn-State NUSLogistics Management Program. He is currently aProfessor in the School of Business IT and Logisticsat RMIT University, Australia. His current researchinterest is on buyer-seller relationships, performancemeasurement, and supply chain strategy.

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