Research and Application of FAHP in Bidding Quotation for Petroleum Geophysical Prospecting Project

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1 Ope Joural of Statistics, 207, 7, ISSN Olie: ISSN Prit: 26-78X Research ad Applicatio of FAHP i Biddig Quotatio for Petroleum Geophysical Prospectig Proect Jig Wag,2, Jiahe Gua, Dogli Liu 3 Chia Uiversity of Geoscieces (Beig), Beig, Chia 2 Tiai Log March Lauch Vehicle Maufacturig Co. Ltd., Tiai, Chia 3 Tiai Geothermal Exploratio ad Developmet Desig Istitute, Tiai, Chia How to cite this paper: Wag, J., Gua, J.H. ad Liu, D.L. (207) Research ad Applicatio of FAHP i Biddig Quotatio for Petroleum Geophysical Prospectig Proect. Ope Joural of Statistics, 7, Received: Jue 6, 207 Accepted: August 4, 207 Published: August 7, 207 Copyright 207 by authors ad Scietific Research Publishig Ic. This work is licesed uder the Creative Commos Attributio Iteratioal Licese (CC BY 4.0). Ope Access Abstract This paper maily talks about the mai layer aalytical method, ad fuzzy comprehesive evaluatio, fuzzy hierarchical aalysis (AHP) method of a deeper cootatio, ad further discusses its applicatio i biddig quotatio for petroleum geophysical prospectig proect. Fuzzy aalytic hierarchy process (FAHP) itegrates may merits of AHP ad fuzzy comprehesive evaluatio orgaically. It determies the weight of each affectig factor usig aalytic hierarchy process at first, ad the uses the fuzzy comprehesive evaluatio method to determie each scheme idex. FAHP ca effectively ehace the decisio-makig efficiecy. Keywords Fuzzy Comprehesive Evaluatio, Fuzzy Matrix, Petroleum Geophysics, Bid Price. Itroductio Evaluatio ad decisio makig is a frequet ad importat cogitive activity i huma society []. As a combiatio of qualitative ad quatitative decisiomakig tools, the aalytic hierarchy process has bee developed rapidly i recet years, but because of the fuzziess of the complexity of thigs ad people s uderstadig of obective thigs, the ordiary AHP has some obvious shortcomigs; that is there are sigificat differeces betwee the cosistecy of the udgmet matrix ad huma s thikig [2]. As a result, the fuzzy aalytic hierarchy process is improved ad optimized. DOI: /os Aug. 7, Ope Joural of Statistics

2 J. Wag et al. 2. Research o AHP 2.. Priciples of AHP I 977, the cocept of aalytic hierarchy process abbreviated as AHP was first proposed by a America operatioal research expert T. L. Satty [3]. The geeral idea of AHP method is decomposig a problem to study, thus the problem is divided ito differet elemets, the we will group ad sort each elemet, ad differet groups have differet levels, so as to form a hierarchical structure. The we compare the elemets at differet levels, ad udge the importace betwee each elemet, ad the combie the subective udgmets of people to give the overall importace order of the decisio pla Model ad Procedure of AHP The AHP model is the foudatio of AHP method, ad it is also the basic characteristic of AHP. The steps of aalyzig a problem ad makig a decisio usig the AHP method are show i Figure. There are six steps to use AHP to make a decisio, they are makig problem clearly, establishig hierarchy structure, makig udgmet matrix, sigle level Figure. Flow Chart of AHP. DOI: /os Ope Joural of Statistics

3 J. Wag et al. sortig ad cosistecy checkig, overall hierarchical sequecig ad make correspodig decisio. 3. Fuzzy Comprehesive Evaluatio Method 3.. The Priciple of Fuzzy Comprehesive Evaluatio Method The fuzzy method was fouded by a America scietist Professor Called Chad i 960s [4]. It is a kid of evaluatio model ad method for a large umber of ecoomic pheomea i the real world with the characteristics of fuzzy desig. The priciple of fuzzy comprehesive evaluatio is this: the first step is to determie the aalysis idex set ad evaluatio set of problems, ad the secod step is to costruct the fuzzy evaluatio matrix o the basis of determiig all the factors membership degree ad weight, ad the third step is to put the weight vector of each factor ad fuzzy evaluatio matrix to do fuzzy operatio, ad the do the ormalizatio processig to get a comprehesive value of fuzzy evaluatio Model ad Procedure of Fuzzy Comprehesive Evaluatio Method Fuzzy comprehesive evaluatio method has a good evaluatio effect, ad it is a good tool especially for complex problems of may factors. Its mathematical model is relatively simple, ad it is easy to master. The fuzzy set i the fuzzy comprehesive evaluatio method break the rules that membership degree ca oly be 0 ad,ad exted two valued logic to ay ifiite values of cotiuous logic, ad it ca be fuzzy cocept as both this ad that. The modelig steps are as follows: to determie the evaluatio factors ad the evaluatio level, ad to costruct the udgmet matrix ad to determie the weights, ad to make fuzzy sythesis ad to make decisios at last. 4. Fuzzy Aalytical Hierarchy Process 4.. The Foudatio of Fuzzy Aalytic Hierarchy Process Fuzzy aalytic hierarchy process (AHP) is based o the followig defiitios ad theorems: Defiitio Let matrix F = ( f ), if 0 f (, ) i Ω, the it is said that F is a fuzzy matrix. Defiitio 2 If the fuzzy matrix R = ( r ) meets r + ri =, the it is said that R is a Fuzzy complemetary matrix. Defiitio 3 If the fuzzy matrix R = ( r ) meets r = rik rk ( ik,, Ω ), the it is said that R is a Fuzzy cosistet matrix. Theorem The ecessary ad sufficiet coditio for the fuzzy matrix R to be a fuzzy cosistet matrix is that the differece betwee the correspodig elemets of ay two rows i R is costat. Theorem 2 The ecessary ad sufficiet coditio for the fuzzy matrix R to DOI: /os Ope Joural of Statistics

4 J. Wag et al. be a fuzzy cosistet matrix is that the differece betwee the specified elemets of ay row ad the rest of the rows i R is costat. Theorem 3 If R is a fuzzy cosistet matrix, its weight ca be expressed as formula (): wi = + r, i Ω () 2a a = ik k 4.2. The Solutio Process of Fuzzy Aalytic Hierarchy Process The method of FAHP uses priority relatio matrix to realize qualitative descriptio ad decisio thikig ito quatitative descriptio decisio thikig, ad its evaluatio flow chart is show i Figure 2. ) Settig up a hierarchy diagram I order to orgaize the problems uder study, we eed to aalyze the subects accurately ad detailedly, ad simplify the complex problems, distiguish the levels, ad costruct the hierarchical structure. The hierarchical structure is geerally divided ito three layers: the top (the target layer): this level has oly oe elemet, ad it is ideal for the geeral problem aalysis or the iteded target, so it is also called the target layer; the middle layer (i.e. criteria): as the target layer uder the rule layer factors; the bottom (i.e. measure layer or layer scheme): that i order to realize the goals ad decisios of various alterative measures, therefore it is also called the proect layer or layer measures. Figure 2. Fuzzy hierarchy evaluatio procedure. DOI: /os Ope Joural of Statistics

5 J. Wag et al. 2) Costructio priority relatio matrix We use the form of matrices to illustrate the importace of the same level relative to its upper level elemet. Let the matrix be F = ( f ), ad if the factor i is more importat tha m m the factor, we defie the weight f =.0. Similarly, if the factor i ad the factor are equally importat, we defie the weight f = 0.5 ; If the factor i is less importat tha the factor, it is to say is more importat, we defie its weight f = 0. 3) Costructio fuzzy cosistet matrix After costructig the priority relatio matrix, the ext step is costructig the fuzzy cosesus matrix. The first thig to do is to sum of each row of the matrix. m ri = fk, i =, 2,, m (2) k = The do the followig mathematical trasformatio: ri r r = (3) 2m Similar to the priority relatio matrix, the fuzzy udgmet matrix ca be expressed as follows: C a a2 a a r r2 r a2 r2 r22 r2 a r r r 2 Elemets have the followig meaig: whe elemets ad elemets are compared with elemets, elemets ad elemets have fuzzy relatioships... Tha... A much more importat degree of membership. The elemet r has the followig meaig: whe the elemet a i is compared with the elemet a relative to the elemet C, the elemet a i ad the elemet a has the fuzzy relatioship of membership degree that... much more importat tha. I the evaluatio process, i order to distiguish differet importace of two elemets at the same level, we use of the 9 scalig value to idicate that, ad umbers betwee this iterval meas their importace is betwee the two values. Scale values ad their meaigs are show i Table. By the above scale, we ca costruct a fuzzy udgmet matrix, as follows: (Figure 3) R has the followig properties: a) rii = 0.5, i =,2,, ; b) r = ri, i =, 2,, ; c) r = r r, i, k, =, 2,,. ik k DOI: /os Ope Joural of Statistics

6 J. Wag et al. Table. Scale ad meaig of fuzzy udgmet matrix. Scale Defiitio Istructio , , 0.4 Equally importat Slightly importat Obviously importat Much more importat Extremely importat Iverse compariso The compariso betwee two elemets is equally importat. Compared to two elemet, oe elemet is slightly importat tha the other. Compared to two elemet, oe elemet is obviously importat tha the other. Compared to two elemet, oe elemet is obviously importat tha the other. Compared to two elemet, oe elemet is extremely Importat tha the other. If the elemet elemet a is compared with the elemet i a is compared with the elemet i a ad The udgmet is a ad the udgmet will be. r, the the r r r2 r r2 r22 r 2 R = r r 2 r Figure 3. Fuzzy udgmet matrix. The fuzzy udgmet matrix i essece is a reflectio of people s thikig ad udgmet, ad it is uavoidable makig some mistakes or errors because of the complicated reality, reflectig fuzzy udgmet matrix is icosistet. Therefore, it is ecessary to adust the cosistecy of this matrix. At this time, we ca adust the matrix by the ecessary ad sufficiet coditios of the fuzzy cosistet matrix. First of all, we ca choose relatively certai udgmet elemets, ad we select r, r 2,, r geerally; the elemets i the first lie mius elemets i the secod lie to see if after dow with secod lie elemets mius first lie correspodig to the elemets, see all the differet is a costat, if ot, the secod elemet is adusted util it is to be. Accordig to this method, usig the third lie elemets, the fourth lie elemets... to subtract the elemets of the first row, ad evetually elemet i the lie mius the first row elemet ad get a costat. 4) Weight calculatio ad hierarchical sigle order The goal of this step is to compute the relative importace order of the factors i the hierarchy relative to the previous level based o the udgmet matrix. The commo methods are root method ad sum method. Here is the formula for the root method, as show below: a = Ws =, i =, 2,, (4) ak k = = The whole calculatio process is as follows: firstly, multiply each row of elemets so as to get N vectors; the do the N root of the vector oe by oe. Fially, the vector is ormalized ad we get the fial weight vector. Next is the formula for the sum law, as show below: DOI: /os Ope Joural of Statistics

7 J. Wag et al. a Ws =, i =, 2,, = a (5) k k = The whole calculatio process is as follows: firstly, each elemet i each colum is ormalized; the sum elemet beig ormalized to get a ew vector; fially the vector divided by N ad fially get the weight vector. 5) Hierarchical total orderig It is usually i a top-dow sequece usig the method FAHP to make a decisio aalysis. We usually calculate the importace of the factors i oe level relative to elemets i the upper level, ad fially give the bottom elemet importace relative to the target layer sequece. Assumig that there are k elemets o the k layer, the the weight of these k elemets relative to the system is a vector. This sort of vector is T ( k ) ( k ) ( k ) ( k ) w w, w2,, w (6) = k Assumig that sort weight vector o the k layer relative to the elemet o the k layer T ( k) ( k) ( k) ( k ), 2,, (7) p p p p = k Weight of elemet ot i cotrolled of is zero, ad make ( k) ( k) ( k ), 2,, p p p p (8) = k This is a matrix of k k, which is a sort of elemet i the level of k relative to elemet i the level of k. The, for the overall destiatio, the rak vector of the elemet o the layer of k is or Ad geerally Here T ( k) ( k) ( k) ( k ) ( k) ( k ) =, 2,, = (9) w w w w p w k ( k) k ( k) ( k ) i = w = p w (0) ( k) ( k) ( k ) ( 2) w = p p w () ( 2) w is the sortig vector for secod layers of elemets to the total target. 5. Applicatio of FAHP i Biddig Quotatio for Petroleum Geophysical Prospectig Proect At preset, there are may problems i the geophysical prospectig market, such as blid price reductio to get bid wiig ad the lack of effective quotatio evaluatio methods. Usig FAHP o the basis of studyig the biddig ad biddig practice of geophysical exploratio market ca effectively guide the oil eterprises to stregthe the costructio of proect maagemet, ad accelerate Chia s petroleum geophysical exploratio market ad the iteratioal DOI: /os Ope Joural of Statistics

8 J. Wag et al. market pace closer [5]. 5.. Overview of Biddig Evaluatio of Petroleum Geophysical Prospectig Proects With the shortage of oil i the whole world, Chia s competitio i geophysical idustry has become icreasigly fierce. It also requires cosiderable techical level to seek for geophysical eterprises suitable for egieerig costructio to esure the smooth progress of costructio proects [6]. Therefore, it is of great sigificace to study the evaluatio methods of petroleum geophysical prospectig proect for the geophysical prospectig biddig practice of petroleum eterprises Quotatio Evaluatio of Petroleum Geophysical Prospectig Proect by FAHP Assumig the expert group select the uit which more excellet i the overall ad havig more reasoable price from three cadidate bidders o the basis of five evaluatio criteria, the it ca be divided ito five stadard geophysical offer like this: direct costs, maagemet fees, iterest i idepedet fees, ad other expeses, ad each criterio is o loger divided ito sub criteria. The, usig FAHP to determie the oil geophysical exploratio productio uits ca proceed from the followig steps: ) Establishig hierarchical structure, show as Figure 4. 2) Determie the weights of the correlatio coefficiets by compariso of the criterio Here, suppose there are three paels of experts to idetify the five idicators ad get the followig matrix, show i Table 2. Accordig to the logarithmic least squares method to calculate the weight vectors of each criterio: W = ( ) 3) Evaluate bidders by sigle idex ad establish fuzzy udgmet matrix V = { v, v2,, v5} First determie use as evaluatio grades, followed by icreasig the degree of satisfactio, show i Table 3. Figure 4. Simplified aalytic hierarchy chart of petroleum geophysical prospectig price. DOI: /os Ope Joural of Statistics

9 J. Wag et al. Table 2. Judgmet matrix of Criterio. Score Directcost Maagemetexpeses Idepedetexpeses Profit-taxiterest Otherexpeses Direct-cost (0.5, 0.5, 0.5) (0.6, 0.7, 0.8) (0.7, 0.8, 0.9) (0.6, 0.7, 0.8) (0.4, 0.5, 0.6) Maagemetexpeses Idepedetexpeses Profit-taxiterest Otherexpeses (0.2, 0.3, 0.4) (0.5, 0.5, 0.5) (0.5, 0.6, 0.7) (0.4, 0.5, 0.6) (0.2, 0.3, 0.4) (0., 0.2, 0.3) (0.3, 0.4, 0.5) (0.5, 0.5, 0.5) (0.3, 0.4, 0.5) (0., 0.2, 0.3) (0.2, 0.3, 0.4) (0.4, 0.5, 0.6) (0.5, 0.6, 0.7) (0.5, 0.5, 0.5) (0.2, 0.3, 0.4) (0.4, 0.5, 0.6) (0.6, 0.7, 0.8) (0.7, 0.8, 0.9) (0.6, 0.7, 0.8) (0.5, 0.5, 0.5) Table 3. Ratig. v i v v 2 v 3 v 4 v 5 Commet Very satisfactory More satisfactory commo dissatisfactory Very dissatisfactory The fuzzy udgmet matrix of each bidder is obtaied: P = P2 = P3 = ) Usig the weight vectors of each criterio obtaied by the secod step ad the fuzzy udgmet matrix obtaied by the third step to calculate the evaluatio result vectors of each bidder. S = W P S = ( 0.630, , , , ) S 2 = ( , ,0.5333,0.053, ) S 3 = ( , ,0.2445,0.4908,0.2929) DOI: /os Ope Joural of Statistics

10 J. Wag et al. 5) Calculate the fial score of each bidder i the evaluatio result vector m = s = k k ( k 2) T = = m s T = , T 2 = , T 3 = Because the smaller the T value calculated by the weighted average, the better the program, so it ca be cocluded that the bidder s offer is optimal, the bidder 3 comes secod, ad the bidder s 2 offer is the most ureasoable. The, i accordace with this sort of selectio, we ca select the bidder to costruct the petroleum geophysical prospectig proect. 6. Coclusio This paper maily studies the method of aalytic hierarchy process ad fuzzy comprehesive evaluatio method, ad explaied the priciple ad modelig process; it also talks about FAHP s priciple ad modelig method which is the combiatio of the aalytic hierarchy process ad fuzzy comprehesive evaluatio method, ad gets the detailed steps of the algorithm, the applies FAHP i biddig quotatio for petroleum geophysical prospectig proect ad achieves good applicatio effect. Refereces [] Du, D., Pag, Q.H. ad Wu, Y. (2008) Moder Comprehesive Evaluatio Method ad Case Selectio. Tsighua Uiversity Press, Beig, -33. [2] Xiao, H.B. ad Guo, F.R. (2006) Theories ad Methods of Maagemet Sciece. Wuha Uiversity Press, Wuha, [3] Saaty, T.L. (996) The Aalytic Network Process. RWS Publicatios, Pittsburgh. [4] Wu, Y.P. (994) Evaluatio of Multicriteria Evaluatio Methods. Decisio ad Decisio Support Systems, 4, No.. [5] Hou, L.Z. ad Wu, J.X. (2006) Applicatio of Aalytic Hierarchy Process i Biddig Evaluatio of Petroleum Egieerig. Techo Ecoomic, No. 5, 3-5. [6] Zhag, B., Wag, H.J. ad Va, Z.J. (2003) Sulta Iteratioal Petroleum Egieerig Techology Biddig Aalysis. Petroleum Plaig ad Desig, No. 5, DOI: /os Ope Joural of Statistics

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