Using Fuzzy-Delphi Technique to Determine the Concession Period in BOT Projects

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1 Usng Fuzzy-Delph Technque o Deermne he Concesson Perod n BOT Projecs Khanzad Mosafa Iran Unversy of Scence and Technology School of cvl engneerng Tehran, Iran. P.O. Box: khanzad@us.ac.r Nasrzadeh Farnad Payame Noor Unversy Tehran, Iran, P.O.Box: f.nasrzadeh@us.ac.r Alpour Majd Iran Unversy of Scence and Technology School of cvl engneerng Tehran, Iran m_alpour@cvleng.us.ac.r Absrac BOT projecs are affeced by several rsks and unceranes. One of he mos mporan ssues n hs ype of conrac s o deermne he lengh of concesson perod consderng hese unceranes. The prevous sudes have developed several models o deermne he concesson perod. However, he unceranes are no akng no accoun n mos of he prevous works. Moreover, none of he prevous researches has he capably o aggregae he opnons of dfferen expers beng nvolved n a projec regardng he values of he unceran npu parameers. In hs research, a Fuzzy- Delph echnque s mplemened o deermne he lengh of concesson perod consderng unceranes. Usng he proposed Fuzzy-Delph echnque, he values of dfferen unceran facors affecng a BOT projec s deermned consderng opnons of a group of expers. The NPV value s calculaed consderng he resuled aggregaed values of unceran npu parameers. Fnally, he concesson perod s deermned usng fuzzy approach. A case sudy s conduced o evaluae he performance of he proposed mehodology. I s shown ha he concesson perod s deermned more effecvely usng he proposed approach. Keywords-componen; Concesson Perod, Fuzzy-Delph Technque, BOT, Rsk Managemen I. INTRODUCTION Takng accoun of he lmaons n he fnancal sources avalable for he execuon of nfrasrucure projecs he governmens are neresed o execue hese projecs usng prvae secor nvesmen. BOT conracs have been appled o fnance new nfrasrucure projecs va prvae secor nvesmen. Ths ype of conrac arrangemen has been wdely appled o nfrasrucure projecs hroughou he world snce he mddle of he 980s []. BOT conracs have been used by prvae secor o fnance, consrucon and operaon n large nfrasrucure projecs such as roads, expressways, ralways, brdges, pors, and power plans [2]. Buld-operae-ransfer (BOT), buld, operae and own (BOO), buld, operae, own, and ransfer (BOOT), buld, ransfer, and operae (BTO), buld and ransfer (BT), reconsrucon, operae, and ransfer (ROT), and operae and ransfer (OT) are examples of dfferen ypes of prvae secor nvesmen for nfrasrucure projecs [3]. The desgn of concesson perod s crucal o fnancal vably of BOT projecs, whch nvolves he deermnaon of he concesson perod lengh [4]. Concesson perod s one of he mos mporan decson varables n he BOT projecs. The erms of a concesson varable, ncludng oll prce and concesson perod of he projec, are ofen dscussed nensvely durng negoaons before he fnal conrac [2]. Alhough a long concesson perod s favorable for he prvae nvesor, a oo long concesson perod may resul n he governmen s loss. On he oher sde, f he concesson perod s chosen shor, he nvesor wll eher rejec he conrac or ncrease he oll prce n order o recover he capal nvesmen as well as he operaon coss o acheve a ceran level of prof. Consequenly, he rsk burden due o he shor concesson perod wll be ransferred o he group of people who use he facles []. Recenly, some of he researchers aemped o deermne he concesson perod appropraely. Shen developed a model o deermne he concesson perod akng accoun of boh governmen and nvesor concerns. In hs research s dscussed ha he concesson perod mus be consdered long enough n order o brng a ceran level of prof o he nvesor and mus be consdered shor enough n order o preven he governmen s loss []. Wu developed a new model o deermne he concesson perod consderng he rsks. In hs research, Consdered more proper o descrbe he projec NPV wh a dsrbuon of esmaes and consder rsk mpacs [5]. A smulaon model whch ams o asss he publc parner o deermne an opmal concesson perod s proposed n anoher research and he amoun of he rsks effecs on he concesson perod was assessed [6]. Anoher researcher developed a fuzzy mul-objecve decson model o evaluae and esablsh he mos sasfacory concesson em opons for BOT projecs [7]. Shen e. al. proposed a Barganng-game heory model ha can acheve a ceran value for concesson perod. In hs research n comparson o he prevous research done by Shen n 2002 specfc value for concesson perod was acheved hrough barganng beween hos governmen and nvesor [8]. Lou & Huang proposed a mulple regresson mehod for oban hgh- and low-rsk scenaros o deermne wheher he conracualnegoaon models vary n accordance wh rsk levels [2]. Zhang proposed a wn wn model for deermnaon of concesson perod. In hs research boh deermnsc and smulaon-based mehods are provded o deermne he concesson perod, va dealed sep-by-sep procedures. These mehods ake no consderaon he fnancal /0/$ IEEE 442

2 characerscs of BOT projecs and he consrucon and operaon requremens [9]. Alhough several researches have been conduced o deermne he concesson perod, hey are faced wh some major defecs. In he prevous works, he unceranes affecng a BOT projec are no normally consdered. In he few researches n whch unceranes are accouned, probably heory has been used. However, hsorcal daa are no normally avalable n nfrasrucure projecs. Hence, he probably heory may no be a praccal choce o accoun for he unceranes. In hs research he possbly heory (fuzzy se heory) s employed o consder unceranes based on he expers judgmens. Moreover, none of he prevous researches has he capably o aggregae he opnons of dfferen expers beng nvolved n a projec regardng he values of dfferen unceran facors affecng a projec. In hs research, a Fuzzy- Delph echnque s mplemened o deermne he concesson perod consderng unceranes. Usng he proposed Fuzzy-Delph echnque, he values of dfferen unceran facors affecng a BOT projec s aggregaed. Fnally, he concesson perod s deermned for he resuled aggregaed values of he unceran nfluencng facors usng fuzzy approach. The proposed model s employed on a real hghway projec n order o evaluae s applcably and performance. The concesson perod s deermned effecvely usng proposed Fuzzy-Delph echnque. II. FUZZY-DELPHI TECHNIQUE The Delph mehod was developed by he Rand Corporaon a Sana Monca, Calforna and s wdely used for long range forecasng n managemen scence. I s a mehod by whch he subjecve daa of expers are made o converge usng some sascal analyss. Ths mehod has been used for a number of forecasng and decson makng problems [0]. In hs research an negraed Fuzzy-Delph echnque s used o assess he values of dfferen unceran facors affecng a BOT projec usng he opnons of a group of expers. The mnmum number of expers requred n Delph echnque has been repored as 2 persons [0]. The fnal consoldaed fuzzy numbers deermned for each unceran facor wll ac as an npu for calculang he value of ne presen value (NPV) based on whch he concesson perod s deermned a a laer sage. The Fuzzy-Delph mehod consss of he followng seps [0], []: ) A group of expers are requesed o gve her opnon regardng he value of an unceran facor whou any nercommuncaon. I s assumed ha each exper gves hs opnon regardng he value of an unceran facor by a rangular fuzzy number. The rangular fuzzy number (T.F.N) proposed by each exper can be shown by : ( a, b c ) A, = () where ndcaes he ndex aached o he h exper, and show ha hs s he frs sage for he forecasng process. a, b and c are he mnmum, maxmal presumpon and maxmum value proposed by expers, respecvely. 2) The mean of he T.F.Ns are hen calculaed. ( Aavr Bavr, Cavr ) = ( a, b c ) F avr =,, (2) n where F s he Fuzzy mean of he exper s avr opnon. 3) For each exper, he devaon from he average s calculaed as follows: D = Favr A = a a, b b, c c n n n (3) Ths dvergence can be null, posve or negave. 4) These daa are hen sen back o each exper and hey are requesed o revse her opnons regardng he dvergences. Each exper now gves a new T.F.N. 5) The seps 2-4 are repeaed unl he mean becomes suffcenly sable, and hen he process s sopped. The dssemblance ndex whch exss beween wo fuzzy numbers [2] can be used as a soppng creron o deermne wheher he TFNs have converged or no [3]. Consder wo rangular fuzzy numbers A and B. The nervals of he confdence a presumpon level of wo menoned fuzzy numbers A and B as show by: ( α ) ( α ) ( α ) ( α ) A = ( a l, a ) B = ( b l, b ) α a l u b l α a u u b u where, and, are her lower and upper boundares, respecvely. The normalzed dsance beween wo fuzzy numbers s gven by: δ ( A, B ) = ( Δ l ( A, B ) + Δ r ( A, B )) 2( β 2 β ) (5) where A and B are respecve.h T.F.N gven by exper A and B and Δ l s he lef dsance, Δ r s he rgh dsance and β, β are arbrary values a he rgh, and a he lef, 2 respecvely chosen such ha 0 δ. In fg Concep of dssemblance ndex of wo fuzzy numbers has been showed [3]. If all he dsances beween TFNs of expers and mean TFN sasfy a gven value of σ, he correspondng mean TFN becomes a fnal npu facor esmae. (4) 443

3 Fgure. Concep of dssemblance ndex of wo fuzzy numbers [Adoped from [3]] III. CALCULATION OF NPV There s a sandard equaon for calculang NPV, and he nvesor s NPV can be calculaed by he followng formula [],[5]: T = Tf ( I ( ) Cm ( )) NPV ( Tf ) = = ( + r T ) Where NPV denoes ne presen value and () as he year, I () =ncome for he year, Cm () =expense n year, r =dscouned rae akng no accoun he effecs of boh neres and nflaon and T (f) as he projec lfe me. Ths can be rewren as follow: NPV ( Tf ) = T = T 0 ( Cc( ) + + T = Tf ( q p Co( )) T = ( r) T = To+ ( + r) Where (0) s he consrucon perod and Cc () as he annual capal nvesmen n year, (q) s he annual raffc volume, (p) s he amoun of he oll prce and Co () s he operaon and manenance cos n year. The value of NPV can be calculaed n dfferen years of projec s lfe cycle usng equaon 7. IV. SIMULATION MODEL In order o calculae he NPV value, he values of dfferen npu parameers affecng he NPV should be deermned. These parameers nclude he capal nvesmen, consrucon duraon, annual raffc volume, oll prce, annual manenance cos and he amoun of annual dscoun rae. The values of hese parameers are unceran and s dffcul o assgn hem a specfc value. Hence, n hs research, he Fuzzy-Delph echnque s mplemened o calculae he values of hese parameers consderng unceranes. Afer calculang he values of hese parameers, he NPV value s deermned usng equaon 7. The flow dagram shown n Fg.2 depcs he sages of work for deermnaon of he concesson perod. The proposed model has been employed on a real hghway projec n order o evaluae s applcably and performance. The followng secons explan n deal how he values of npu parameers are calculaed Then, he NPV value and he (6) (7) concesson perod are deermned for hs hghway projec case example. A. Calculang he Values of Inpu Parameers As menoned before, he values of npu parameers are calculaed usng Fuzzy-Delph echnque. For hs purpose, he opnons of 2 expers are gahered regardng he values of dfferen npu parameers ncludng he annual capal nvesmen, consrucon perod, annual raffc volume, oll prce, operaon and manenance cos and annual dscoun rae. Each exper gves hs opnon regardng he value of an npu parameer by a rangular fuzzy number (T.F.N) consderng exsng unceranes.. As an example, he value of one of he npu parameers namely annual capal nvesmen s calculaed below.mananng he Inegry of he Specfcaons Annual capal nvesmen: C(c) Toal capal nvesmen ncludes prmary assessmen cos, desgn cos, consrucon cos, and ec. I s assumed ha oal capal nvesmen s evenly consumed durng he consrucon perod (0) [5]. There for he annual capal nvesmen can be obaned by equaon 8: C ( c) = I / o (8) Where (I) s he oal capal nvesmen and (0) s he consrucon duraon. A group conss of 2 expers were asked o express her opnon regardng he oal capal nvesmen as a rangular fuzzy number. The frs round esmaons of 2 expers are presened n able. Expers o m Deermnaon of values of npu facors (= n) affecng he NPV as fuzzy numbers Consoldaon of values of npu facors by Fuzzy-Delph echnque Deermnaon of fnal consoldaed fuzzy number of npu facors (=, 2.n) Calculaon of he NPV Deermnaon of he concesson perod Fgure 2. The flow dagram for deermnaon of he concesson perod 444

4 TABLE I. FIRST ROUND ESTIMATES OF 2 EXPERTS REGARDING THE VALUE OF TOTAL CAPITAL INVESTMENT X(a) X(b) X(c) frs exper opnon second exper opnon Thrd exper opnon h exper opnon h exper opnon h exper opnon h exper opnon h exper opnon h exper opnon h exper opnon h exper opnon h exper opnon The mean value of annual capal nvesmen has been calculaed usng equaon 2 as a T.F.N of (57.9, 63.3, 73.3) mllon $. Then he dvergence beween each exper and he mean value calculaed usng equaon 3. The calculaed dvergences n he frs round, has been gven n able 2. The calculaed dvergences are sen back o each exper and hey are asked o modfy her esmaons accordngly. Ths cycle repeas unl he mean value receve a sable value. Fnally, he value of he oal capal nvesmen was calculaed as a rangular fuzzy number of (59, 72,63) where he lef, md and rgh values represens he mnmum, mos lkely and maxmum values of annual capal nvesmen, respecvely (Fg. 3). The values of oher npu parameers were calculaed smlarly. The value of he consrucon perod was deermned as a T.F.N of (4, 4.5, 5) years. Operaon and manenance cos deermned as a T.F.N of (26, 27, 29) mllon$. The nal value of oll prce was deermned as 0.6 dollar whch wll be ncreased annually. The raffc volume was deermned as a T.F.N of (25, 26, 28) for he frs year of operaon. Ths value wll be ncreased annually. Fnally, he annual dscoun rae was deermned as a T.F.N of TABLE II. FIRST DIVERGENCE OF ESTIMATES OF DIFFERENT EXPERTS WITH THE CALCULATED MEAN VALUE X(a) X(b) X(c) frs exper dvergence second exper dvergence Thrd exper dvergence h exper dvergence h exper dvergence h exper dvergence h exper dvergence h exper dvergence h exper dvergence h exper dvergence h exper dvergence h exper dvergence (0.065, 0.072, 0.078). In hs Projec, s assumed ha annual dscoun rae s consan hroughou he projec lfe cycle. B. Calculaon of NPV Afer deermnng he values of npu parameers usng fuzzy-delph echnque, he amoun of NPV for each year can be calculaed usng equaon 7. In he prevous researches he Mone Carlo smulaon approach was used for calculaon of NPV. In hs research, however, he exenson prncple s used o deermne he value of NPV [4]. The value of NPV s calculaed for each year durng he projec lfe cycle. In Fg 4, he cumulave NPV s shown. C. Deermnaon of he lengh of concesson perod The concesson perod can now be deermned usng Fg4. For hs purpose, frs he oal nvesmen n he projec should be calculaed. For hs purpose he mnmum value n- Fgure 3. Toal capal nvesmen Calculaed by Fuzzy-Delph Technque Fgure 4. Cumulave NPV durng projec lfe cycle 445

5 -he NPV values have been obaned. I can be calculaed by he equaon (8) = f I ( p) = mn = { NPV } (8) Then he nvesor s expeced nvesmen reurn has been calculaed. Ths value can be calculae by equaon (9) IR = I ( p) R (9) Where IR denoes he nvesor s expeced nvesmen reurn and R denoes nvesmen s expeced rae of reurn and I(p) = oal nvesmen. Afer ha he concesson perod can be deermned by he am of fg 4. The above seps mus be repeaed for each α cu and for each rgh and lef value of heα cu a crsp number s obaned for concesson perod. Fnally, he concesson perod s defned as a fuzzy number. The Fuzzy number of concesson perod for he hghway projec case example has been shown n Fg5. If he projec manager wans o consder all he unceranes, he value of α cu s seleced as 0 and he concesson perod s deermned n he range of 24 o 40 years. Usng COA dfuzzfcaon mehod, he crsp value of 32.3 years could be consdered as he concesson perod. Onhe oher sde, f he projec manager wans o dsregard unceranes, α cu value s seleced as and he concesson perod s deermned as 29 years. V. CONCLUSIONS AND REMARKS BOT conracs have been used by prvae secor o fnance, consrucon and operaon phases n large nfrasrucure projecs. A key facor of a BOT projec s he agreemen on he lengh of concesson perod. In hs research a Fuzzy-Delph echnque has been developed o deermne he lengh of concesson perod consderng unceranes. Usng he proposed fuzzy-delph echnque he opnons of a group of expers regardng he values of dfferen npu parameers affecng he NPV of he projec was gahered. The opnons of dfferen exers was aggregaed usng fuzzy Delph echnque. Then he NPV value was calculaed for he resuled fuzzy numbers of npu parameers usng fuzzy approach. Fnally, he lengh of concesson perod was deermned effecvely consderng all he unceranes. The proposed mehodology offers a fuzzy number for he lengh of concesson perod. Hence, he projec manager can deermne he concesson perod a dfferen confdence levels. I s beleved ha he proposed mehodology can deermne he concesson perod more precsely snce unceran npu facors affecng a BOT projec as well as he opnons of a group of expers are accouned for. Fgure 5. Trangular fuzzy number of concesson perod REFERENCES [] Shen, L. Y., L, H., and L, Q. M. (2002). Alernave concesson model for buld operae ransfer conrac projecs. J. Consr. Eng. Manage., vol.28 (4) pp [2] Lou. Fen-May. and Huang. Chh-Pn. (2008). Auomaed Approach o Negoaons of BOT Conracs wh he Consderaon of Projec Rsk. J. Consr. Eng. Manage., vol.34 (), pp [3] Kumaraswamy, M. M., and Morrs, D. A. (2002). Buld-operaeransfer-ype procuremen n Asan Mega projecs. J. Consr. Eng. Manage.,vol. 28(2), pp [4] Ye.S, Tong.R.L.K, (2003). The effec of concesson perod desgn on compleon rsk managemen of BOT projecs. j. Consrucon Managemen and Economcs 2 (5), [5] Shen, L. Y., and Wu, Y. Z. (2005). Rsk concesson model for buld operae ransfer conrac projecs. J. Consr. Eng. Manage.,vol. 3(2),pp [6] Thomas.S. Ng., Xe. J. Z, Cheung., Y. K, and Jefferes. M,. ( 2007). A smulaon model for opmzng he concesson perod of publc prvae parnershps schemes, Inernaonal Journal of Projec Managemen., vol. 25, pp [7] Thomas,S. Ng., Xe. J. Z, Skmore. M, and Cheung. Y. K, ( 2007). A fuzzy smulaon model for evaluang he concesson ems of publc prvae parnershp schemes, j. Auomaon n consrucon., vol. 7, pp [8] Shen, L. Y., Bao, H. j., Wu.y. z.,and Lu, w. s. (2007). Usng Barganng-Game Theory for Negoang Concesson Perod for BOT-Type Conrac. J. Consr. Eng. Manage.,vol.33(5)pp [9] Zhang. Xueqng, (2009). Wn Wn Concesson Perod Deermnaon Mehodology, J. Consr. Eng. Manage., Vol. 35(6), pp [0] Kaufmann, A., and Gupa, M.M. (988). Fuzzy mahemacal models n engneerng and managemen scence. Elsever scence publshng company nk., New York. PP [] Shaheen, A., Fayek, A. and AbouRzk, S. (2007) Fuzzy numbers n cos range esmang. ASCE J. Consr. Eng. Manage, vol.33(4), pp [2] Kaufmann, A. and Gupa, M.M. (985) Inroducon o Fuzzy Arhmec, Norh-Holland, Amserdam. [3] Nasrzadeh.F, Afshar.A, Khanzad.M, Howck.S,(2008) Inegrang sysem dynamcs and fuzzy logc modellng for consrucon rsk managemen, j. Consrucon Managemen and Economcs,vol 26.pp [4] Dong.w.m and Wong.f.s (987). Fuzzy weghed averages and mplemenaon of he exenson prncple. j.fuzzy ses and sysem., vol.2, pp