A SYSTEM OPTIMIZATION MODEL OF ADOPTION OF A NEW INFRASTRUCTURE WITH MULTI-RESOURCE AND MULTI-DEMAND SITES

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1 A SYSTEM OPTIMIZATION MODEL OF ADOPTION OF A NEW INFRASTRUCTURE WITH MULTI-RESOURCE AND MULTI-DEMAND SITES Yaru Zhang, Huayi Chen, 2, *, Tieu Ma School of Business, Eas China Universiy of Science and Technology Meilong Road 3, Shanghai 2237, China 2 Inernaional Insiue for Applied Sysem Analysis Schlosplaz A-236 Laxenburg, Ausria Absrac This sudy develops a concepual sysem opimizaion model of adopion of a new infrasrucure echnology wih muliple resource sies and muliple demand sies. Wih he model, his paper analyzes how he adopion of a new infrasrucure echnology is influenced by heerogeneous disances beween differen resource-demand pairs, echnological spillover among differen resource-demand pairs, differen demand dynamics, and differen echnological learning raes. The main findings of he sudy are: from he perspecive of sysem opimizaion, () heerogeneous disances among differen resource-demand pairs will resul in differen adopion ime of a new infrasrucure; (2) echnological spillover among differen resource-demand pairs will accelerae he adopion of a new infrasrucure; (3) i is hard o say ha higher demand will pull faser adopion of a new infrasrucure, and he opimal ime of adoping of a new infrasrucure is very sensiive o is echnological learning rae. Keywords: Sysem opimizaion model, echnology adopion, new infrasrucure. Inroducion Adopion of new echnologies is recognized as an imporan driver of economic growh and compeiive advanage (e.g., Kuan e. al 25). Researchers have developed various echnology adopion models, such as he echnology adopion life cycle model (Rogers 962), he Bass diffusion model (Bass 969), he echnology accepance model (TAM) (Bagozzi e. al 992, Davis 989), and sysem opimizaion models of echnology adopion (e.g, Messner & Srubegger 994, Seebregs 2). Adopion of a new infrasrucure echnology, such as a UHV (ulra high volage) ransmission grid, commonly requires very high invesmen cos. The cos of esablishing a new infrasrucure could decrease in he fuure wih echnological learning effec as he experience of using he new echnology accumulaes (Arrow 962, Arhur 989). The cos reducion in he fuure relies on invesmen in he early sages of infrasrucure developmen, and hisorical observaions have shown ha echnological learning is quie uncerain (McDonald & Schraenholzer 2). Adopion of a new infrasrucure commonly accompanied wih sysem reconfiguraion. For example, adopion of a UHV grid is commonly associaed wih relocaing coal power plans, i.e., coal power plans can be moved from demand sies o * Corresponding auhor ma@ecus.edu.cn; ma@iiasa.ac.a( )

2 resource sies (e.g. Ma & Chi, 22, Zhuang & Jiang 29); adopion of a cloud compuaion infrasrucure is associaed wih moving compuaion capaciy from he end-use sie o he cloud. In shor, adopion of a new infrasrucure is accompanied wih uncerain echnological learning in he ime dimension and sysem reconfiguraion in he spaial dimension. Thus i maes sense o analyze when and a wha pace a new infrasrucure should be implemened from a sysem opimizaion perspecive. Mos sysem opimizaion models of echnology adopion rea infrasrucures as lins among differen echnologies or aciviies, rarely as main obecs under sudy. Ma and Chen (25) developed a sysem opimizaion adopion model of a new infrasrucure wih uncerain echnological learning and spaial reconfiguraion. Their concep model assumes a new infrasrucure can be adoped o replace an exising one. The new infrasrucure has echnological learning poenial bu i is uncerain, and wih he adopion of he new infrasrucure, a produc producing echnology can be relocaed from he resource sie o he demand sie. There was only one resource sie and one demand sie in heir model. In realiy, i is mos liely ha here are muliple resource sies and muliple demand sies, and he disances beween differen resource sies o demand sies could be differen. This paper exends he model wih a single resource sie and a single demand sie ino a model wih muliple resource sies and muliple demand sies. The exension enables us o analyze how he following facors influence he adopion of a new infrasrucure which was missing in he previous model. Heerogeneous disances beween differen resource-demand pairs. Wih differen disance, he cos of esablishing he new infrasrucure beween differen resource-demand pairs could be differen. Then wha is he opimal ime of adoping he new infrasrucure beween differen resource-demand pairs from a sysem opimizaion perspecive? Technological spillover among differen resource-demand pairs. Differen resource-demand pairs migh adop he new infrasrucure echnology a differen pace. The experience in he new infrasrucure echnology accumulaes in resource-demand pairs which adop he new infrasrucure earlier will benefi hose pairs which adop he new infrasrucure laer, i.e, he cos of esablishing he new infrasrucure will be lower in he pairs which adop he new infrasrucure laer. Then how his echnological spillover effec influences he adopion of he new infrasrucure from a sysem opimizaion perspecive? In addiion o exploring how he above wo facors influence he adopion of a new infrasrucure echnology from a sysem opimizaion perspecive, his paper also analyze how differen demand dynamics, iniial invesmen cos and echnological learning rae of a new infrasrucure echnology influence he adopion of he new infrasrucure wih a opimizaion framewor including muliple resource sies and muliple demand sies. Diffusion of new echnologies, especially a new infrasrucure echnology, commonly aes a long ime (Grubler, 24). The model presened in his paper is developed from a long-erm perspecive. The model and analysis presened in his paper do no aim o represen he realiy in erms of echnological or economic deails; insead, i is mainly for heurisic purposes. The res of he paper is organized as follows. Secion 2 inroduces he opimizaion model wih muliple resource sies and muliple demand sies. Secion3 analyzes how he adopion of a new infrasrucure is influenced by heerogeneous disances, echnological spillover effec, demand dynamics, and so on. Secion4 gives concluding remars. 2. The model 2. Model framewor For he sae of ransparency, he 2

3 echno-economic sysem of our model is quie simple and sylized. The simplificaion also follows previous research on endogenous echnological change models (e.g., Grubler and Grievsyi 998, Manne and Barreo 22, Ma and Naamori 29, Chi e al. 22). Fig. gives an illusraion of he model framewor. In he model, he economy demands one ind of homogeneous good, for example, elecriciy. And he good can be generaed wih a producing echnology from resources. There are muli-resource sies and muli-demand sies in he sysem. The lef side of Fig. liss resource sies, and he righ side liss demand sies. T and T2 are he same echnology bu locaed in differen places for producing he good from resources o saisfy he demand, for example, coal power plans which can generae elecriciy from coal resources o saisfy he demand for elecriciy. There are wo ypes of infrasrucure echnologies. One is exising infrasrucure which is denoed wih T3 in Fig., and he oher is a new infrasrucure echnology which is denoed wih T4 in Fig.. Wih he exising infrasrucure (e.g, railways for ransporing coal), he resource has o be ranspored o demand sies where i will be used as he inpu for T. Wih he adopion of he new infrasrucure (e.g, UHV ransmission grid), he producing echnology T can be moved from demand sies o he resource sies and hus becomes o T2 in Fig., and he good produced by T2 will be ranspored (or ransmied) o demand sies wih he new infrasrucure. The model assume ha he bes mach beween differen resource sies and demand sies is already nown, ha is o say, one demand sie will provide he resource for one demand sie, and one demand sie will be served by one demand sie. This assumpion is for simplifying he model formulaions and searching for opimal soluions. We will relax his assumpion. in our fuure wor. We use q (,, n) = o denoe he disance beween he resource sie and demand sie in he h resource-demand pair. No losing generaliy, we assume q q2 < qn. The exising infrasrucure T3 is maure wihou learning effec, while he new infrasrucure T4 has learning poenial which means is cos could decrease in he fuure, depend on accumulaed adopion of i. The disances beween differen resource-demand pairs are differen, and hus he efficiencies and coss of using he new infrasrucure could be differen. When conducing a sysem opimizaion, differen resource-demand pairs will adop he new infrasrucure a differen ime wih differen pace. The echnological learning gained in resource-demand pairs which adoped he new infrasrucure earlier can be spillover o pairs adoping he new infrasrucure laer. Tha is o say, he cos of esablishing he new infrasrucure in resource-demand pairs which adoped he new infrasrucure laer will be lower han he iniial cos of he new infrasrucure. Diffusion of a new echnology commonly aes a long ime. We assume he enire decision ime horizon is composed of decision inervals. A decision inerval is he basic ime uni for insalling new capaciies of echnologies. We assume a decision inerval as of years, and hus he enire decision ime horizon is of years. The model framewor and main assumpions follow exising operaional opimizaion models such as MESSAGE model (Messner & Srubegger 994) and he MARKAL model (Seebregs 2). Wha is new in he model inroduced in his paper is ha we address he relocaion of producing echnologies wih adopion of a new infrasrucure wih muliple resource sies and muliple demand sies 3

4 Resource sies Demand sies T3 T2(T) T T4 s Resource-Demand Pair T3 T2(T) T T4 2 nd Resource-Demand Pair T3 T2(T) T T4 n h Resource-Demand Pair Symbols q Noe. T2/T: Producing echnology; T3: Exising infrasrucure; T4: New infrasrucure. Symbols meaning Figure An illusraion of he model framewor Table Symbols for describing he model Disance beween he resource sie and demand sie in he h resource-demand pair T ( T 2) Technology of producing he good from resource T 3 Exising infrasrucure echnology T 4 New infrasrucure echnology Time period ( year = + 2, =,, ) d Demand a ime in he h demand sie c E Resource exracion a ime sep in he h resource sie r Cumulaive exracion of resource by ime in he h resource sie η Efficiency of echnology i ( i =,2,3,4 ) in he h resource-demand pair i i i C Toal insalled capaciy of echnology i a ime in he h resource-demand pair C Toal insalled capaciy of echnology i a ime C i Experience in echnology i by ime in he h resource-demand pair c Fi Uni invesmen cos of echnology i a ime in he h resource-demand pair b 4 Elasiciy of he uni invesmen cos of he new infrasrucure wih regard o is cumulaive insalled capaciy C OMi Operaion and mainenance cos of echnology i Plan life of echnology i τ i δ θ Discoun rae Decision Variables: Technological spillover rae x i Oupu of echnology i a ime in he h resource-demand pair y i New insallaion of echnology i a ime in he h resource-demand pair 4

5 2.2 Model formulaions Table inroduces he meaning of symbols which will be used o describe he model. The obecive of he model is o minimize he oal cos of he sysem while saisfying dynamic demand from a long erm perspecive. Eq. () is he obecive funcion of he model. min n T 4 = = i= + δ n T ( cfi yi + comixi ) + cer = = + δ () The oal cos of he sysem includes wo iems. The firs iem of he obecive funcion includes he invesmen cos of building new capaciies and he O&M (operaion and mainenance) cos. The second erm represens he cos of exracing resource. Wih echnological learning, he uni invesmen cos cf 4 of he new infrasrucure in Eq. () will decrease as a funcion of cumulaive insalled capaciy wih b 4, as shown in Eq.(2). c b F 4 F 4 ( 4 4 = c C ) (2) There is echnological spillover effec. The echnological learning gained in resource-demand pairs which adoped he new infrasrucure earlier can be spilled over o pairs adoping he new infrasrucure laer. The C 4 in Eq. (2) is he sum of experience (quanified wih cumulaive insalled capaciy) gained in he h resource-demand pair and experience spilled over from oher resource-demand pairs, as shown in Eq. (3) C C Cˆ 4 = 4 + θ =, (3) where Ĉ is he experience spilled over from oher resource-demand pairs. The C 4 in Eq. (3) is a funcion of previous decision on adoping he new infrasrucure, and h y4 h= τ i C4 =. (4) T/T2 and T3 are assumed maure wihou learning poenial, and so cfi ( i =,2,3 ) in Eq. () are consan. The exracion cos of resource increases over ime as a funcion of resource depleion, as shown in Eq. (5). c E E = c + β r, (5) where β is a consan coefficien, and where r η2 r = r = 3, (6) 2 x x = +, (7) η η η 2 η = because T and T2 are he same echnology locaed a differen places. The obecive funcion is subec o several ses of consrains. The firs se represens demand consrains. Eq. (8) denoes ha he demand a each demand sie mus be saisfied a each decision inerval. + 4 x2 x η d (8) The second se includes balance consrains. Eq. (9) indicaes ha he maximum inpu of T is less han or equal o he oupu of T3. Eq. () denoes ha he maximum inpu of T4 is less han or equal o he oupu of T2. x3 x η (9) x2 4 x4 η () The hird se represens capaciy consrains. Eq.() denoes ha he producion of each echnology canno go beyond is oal insalled capaciy a each decision inerval. i i C x () 5

6 The fourh se consrains conain he decision variables. Non-negaiviy consrains are placed on he decision variables, as shown in Eq. (2) and (3). i x (2) i y (3) The efficiency of he new infrasrucure will decrease as he disance increases. We analyze he adopion of he new infrasrucure wih hree ypes of dynamics of η 4 which is a funcion of he disance beween a resource sie and a demand sie, as shown in Fig. 2. In all of he hree ypes of efficiency dynamics, he value of efficiency is from.7 o. The hree ypes efficiency dynamics are namely E, E2, and E3, which are described wih Eq.(4), Eq.(5), and Eq.(6), respecively. As shown in Fig.2, T4 s efficiency wih E2 is always higher han ha wih E and E3. Efficiency(η 4 ) E E2 E Disance(q ) demand dynamics, namely D, D2, and D3, which are described wih Eq. (7), Eq. (8), and Eq. (9), respecively. As shown in Fig. 3, wih D, he demand a each demand sie grows very slowly a he beginning, and hen i grows faser; wih D2, he demand grows slowly a he beginning, hen i grows faser, and hen i grows slowly again; wih D3, he demand grows very fas a he beginning, hen he growh rae sars o decrease, and finally he demand sars o decrease. D: D2: d = d ( +.5) (7) d 6 d = + 6 e.8 2 D3: d = d (8) (9) In he following, we presen opimizaion resuls of he model in differen scenarios and explore how he disance, spillover effec, demand, iniial invesmen cos, and learning rae influence he adopion of he new infrasrucure echnology. Demand 7 x D D2 D3 Figure 2 Three ypes of efficiency dynamics of he new infrasrucure E: η =. 3 q (4) 4 q 4 + E2: η = (5) 2 4 = + E3: η.3 q -.6 q (6) The demand in he model is exogenous and change over ime. We analyze he adopion of he new infrasrucure under hree scenarios of Figure 3 Three ypes of demand dynamics 3. Simulaions and analysis 3. Adopion of he new infrasrucure wih a baseline simulaion We assume here are 5 resource sies and 5 demand sies. One resource sie corresponds o 6

7 one demand sie, which means here are 5 resource-demand pairs in he enire sysem. The value of disance beween resource-demand pairs are q =. 2, q 2 =. 4, q 3 =. 6, q 4 =. 8, q 5 =, respecively. For exploring how he adopion of he new infrasrucure echnology is influenced by differen facors, we firs do a base line simulaion wih he model and hen conduc simulaions wih differen parameer values. Parameer values as well as efficiency and demand dynamics in he baseline simulaion are presened in Table 2. Table 2 Parameer values in he baseline simulaion Parameers T T2 T3 T4 Fi Iniial invesmen cos (US$/ilowa) ( c ) Efficiency ( η ) i Plan life (year) ( τ i ) i Iniial oal insalled capaciy (ilowa) ( C ) 5 O+M cos (US$/ilowa ) ( C OMi ) bi learning rae ( 2 ).2 Iniial demand d 5 E Iniial exracing cos(us$/ilowa) ( c ) 5 Exracion coefficien ( β ) - Discoun rae ( δ ) 5% Spillover rae of echnological learning (θ ) Efficiency dynamics E: Eq. (4) Demand dynamics D: Eq.(7) Fig. 4 shows he adopion of he new infrasrucure echnology in he five resource-demand pairs as well as he enire sysem wih he baseline simulaion, from which we can see ha he longer he disance is, he laer he adopion is. The new infrasrucure echnology dominaes he s resource-demand pair from 25, he from 26, he 3 rd and he 4 h pairs from 27, and i does no appear in he 5 h pair a all which is of he longes disance. This is because wih he longer disance, he lower he efficiency of he new infrasrucure is, and hus i becomes more and more uneconomic o adop he new infrasrucure wih he increase of disance. The resource-demand pair wih he shores disance adops he new infrasrucure firsly, wih echnological learning, he cos of adoping he new infrasrucure decreases, and hen i becomes economic for resource-demand pairs wih longer disance and hey sar o adop he new infrasrucure s pair 4 h pair 5 h pair Enire Sysem Figure 4 Adopion of T4 wih he baseline simulaion 7

8 3.2 Adopion of he new infrasrucure wih differen echnological spillover rae In he baseline simulaion, he echnological spillover rae (θ ) is assumed o be, which means he experience gained in one resource-demand pair can be spilled over o ohers compleely. In order o explore how differen spillover effec influence he adopion of he new infrasrucure, we conduced simulaions wih differen spillover rae values, θ =.8 and θ =. 5. The lef par of Fig. 5 plos he adopion of he new infrasrucure in he five resource-demand pairs wih θ =. 8, and he righ par of Fig. 5 plos ha wih θ =.5. From Fig. 5 we can see ha he lower he spillover rae is, he laer he adopion of he new infrasrucure is. Wih θ =. 8, he adopion of he new infrasrucure in he firs hree resource-demand pairs is similar wih ha wih θ =, and i is years lae in he 4 h resource-demand pair; wih θ =. 5, he adopion of he new infrasrucure in he firs four resource-demand pairs is 2-3 years lae han ha wihθ =. The new infrasrucure does no appear in he 5h resource-demand pairs wih eiher θ =. 8 or θ = s pair 4 h pair 5 h pair Enire Sysem θ= s pair 4 h pair 5 h pair Enire Sysem θ= Figure 5 Adopion of T4 wih differen echnological spillover rae 3.3 The adopion of he new infrasrucure wih differen efficiency dynamics In he baseline simulaion, he efficiency of he new infrasrucure decrease wih E -- a linear funcion of is implemened disance, as shown in Eq. (4). For exploring how differen efficiency dynamics influence he adopion of he new infrasrucure, we conduced simulaions wih efficiency dynamics E2 -- an exponenial funcion of he disance, and E3 -- a quadraic funcion of he disance. E2 and E3 are described wih Eq. (5) and Eq. (6), respecively. The lef par of Fig. 6 plos he adopion of he new infrasrucure in he five resource-demand pairs wih E2, and he righ par plo ha wih E3. As we can see, wih E2, he new infrasrucure does no appear in he 5 h resource-demand pair, he same as ha wih E, bu he adopion of he new infrasrucure in he 2 nd, he 3 rd, and he 4 h resource-demand pairs are brough forward for around years; wih E3, he new infrasrucure does no appear in he 3 rd, 4 h, and 5 h resource-demand pairs, and he adopion of he new infrasrucure in he s and 2 nd resource-demand pairs are around 2-4 years lae han ha wih E. In a summary, for he earlier adopion of he new infrasrucure, E2 E E3, his is because wih E2, he 8

9 efficiency is always higher han ha wih E and E3 for any given disance, and wih E, i is higher han ha wih E3, as shown in Fig. 2. Wih any of he efficiency dynamics, he new infrasrucure inends o be adoped wih resource-demand pairs wih shor disances firsly, and hen hose wih he longer disances. This is because wih any of he efficiency dynamics, he longer he disance, he lower he new infrasrucure's efficiency is and hus he more uneconomic i is s pair 4 h pair 5 h pair Enire Sysem E s pair 4 h pair 5 h pair Enire Sysem E Figure 6 Adopion of T4 wih differen efficiency dynamics 3.4 The adopion of he new infrasrucure wih differen demand dynamics In he baseline simulaion, he demand a each demand sie increases wih a consan annual growh rae (5%), as shown in Eq. (6). For exploring how differen demand dynamics influence he adopion of he new infrasrucure, we conduced simulaions wih demand dynamics D2 -- a logisic funcion of ime, and D3 -- a quadraic funcion of ime. D2 and D3 are described wih Eq. (7) and Eq. (8), respecively. The lef par of Fig.7 plos adopion of he new infrasrucure in he five resource-demand sies wih demand dynamics D2, and he righ par of Fig. 7 plo ha wih demand dynamics D3. As we can see from Fig. 7, wih demand dynamics D2, he new infrasrucure will no be adoped a all; and wih demand dynamics D3, he adopion of he new infrasrucure is similar o ha in he baseline simulaion, i.e., wih demand dynamics D. From Fig. 3, we can see ha for any given ime before 27, D3>D2>D, bu his does no resul in ha higher demand pulls earlier adopion of he new infrasrucure, wih oher parameer values and dynamics as he same. Alhough D2 is higher han D before 27, he new infrasrucure is no adoped wih D2. Alhough D is much higher han D3 afer 29, i does no resul in much earlier adopion of he new infrasrucure. Wih he hree demand dynamics, we can hardly conclude wha ind of demand dynamics will induce he fases adopion of he new infrasrucure. Wha we can conclude is ha higher demand does no have o pull earlier adopion of he new infrasrucure, a leas for a cerain ime period. In our fuure wor, we will explore in deails how differen demand dynamics influence he adopion of a new echnology. 9

10 s pair 4 h pair 5 h pair Enire Sysem D s pair 4 h pair 5 h pair Enire Sysem D Figure 7 Adopion of T4 wih differen demand dynamics 3.5 The adopion of he new infrasrucure wih differen invesmen cos In he baseline simulaion, he invesmen cos of building he new infrasrucure is assumed no relaed o is implemened disance. In his subsecion, we assume he invesmen cos of he new infrasrucure is a linear funcion of he disance wih Eq. (2). c Fi = c q Fi q, (2) Wih Eq. (2), he longer he disance is, he higher he invesmen cos is. In he baseline simulaion, he new infrasrucure's efficiency will decrease wih he increase of he disance. For exploring how dynamic invesmen coss as a funcion disance influence he adopion of he new infrasrucure, we run a simulaion wih he new infrasrucure's efficiency as a consan value (.9), i.e., no influenced by is implemened disance. The lef par of Fig. 8 plos he adopion of he new infrasrucure in he five resource-demand pairs in his simulaion. As we can see, in his simulaion, he longer he disance is, he laer he adopion of he new infrasrucure is. This is because, he longer he disance is, he more uneconomic is o adop he new infrasrucure early. I is afer experience in he new infrasrucure is accumulaed in he resource-demand pairs wih shor disance o reduce he invesmen cos wih echnological learning effec, hen i becomes economic o adop he new infrasrucure in he resource-demand pairs wih longer disances. We also run a simulaion wih boh he new infrasrucure's invesmen cos and is efficiency as funcions of is implemened disance, i.e., wih boh Eq. (2) and Eq. (4). The righ par of Fig. 8 plos he adopion of he new infrasrucure in he five resource-demand pairs in his simulaion, from which we can see ha he adopion in he 2 nd and he 3 rd resource-demand pairs is posponed much and he new infrasrucure does no appear in he 4 h and he 5 h pairs. In his simulaion, he influence of disance on he adopion of he new infrasrucure is srenghened hrough boh invesmen coss and efficiency.

11 9 8 7 s pair 4 h pair 5 h pair Enire Sysem Wih consan efficiency s pair 4 h pair 5 h pair Enire Sysem Wih dynamic efficiency (E) Figure 8 Adopion of T4 wih differen invesmen cos 3.6 The adopion of he new infrasrucure wih differen learning rae Technological learning is hough as he endogenous driving force for he adopion of currenly uneconomic new echnology. We run simulaions wih differen echnological learning rae of he new infrasrucure o analyze how i influences he adopion of he new infrasrucure. In he baseline simulaion, he echnological learning rae of he new infrasrucure is assumed o be 2%. The lef par of Fig. 9 plos he adopion of he new infrasrucure in he five resource-demand pairs wih he echnological learning rae as 8%, wih oher parameer values and dynamics he same as in he baseline simulaion, from which we can see ha, he adopion of he new infrasrucure in he s o he 4 h resource-demand pairs is posponed for around 2~5 years. And he new infrasrucure does no appear in he 5 h resource-demand pair. The righ par of Fig. 9 plos he adopion of he new infrasrucure in he five resource-demand pairs wih he echnological learning rae as 22%, wih oher parameer values and dynamics he same as in he baseline simulaion, from which we can see ha he adopion of he new infrasrucure in he 2 nd o he 4 h resource-demand pairs is brough forward for abou ~2 years, and he 5 h resource-demand pair also adops he new infrasrucure which was no in all previous simulaions presened in his paper. Wha we can summarize from he wo simulaions presened in Fig. 9 is ha he model is very sensiive o he learning rae of he new infrasrucure. Hisorical observaions have shown ha echnological learning raes could be very uncerain (McDonald & Schraenholzer, 2). In our fuure wor, we plan o develop he model in o a sochasic opimizaion model o analyze wha are he robus sraegies of adoping he new infrasrucure wih uncerain echnological learning.

12 9 8 7 s pair 4 h pair 5 h pair Enire Sysem -2 -b 4=8% s pair 4 h pair 5 h pair Enire Sysem -2 -b 4=22% Figure 9 Adopion of T4 wih differen learning rae 4. Conclusions This paper developed a concepual sysem opimizaion model wih muliple resource sies and muliple demand sies o sudy adopion of a new infrasrucure echnology. The main findings of he simulaions presened in his paper include he following poins: () Heerogeneous disance among differen resource-demand pairs will resul in differen adopion ime of a new infrasrucure because is invesmen cos migh increase and is efficiency migh decrease wih is implemened disance increases. I is afer experience in he new infrasrucure is accumulaed in he resource-demand pairs wih shor disance o reduce he invesmen cos wih echnological learning effec, hen i becomes economic o adop he new infrasrucure in he resource-demand pairs wih longer disances. (2) Technological spillover among differen resource-demand pairs will accelerae he adopion a new infrasrucure, he higher he spillover effec, he faser he adopion is. (3). From a sysem opimizaion perspecive, i is hard o say ha higher demand will pull faser adopion of a new infrasrucure wih our concepual model, and he opimal ime of adoping of a new infrasrucure is very sensiive o is echnological learning rae. The policy implicaions of he above poin () and poin (2) are ha auhoriies in planning he adopion of a new infrasrucure should pay aenion o heerogeneous disances among differen resource-demand pairs, i is beer o sar wih he mos economic one o accumulae enough nowledge/experience, and i is imporan o promoe he echnological spillover among differen resource-demand pairs. The above poin (3) implies ha in our fuure wor, i is necessary o do a more deailed analysis on demand dynamics and heir influence on he adopion of a new infrasrucure, and i maes sense o develop a sochasic opimizaion model o analyze he robus sraegies on adopion a new infrasrucure wih uncerain echnological learning. References [] Kuan J, Rombe-Shulman S, Shiu E (25) The poliical economy of echnology adopion: The case of Saharan sal mining[j]. The Exracive Indusries and Sociey, 25, 2(2): [2] Rogers, E. M. (962) Diffusion of innovaions. Glencoe: FreePress. [3] Bass, F. (969) A new produc growh model for consumer durables. Managemen Science, 5(5), [Managemen Science,5 (Number 2 Supplemen), Dec 24 ISSN 25-99, pp ]. [4] Bagozzi, R. P., Davis, F. D., Warshaw, P. R. 2

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