R(t)=1-f Qb(x-x(wt))P(w)dw 1forvbuxz0 0forbjv5rx<0

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1 kuciv. kyoto-u. ac. jp cv. titech. ac. jp Key Words : infrastructure management, maintenance/replacement, stochastic control, accounting, mechanism design

2 R(t)=1-f Qb(x-x(wt))P(w)dw 1forvbuxz0 0forbjv5rx<0

3 A(t)=R(t)+1F(t-i)M(i)di i(w)=mintlxzx(wt)} i=e(z(w))=fr(w)p(w)dw

5 1ift=ek(k=i) 0otherwise x(t)=h(x(t)w(t))+{x-x(t)}u(t) x(8k)=limjh(x(r)w(t))di (11. a) x(bk)=x(k=1,) (11. b)

6 V(x(0))=maxEw[fr(x(t))exp(Pt)dt o -{F(x(O)X)+Q}exp(-Pe) al $sggt. x(t)=h(x(t)w(t))+{x-x(t)}u(t) (12. b) x(0)=x(0)given (12. c) V(x(t))=Ew[ft+dt(xQ)exp{-p(u-t)}du (13) +exp(-pdt)v(x(t+dt))] x(t)=-ax(t)dt-/3x(t)dw(t) (14) V(x)=max-f(X-x)-Q+V(X) V(x)=-f(X-x)-Q+V(x*) (17. a)

8 P P3 0 0 P= 0 0 P33 P h(r) P(t)=Ph P00 = n(t)={b(r-lu(t)h(t)-c}-cu(t -(20) =(brh(t)-c)-(blh(t)+c)u(t) Q=(1-u(t))P7(t)+u(t)P (24) forallije{1 4} max Ea(t)(flt-1n(t)) {ui(t)}e{1 4}, te{l40} te{1 40} Y(t) maa{o1}{brh(t)-c)-(blh(t)+g)u(t) ( 26) +f3qj(u(t))vj(t+1)}forallie{14} j=1 4 (blh(t)+c)+(-p (t)+p)v(t+1) (27)

9 forallie{1 4}tE{l 40}

11 3) Aven, T. and Jensen, U:. Stochastic Models in Reliability, Springer, 1999.

5) Rigdon, S. E. and Basu, AR: Statistical Methods for the Reliability of Repairable Systems, Wiley- Interscience, 2000. 6) Gertsbakh, I.

12 5) Rigdon, S. E. and Basu, AR: Statistical Methods for the Reliability of Repairable Systems, Wiley- Interscience, ) Gertsbakh, I. : Reliability Theory with Applications to Preventive Maintenance, Springer, ) Blischke, W. R. and Murthy, D. N. P. : Reliability, Wiley, ) Merton, R. C. : Continuous Time Finance, Basil Blackwell, 8) DeGarmo, ER, Sullivan, W, and Bontadelli, J. : Engineering Economy, 8th eds, Maxwell Macmillan, ) Young, D. : Modem Engineering Economy, Wiley, ) Steiner, H. M. : Engineering Economic Principles, 2nd eds., MacGraw-Hill, ) Canada, J. R., Sullivan W. G and White J. A. : Capital Investment 33) Dixit, A. and Pindyck, R. S. : Investment under Uncertainty, Analysis for Engineering and Management (2nd eds), Prentice Hall, ) Park C. S. : Contemporary Engineering Ecomomicss, 2nd eds., Addison Wesley, ) Sudivan, WG, Bontadelli, JA. and Wicks, E. M. : Engineering Economy, Prentice Hall, ) Collier, CA and Glagola, C. R. : Engineering Economics and Cost Analysis, Prentice Hall, ) White, JA: Principles of Engineering Economic Analysis, 4th eds., Wiley, ) Bowman, MS. : Applied Economic Analysis for Technologists, Engineers and Managers, Prentice Hall, ) Newman, D. G, Lavelle, J. P. and Eschenbach, T. G: Engineering An Introduction to Derivative Pricing, Cambridge University Economic (8th eds), Engineering Press, ) Thuensen (ij. and Fabrycky, W. J.. Engineering Economy (9th eds. ), Prentice Hall, ) Vajpayee, S. K. : Fundamentals of Economics for Engineering 40) Madanat, S. M. and Guillaumot, V. C. : Inspection, Prediction and Technologists and Engineers, Prentice Hall, ) Beichelt, EE. and Fatti, L. P. : Stochastic Processes and Their Applications, Taylor & Francis, ) Jones, P. W. and Smith, P. : Stochastic Processes: An Introduction, Arnold, ) Ross, S. : Stochastic Processes (2nd eds. ), Wiley, ) van Moerbeke, P. LJ. : On optimal stopping and free boundary problem, Arch. rational mech. Anal., Vol. 60, pp , ) Bensoussan, A. and Lions, J. L. : Impulse Control and Quasi- Varuational Inequalities, Gauthier-Villars, Princetone University press, ) Dixit, A. : The Art of Smooth Pasting, Harwood Academic Publishers, Press, Decision-Making in Infrastructure management; Framework, 43) Hudson, W. R., Hass, R. and Uddin, W: Infrastructure Management: Integrating Design, Construction, Maintenance, 46) Judd, K L: Numerical Methods in Economics, MIT Press,

13 Incentives, Princeton University Press, ) Hart, 0. : Firms, Contracts, and Financial Structure, Oxford University Press, PERSPECTIVES AND RESEARCH AGENDAS OF INFRASTRUCTURE MANAGEMENT Kiyoshi KOBAYASHI and Takayuki UEDA This paper overviews traditional approaches in engineering economics and reliability engineering to maintenance and replacement and examines their applicability to infrastructure management. Problem of infrastructure management is formalized as a general stochastic impulse control (SIC) model and then a way for solving it is instructed. As a special case of the problem, the discrete stochastic dynamic programming (SDP) is illustrated with its application to replacement of an infrastructure. Finally, the research agendas for the methodological development of infrastructure management, particularly topics in project accounting system, mechanism design are discussed in perspective view.

p 2 DSGEDynamic Stochastic General Equilibrium New Keynesian 2 2

p *2 DSGEDynamic Stochastic General Equilibrium New Keynesian *2 2 2013 1 nabe@ier.hit-u.ac.jp 2013 4 11 Jorgenson Tobin q : Hayashi s Theorem : Jordan : 1 investment 1 2 3 4 5 6 7 8 *1 *1 93SNA 1 p.180 1936 100 1970 *2 DSGEDynamic Stochastic General Equilibrium New Keynesian