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25 () O DATA BASE : ) % F (2) O..." 6<..."....>...: H.... "...^!...N... 2 T+... / /! :. O 63

26 /. +!% '. 0 23, :! /( ++ & --7- :* + /+ 6< > /%, B 3 &.H. + / -.J%,. + / -2 * #0! : * + / -3. /& / -.0 ^!. C< ^! + / -. + / -6 /% + /%! () 80! "% /% <!?) % 6+ G?).K03 c% & /%! C<! :! /( ++ G /% 6+ I!! 0!!! 3, B (-) " 7% % '.%!! 2! % "!!!. 0+ I! % -% ' H! I) "% "!! /% 6+ I!! > /& 6+ 2+>% J)*.%!!.2! /,.> /, /80 "% "%.& /%! ' 28!&!! /% /%!!!, /% + < )' (3-) (2-) " :!L & 0 6+ I!! 3 - ). %! (% < $%.'< /% 0 2< c% /!.!.! % -3 6

27 :B % - % -6 >. * D#0 >!! (PCI) #0 >.!+! '!!" - >! 6+!! >! I). 00 ( (00-0) >! 6+!!. J)*..>.(6). (80) -+ H' 7! G!& H!'! %" -?!?)".> ' 7!! -!!, 88 2 ) * * -+ " 2 > 6< '3% ".>.> > X!!!?)% 0 / &.+ 2,.!.>?!!! DN. ' -+ " =! >!!.#0.! 00 0! :#0-8" %!!L PCI = 00-9 (Tij) )F! -! '" > :(Tij).-+ " 0 / (PCI=00) +!,% >! a)b< DPCI - #0 >!!.(PCI=0) + # 6<! 9:.> " % 0 /+! ' )*!!! 6+! % 0 /.% : % % -7 2 *. "% 0 2< c%.! # "%. "% 0 8 % /> )! ' 0 + / 2+ 0 B! F!!, -! %"?*?)".0 6

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29 .)! /( ++ $! :(2-) /&+.) ;! /( ++ $! :(3-) /&+ 67

30 /. +!% '. 0 23, : -2-7! e% 0 /"..!!! / 7 %G a)b< 0 / )!G *, N! D/'0 :(9) + %3 >! % 0! H%! h(- " -) "% 6+ 0 C< -, h(" 0 /C< )?) % 0 O h0?! C< - 6! 0 )!G!+!?) :!L -?) #0 - " - 0 /' 6< C!' PCI D 7 N * " (-7) ' " E0-0).(-7) "% -!L (2-7) 0 /' 6< C!' PCI E 7.PCI 68

31 20 < & ; + ;% B $! :(-7) / & + ;%! ; + % & 6-20 ; 20 < + % & 6-20 ; 20 < :: + % & 6-20 ; ; ; 3 3 % )+ D 3 3 &! )+ D2 3 3 % )+ B D3 3 3 )+ D 3 3 UGU )+ D D6! D7 B & 0 U D8 9 D9 B V: D $ &!!- B D : F D2 D3 B F /&W 0 D :% D : D6 69

32 /. +!% '. 0 23, %! B &9 /% $ / $! B % / : /&+! ;! N D 7( N N -X :% N2 N6 + N3 N7 (PCI) * ;% :(2-7) / % P PCI < 2 B! 7+( ( 3 > PCI > 2 +&! 0 I! 2 0 > PCI > 3 +&! I! 3 6 > PCI > 0 +&! I! 7 > PCI > 6 % PCI > 7 *, ()+* * :% 7"() (-7) / 6.! + $! :(-7) /&+ 70

33 : % -8 O!!, * 0 +, /,! ' I>! - +, H',%! # I) O! 0 6< X!!!. ' O -!!!, 6< )"* H!= I) H!= 0 /! "%. 2< ' 6+!+G%?)!, - K * h, K. * *. *,?)".?! ' *! *.?) ' " 6+!G >,% 6+!! >. D0 +, '" 2W0 "% V -,. 2+?*.@ 2%" "% "! + H' -A A )*. "%!!!. -!!! I).% 0 /, %?) ' /& 6+! I), '! 6+.(0) : % /9 /% --8 %" N "%!. "% 0 /! #* %. >! '" A N%0!! ', 6< 0! -%!!! 0 c% % G H$' 2!. -! 2! K% > %. #* >! :!,! 6< (% )* ' /! ' >! "! ' % >. '!.9 % "% (Maximize) 7!! '.%. 0 /! 6+!, (Minimize) 8"! >! %> H - J!+! U +,!=W! % + 78 "% ' " 7+=% 28!G # C< % G * "% 2C8" /%.!% 8! 7

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35 &!+ % $! :(2-8) /&+ :0 /! 6+! :.9 % J #!!= '. #* %! 6+ >.!! :(% '! :0 O,!!+! :(i) /3! N.#0 />%. C< 2+< -.." % 0.W! >%. -2. /." %.W! >%. -3.." %.W! >% (> D! D8 C&<) 0-6 :B %. P 8 N + *. C% C0>!G C>!G% )F! '80 '!! >!, >! ' 0 O! =! B

36 /. +!% '. 0 23, J)* #0 N. ' F! - 7 N. 9< )<.#0 :(-8) ' " * (% )* ' '80 B % P 8 : $! :(-8) / %! I! I! +&!! 0 I! ( 7+ P +& +& : (Pi) :6 /&0!G : % J N2N2N8 + " K+, < /&0 >! 6+! "?) #0 ( ( /80%! "! /+!!.(2-8) ' " 0 O.8 0!G B! 6-0 O B! I!G B!,, * c 9: D. >%! 6+ I) (00-PCI)

37 $! :(2-8) / Pavement Condition Traffic level Index Level L M H 00 > PCI > > PCI > > PCI > > PCI > > PCI > 0 0 : ;9 J -3-8! #*, % :.9 % J :(--3)!> 0 8" 2 T'! a)b< : >! 8"..0 )F (00-0) % > :J I) #!.2.#0 ' 0 =! '80 O " J! -. "% C. * :J! -. W!.3. 0 O %.!! H+ I) (X) 0 '! B! >>!! #* * :#*. :!= " ' + % D#0 N. 6 L i= P ( X ) i i T... ().#* ' (i) 0 =! '80 = P :a)b< i 7

38 /. +!% '. 0 23,.(#0 ) *! #! = T - #G!.%!%!"! ' #* J)* :!= " # >! % 6+ I) 6 L 6 i= i= d - P i ( X i ) + d - d + = T... (2) d + :!= " + %, " : >. C ( X ) i i B... (3).(i) 0 O ". "/ 0 8" : C :a)b< i.0 2'! : B! G 2! 0 /'., O, T!8 a)b< :..6 :0 /! " H!0 -. " i= X i L... () :H!0-6+ G 0 O X i L... () i /' c%! : O I,! "!,! G K 80 I.% 0!?) + B>!U #>3.! G " 80 :!= ". 6 6 X i a * L... (6) i i.. 6 " K %" /% : a i :a)b< + % # > % /'G >, * # :' &.8 :!= " 76

39 Minimize Z = W d... (7) '! * H>>! - # > - #G :.#0!G. % : % J :(6) d :a)b< "% /&0 0 O " 2+ /+ '!G 6+ ") "! "% /&0 I,!> ' D. % 6+!.! % -. X!G 0 *!! # : /+ I,! * :J! -. W! ( :a)b< Xij:% + % 2 %!0! # 0 O ".i + %. 0 O j 2+ 6< 0 O " /&0!! :/+! (2 /! &%! /&0 6+ I! + " +.#0 /! :!= " 0 O " /+! * :c% 7 #* (3 X ij 0, I =,...,.+ J =,..., 6.0 O /&0 /+!G B! 0, * :' & ( :0 O " Maximize Z= ((L ij * T ij *(00 - i = PCI) ) ij * X )... (8) ij 77

40 /. +!% '. 0 23, :> ( c!. 6+ G 2+ /+., O :0 O " 6 i = X ij L j... (9)! c!. 6+ G 0 O " + ". :/+ X ij L... (0) i % e% I!, - 0 O :6 C j * i = X ij B j... () Xij 0 : O " /+ * J< -. W! : X :a)b< ij.0 O " + " /&0., O : L ij.+ " /&0 B! : T ij.+ " /&0 #0.! : PCI. j 0 O 6 c!.: L j." / 0 8" :.6 )= j 0 O " : C j B j 78

41 : J! -9 /. /% 3!G )'% c%.!! c%, ") *.K. =% ck! 6+ 0! 0., /"!. / 2+ - =%! N! 0..!! " U?* D! *! ', > ' %. '! O B! 6+ /&0! 2 '.#0.! & > 2>8 ' H! " D0 6< % * : " -0,%!!?) D@& -0,. 0 6+! >! (%. 0!! ' % >! 6+!,% )*./ > 7 #* 2C8" 6+,.%. > " -=% # X!G H!0 -! 0 O "! %! /+ 6< 0 O " /&0!. %!! /) /&0!!!*, /&0!!% %! 0! " )% >! %"!G > 0 6< % "!! "% ! 6<./ +!!G )'% c% &?)!.2 A. "% /% 79

42 /. +!% '. 0 23, : L! 7!% #0 >! + / 2 -! /! N0! 6! 6! % 2+>?!.! 9: /%.! /W! ' 0! !. #0 *! ' %. / 80

43 References - [FHWA 90] Federal Highway Administration, " An Advanced Course in Pavement Management Systems," Course Text, 990., 2 ("3) U %W +!G 0!G ) -2.("! > "% /% [Haas 9] Haas, Ralf, "Generically Based Data Needs and Priorities for Pavement Management." ASTM STP 2,99. " '. 0 /! #0 >!" -. % (% D *> 2*> D! - [Zaniewski 8] Zaniewski, J. P., W. +R. Hudson, R. High, and S. W. Hudson, "Pavement Rating Procedures," Federal Highway Administration Final Report, Contract DTFH6-83-C-003, Washington, DC, [Shahin 79] Shahin, M. Y., S. D. Kohn, "Development of Pavement Condition Rating Procedures for Roads, Streets and Parking Lots- Volume I Condition Rating Procedure," Technical Report M-268, Construction Engineering Research Laboratory, United States Corps of Engineers, [Mouaket 8] Mouaket, I. M., "A Framework for Structuring Decision Levels and its Application to Ontario", Proceeding of North American Pavement Management Conference, Toronto, Vol., > < [Haas 9] Haas, R., Hudson, W. Ronald, and Zaniewski J., Modern Pavement Management, Krieger Publishing Co., Malabar, Florida, 99. T "/.. #0 0 2<" D-* %+ D % " 7 %.!%. 0 E0!.<.! D % - 0 D2*> 2*> DJ!" "2! #*j

44 /. +!% '. 0 23, 2- [Lytton 8] Lytton, R. L., Moderator Report, from Ranking to True Optimization, Proceeding of North American Pavement Management Conference, Toronto, Vol. 3, [Frederick 89] Frederick, S. Hillier & Gerald J. Lieberman, Introduction to Operation Research, Fourth Edition, Holden-Day, Inc, Okaland, California, [Ravindran 87] Ravindran & Don T. Phillips & James J. Solberg, Operation Research: Principles and Practice, Second Edition, John Wiley and Sons, Inc., [Kumares 8] Kumares, C., Sinha, M. Mathusubramanyam, And A. Ravindran, An Optimization Approach for Allocation of Funds for Maintenance and Preservation of the Existing Highway System, Transportation Research Record 826, TRB, Washington, D. C., [Feighan 87] Feighan, K. J., Shahin, M. Y. and Sinha, K. C., A Dynamic Programming Approach to Optimization for Pavement Management System, Proceeding of North American Pavement Management Conference, Vol. 2,

45 A%! /% : :(3-8) /&+.200/3/0: 6< (% ^! 83