Computing a Model for Asset Management with Risk - Global Drinking Water Management and Conservation - page 178

Fig. 8.8 A nonlinear, logistic
S function approximating F
(x) in City A

e 0 : 0423x dx þ 41278

R

t 1

35000e 0 : 15x
3500 þ 10 e 0 : 15x

0 : 00045e 0 : 31x

: 46e 0 : 0423t

ð 1 Þ 4 : 5 þ 0 : 0001 e 0 : 31x ð 1 Þ

1

C ðÞ¼ ð 8 : 13 Þ

1 e 0 : 0423 t þ 1

ð Þ

Continuous optimization yields a solution of 34.89, which is consistent with the
graphical solution shown in Fig. 8.9 .

8.4.3 City B

Techniques similar to those used for City A were also used for City B. It should be
noted that the investment cost for City B is set at $119,178, which is half of the total
of all failure costs as explained in the introduction to this chapter.

Fig. 8.9 The service cost of
this asset is minimized if it is
renewed approximately every
34.9 years