Computing a Model for Asset Management with Risk - Global Drinking Water Management and Conservation - page 187

e 0 : 29x

F ðÞ¼ 0 : 001 ð 8 : 23 Þ

10 þ 0 : 0001 e 0 : 29x ð 1 Þ

Utilizing Eqs. 8.22 and 8.23 in conjunction with the other parameters for City C
yields Eq. 8.24 , the DSS cost function for this municipality is:

e 0 : 0423x dx þ 119178e 0 : 0423t

R

t 1

0 : 001e 0 : 29x

5100 þ 300 sin 4 x 1 : 5

10 þ 0 : 0001 e 0 : 29x ð 1 Þ

1

ð 8 : 24 Þ

C ðÞ¼

1 e 0 : 0423 t þ 1

ð Þ

Continuous optimization of Eq. 8.24 yields a minimum at 35.03 and iterative
graphical minimization yields a consistent result as demonstrated in Figs. 8.22 and 8.23 :

Fig. 8.22 The service cost of
this asset is minimized if it
renewed at approximately
every 30 - 40 years

Fig. 8.23 Iterative
adjustment reveals that the
precise solution is 35.03 years