Titel_SS06

True capacity of the reservoir

Indicators : 1 : Less than 100 : 2 : Larger than 100

I 1 : Capacity >105 0.1 0.8

I 2 : Capacity < 95 0.7 0.1

I 3 : 95Capacity105 0.2 0.1

Table 3.1: Likelihood of the true capacity of the reservoir given the trial pump test results.

Given that a test well is established and a trial pump test conducted with the result that a
capacity is indicated smaller than 95 water volume units a posterior decision analysis can be
performed to identify whether the optimal decision is to establish a well locally or if it is more
optimal to construct a pipeline to the existing well.

Therefore, the posterior probabilities given the new information Pz@@: can be given as:

21 1

12

21 1 2 2 2

[ | ] [ ] 0.7 0.6 0.42

[ | ] 0.913

[ | ] [ ] [ | ] [ ] 0.7 0.6 0.1 0.4 0.46

PI P

PI

PI P PI P

::

:

:: ::

@ 

@@ 

@@



22 2

22

21 1 2 2 2

[|][] 0.1 0.4 0.04

[ | ] 0.087

[ | ] [ ] [ | ] [ ] 0.7 0.6 0.1 0.4 0.46

PI P

PI

PI P PI P

::

:

:: ::

@@ @ 



@@



which are also shown in Figure 3.5. Having determined the updated probabilities the posterior
expected values ECI'' 2  of the utility corresponding to the optimal action alternative is

readily obtained as:

  >?

>?

| 212 min [ | ] (100 10) [ 22 | ] 10; 100

min 101.3;100 100

ECI P I P I

MU

@@ @@::@@



and indicated in boxes in Figure 3.5.

Considering the additional information the optimal decision has been switched to a 2.

Action / Choice Event Concequence

a 1

a 2

2

10 MU

(100 + 10) MU

100 MU

101

100

PI( | 12 ) 0.913

PI( 22 | ) 0.087

1

Figure 3.5: Illustration of decision/event tree for water supply decision problem.