SEMAINE D'ÉTUDE SUR LE ROLE DE L ANALYSE ECONOMETRIOUE ETC.
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ticular operating policy. For example, if the structure is a
school, the #’s would specify the average size of class, the
number of sessions per day, and the like; if it is a dam, the
u's would specify the release rules as a function of reservoir
content, etc. The target values, T, need not denote deter-
ministic results if the process is stochastic; they should denote
parameters of the probability distribution of outputs. For a
hydroelectric project, T, might be the expected level of power
output in June and T, might be its variance. The problem is
then to minimize c¢(x,, ..., x,) subject to Fi(x,, ..., x,
up, ul) >T, 1=1, ..., k.
This 1s a standard constrained minimization problem to be
solved by any of the usual methods. In general it will be a
very difficult problem to solve, but when projects are planned
with costs expressed in eight or nine digits, the expense of solv-
ing a minimization problem of any imaginable difficulty is as
dust in the balance. Indeed, the expense of computation is
likely to be insignificant in comparison with the cost of gather
ing the data.
You will note that though project selection and design are
at issue, the determination of operating policy has intruded
itself into the problem. This is inevitable, as has long been
recognized. « Operations studies » are a standard component
of project design work.
Assume this minimization problem to be solved. A by-pro-
duct of the solution is a set of shadow prices associated with
the assigned targets. In the early stages of the work these
by-products are the main product of the analysis. They inform
us how much costs could be reduced by a one-unit relaxation
in each of the targets. Ratios between them are the trade-off
ratios between different objectives. If several projects are being
considered simultaneously, discrepancies between their shadow
prices for the same objective indicate misallocations and in-
consistences in the overall investment plan
Dorfman - pag. 11
