Meeting Environmental Outcomes – A Planning Framework - Water and Agriculture: Sustainability, Markets and Policies - page 199

While the environmental objective can be specified in terms of reliability, we can take
advantage of a clear relationship between reliability and the resource costs of meeting
environmental objectives.
Again there is a clear analogy to queuing theory where the waiting costs of remaining
in a queue exceed a threshold that leads to reneging and a subsequent loss of business for
the service provider. The problem faced by the service provider is to supply sufficient
resources such that the cost of an additional service provider equals the expected cost
associated with a reduction in the demand for services. There is a direct correspondence
between the reliability that the service will be provided within the threshold period and
the cost of failure to provide that service. In the context of the problem at hand, the
desired level of reliability can be achieved by imposing a penalty for failing to meet the
environmental objective.
An optimal release strategy with a well defined set of expected outcomes and
resources may be determined by formalising the problem as a constrained cost
minimisation problem. This set of outcomes and resources includes:
an expected time between well specified events, and
an expected level and distribution of the volume of water released to meet the
environmental objective.
While setting a threshold and a level of reliability must be seen in the wider context
of river ecology, hydrology and other assets at risk, such as farm and urban infrastructure,
this underpins the development of a release strategy that takes into account the benefits
and costs, and hence the efficiency, of alternative environmental flow regimes.
The cost minimisation problem
An optimisation problem is specified in terms of an objective function and
constraints. The range of potential environmental objectives requires this to be done using
a hypothetical example; however, the example provides some useful insights into the
design of an optimal release strategy. Costs include the environmental benefits forgone if
the flow objectives are not met, as well as the resource costs. The constraints set out the
conditions that define the criteria that must be met for a successful high flow event.