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Abstract
Hydro-economic river basin models (HERBM) based on mathematical programming are
conventionally formulated as explicit ‘aggregate optimization’ problems with a single,
aggregate objective function. Often unintended, this format implicitly assumes that
decisions on water allocation are made via central planning or functioning markets such
as to maximize social welfare. In the absence of perfect water markets, however,
individually optimal decisions by water users will differ from the social optimum.
Classical aggregate HERBMs cannot simulate that situation and thus might be unable to
describe existing institutions governing access to water and produce biased results for
alternative ones. We propose a new solution format for HERBMs, based on Mixed
Complementarity Programming (MCP), where modified shadow price relations express
spatial externalities resulting from asymmetric access to water use. This new problem
format, as opposed to commonly used linear (LP) or non-linear programming (NLP)
approaches, enables the simultaneous simulation of numerous ‘independent optimization’
decisions by multiple water users while maintaining physical interdependences based on
water use and flow in the river basin. We show that the alternative problem format allows
formulating HERBMs that yield more realistic results when comparing different water
management institutions.