Modeling water allocating institutions based on Multiple Optimization Problems with Equilibrium Constraints

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 Multiple Optimization Problems with Equilibrium Constraints (MOPEC), which allows, inter alia, to 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.