Mathematical programming for the support of river water management: water allocation and reservoir location

Abstract

Surface and ground water availability is variable in space and time and the spatio-temporal pattern of this variability often does not match with the distributed use pattern of sectors and individual consumers. This mismatch can become controversial when overall water availability decreases, e.g., due to climate change, and competition for water increases. It is in this context that the so called WEF-nexus between water for human consumption and industrial use, water for Energy (hydropower) and water for Food (irrigated agriculture) (WEF) has gained increasing attention in research, business and policy spheres, especially in regions with more arid climate. An additional dimension of this nexus is the water required for sustainable functioning of ecosystems in general and wetlands in particular. Allocation of scarce water has challenged water managers for decades. The construction and operation of reservoirs is the typical solution put forward. In this research we addressed the optimization of the allocation of water available in a river-with-reservoir system towards multiple users as a network flow optimization (NFO) problem. There are two classes of methods to tackle NFO problems: heuristic models and mathematical models. Heuristic models are able to provide a feasible solution within reasonable computation time whereas mathematical models are able to come up with the optimal solution but often requiring longer computation times. Since for strategic decisions computation times are less crucial, the latter, i.e. linear programming (LP) models and mixed integer linear programming (MILP) models were the subject of this research. LP and MILP models were formulated to optimize the flow and storage of water through Water Supply Networks (WSN) created from geographic information describing the river basin under study. A WSN encompasses a set of oriented lines connected in georeferenced nodes whereby the lines represent river segments and the nodes represent reservoirs, natural water bodies, inflow points and abstraction points. Whereas inflow and abstraction points are characterized by time series of incoming and required water volumes, the water volume available in river segments, reservoirs and other water bodies, each having predetermined capacities, is updated throughout the simulation period.