From Linear Programming Model to Mixed Integer Linear Programming Model for the Simultaneous Optimisation of Water Allocation and Reservoir Location in River Systems

The allocation of water flowing through a river-with-reservoirs system to optimally meet spatially distributed and temporally variable demands can be conceived as a Network Flow Optimisation (NFO) problem and addressed by Linear Programming (LP). In this paper we present an extension of the strategic NFO-LP model to simultaneously optimise the allocation of water and the location of one or more reservoirs. The applicability of the MILP model has been illustrated by applying it to a hypothetical river network configuration consisting of seven candidate reservoir nodes and seven demand nodes, and by comparing the outcome (water levels in selected reservoir, penalties) with the values obtained by the original LP-model for the same network with six reservoirs present.