An Introduction to Temporal Optimisation using a Water Management Problem

Optimisation problems usually take the form of having a single or multiple objectives with a set of constraints. The model itself concerns a single problem for which the best possible solution is sought. Problems are usually static in the sense that they do not consider changes over time in a cumulative manner. Dynamic optimisation problems to incorporate changes. However, these are memoryless in that the problem description changes and a new problem is solved - but with little reference to any previous information. In this paper, a temporally augmented version of a water management problem which allows farmers to plan over long time horizons is introduced. A climate change projection model is used to predict both rainfall and temperature for the Murrumbidgee Irrigation Area in Australia for up to 50 years into the future. Three representative decades are extracted from the climate change model to create the temporal data sets. The results confirm the utility of the temporal approach and show, for the case study area, that crops that can feasibly and sustainably be grown will be a lot fewer than the present day in the challenging water-reduced conditions of the future.