Combined aggregation and column generation for land-use trade-off optimisation

In this paper we developed a combination of aggregation-disaggregation technique with the concept of column generation to solve a large scale LP problem originating from land use management in the Australian agricultural sector. The problem is to optimally allocate the most profitable land use activities including agriculture, carbon sequestration, environmental planting, bio-fuel, bio-energy, etc., and is constrained to satisfy some food demand considerations and expansion policies for each year from 2013 to 2050. In this research we produce a higher resolution solution by dividing Australia’s agricultural areas into square kilometer cells, which leads to more than thirteen million cells to be assigned, totally or partially, to different activities. By accepting a scenario on agricultural products' return, carbon related activities, future energy prices, water availability, global climate change, etc. a linear programming problem is composed for each year. However, even by using a state of the art commercial LP solver it takes a long time to find an optimal solution for one year. Therefore, it is almost impossible to think about simultaneous scenarios to be incorporated, as the corresponding model will become even larger. Based on the properties of the problem, such as similar economical and geographical properties of nearby land parcels, the combination of clustering ideas with column generation to decompose the large problem into smaller sub-problems yields a computationally efficient algorithm for the large scale problem.