A methodological approach for determining eligible units in the 2010 Italian Agricultural Census

Censuses of Agriculture, Industry and other economical entities are periodically held in every nation. They are expensive, but essential for analyzing and understanding a large variety of economical aspects. A main problem, in similar Censuses, is deciding what should be included in the survey. From a conceptual point of view, there is a very large set of units (e.g. farms, companies, etc.) that could be surveyed. Surveying each one has a cost and represents a different portion of the whole situation that should be surveyed (e.g. the agricultural situation, the industrial situation, etc.). One would like to choose a subset of units producing the minimum total cost for being surveyed and representing at least a certain total portion of the whole situation. A combinatorial optimization structure is therefore present. Besides, the portion of information carried by each unit is not perfectly known in advance, since generally units were last surveyed only during the former Census, and things may have changed in the meanwhile. By using binary variables associated with the above units, the above selection problem is here modeled as a multidimensional binary knapsack problem. Since those models may reach in many cases very large dimensions, a separation procedure based on covers is also developed. In order to deal with the above uncertainty aspects, a sequence of selection problems are solved, so that reliable survey inclusion criteria can be computed. The procedure have been implemented in c++ and tested on real data from Agriculture Census. Results are very encouraging both from the computational and from the statistical point of view.