The process of awarding a public contract to the most economically advantageous tender (according to the LCSP 2007) when taking more criteria into account besides price, is a complex task. The law specifies that the criteria and their weighls, as well as how to value the bidders according to these criteria have to be determined, following the principies of transparency and equality among bidders, In this paper we propase the use of the Analytic Network Process (ANP) to help the technicians, who must make reports, to make the process more systematic, transparent and traceable, This method allows to weight the decision criteria, which are included in the tender documents, to value each of the altematives and to prioritize the tenders, in a consistent and scientifically way. The method is applied to a case study involving the award of the development and maintenance of a software application for managing patient appointment request.