For most of the last century, the role of private and public sectors in the infrastructure projects were clear. For instance, public authorities were generally in charge of financing and building new infrastructures. Over the last decade, that position has begun to change. Faced with pressure to reduce public sector debt and, at the same time, expand and improve public facilities, governments and public authorities have looked to private sector finance, and have invited private sector entities to enter into long-term contractual agreements which may take the form of construction or management of public sector infrastructure facilities by the private sector entity, or the provision of services (using infrastructure facilities) by the private sector entity to the community on behalf of a public sector body. This paper deals with the new issues raised by the public-private partnerships system or, more generally, by any system in which the new infrastructure is partially financed by its users. Is there, in this case, a new economic rationality of public authorities? Particularly, is there an optimal way to rank projects? This paper discusses the choice by the public authority of the most efficient investing programme in irrigation water infrastructures. More specifically, it studies the optimal ranking of project implementation when these projects are partially self-financed by their own revenues. In this case, the optimal investment programme must be defined under a constraint of annual subsidies. This paper demonstrates that the optimal ranking is not necessarily the ranking of decreasing socioeconomic internal rate of return. This counter-intuitive result can be demonstrated by a general approach. Analytical calculations are not useful in this discrete problem because each programme is an ordered subset of projects. Therefore, there is no continuous variation linking the various programmes and the usual tools of optimization, such as differential calculus, are useless. Thus, we adopt here a discrete optimization analysis based on standard techniques in the physics area, such as Monte Carlo sampling.