Over the last few years, many studies (WAES, WEC, CIA, oil companies, etc.) have popularized the idea that world oil production will reach a maximum in the 1980's or 1990's and progressively decline. If cumulative production up to the maximum is calculated and compared to the remaining resources to be recovered or produced (taken from the WEC Delphi Study, for instance) it is possible to assume other types of evolution for world oil production as well, in particular a plateau extending over a few decades. Because of the continuing importance of oil in the world economy, such an evolution would be far more desirable than a prompt decline. But of course it is important to assess whether this is even possible and/or realistic. The IREP model (IIASA Resources, Exploration and Production model) has essentially been designed, in the initial version which is presented here, to explore such a possibility. Preliminary ideas for the resource model came from the Enerdym model (which was developed with Igor Zimin), especially the conceptual aspects of describing the "life" of a resource, from its initial status of "speculative resource" to its possible production. The IREP model is composed of a number of submodels: resource assessment (the most developed to date), an exploration submodel primarily aimed at obtaining an idea of the effort necessary (drilling, investment, etc.) to discover the assumed resources, and a production submodel directly linked to the exploration submodel but allowing the examination or various scenarios influenced by politico-economic decisions. In addition, the IREP model can also be used as a sensitivity analysis tool to explore how changes in some parameters -- generally linked to the progress of exploration and/or knowledge of petroleum prospects or basins -- can influence oil resources and their future production potential. As such, this model is not only a tool which can be used in a preliminary way for forecasting or assessing, but also a working tool for enabling a better understanding of world oil assessment. The resource assessment submodel has been developed in detail and tested with an application case. Results -- although preliminary -- are encouraging, and it was thought that this work could usefully be presented and offered for discussion. The input data for the application case will be refined, and more importance should be attached to the potential validity of the approach than to the first results, shown here in a sample run.