This paper focuses on a real case of connection of subsea oil wells to offshore platforms using pipe laying support vessels. The objective of this study is to maximize the oil production curve through an optimized use of the outsourced fleet. Specific features of this scenario are considered, such as technical constraints of each vessel, the availability of the vessels, materials for connection, and the end of the previous phase, called completion. A mixed integer linear programming model is developed considering several constraints that structure this complex situation, among which a relevant characteristic of the problem: the increase of the production curve using injection wells to fight the natural decline of producing wells over time. This mathematical model was tested in small computational instances, showing adequate behavior, which demonstrates that it faithfully represents the situation portrayed and can be used, combined with more advanced computational resources, to achieve better results.