In this paper an original simulation and optimization model for flat solar collector coupled with a flat bottom reflector has been developed. The problem of simulation and optimization for such system is essential in order to find the proper configuration of the reflector able to obtain the expected maximum efficiency of the whole system. The proposed simulation model analytically determines the solar energy on the collector-reflector system and therefore the optimization model estimates the optimal values of the design parameters. A new comprehensive formulation of the shadowing and irradiating level on the collector, able to take into account the finite length geometry with variable dimensions, is presented. The number and the value of the angular positions, the time periods over which the angular positions should be adjusted, the size, the aspect ratio, between the length and the width of the reflector, and the overhangs are parameters treated simultaneously with a global optimization procedure. The model is integrated with an original scheme of optimization where energetic and economic aspects are both taken into account. The simulations results of the study reveal the optimal number of angular adjustments per year, the existence of a small optimal neighborhood of the aspect ratio and the optimal size of the reflector, for which the maximum reduction of the payback time of the augmented system compared to its reference collector is achieved. The results presented in the study are related to the solar data of Italian latitude, but they can be easily extended for any geographical location.