This study considers an original equipment manufacturer (OEM) who produces a single kind of new product, and collects the end-of-use cores for remanufacturing in a closed-loop system. The decision problem facing the OEM is to determine the selling prices for both new and remanufactured versions of the same product, and the collection effort devoted to acquire the cores. Key features of the underlying problem include supply constrained from the reversed logistics and finite multi-period product life cycle, i.e. the product will be phased out after a finite number of periods in the market. This study formulates the problem using Lagrangian relaxation technique, and proposes an iterative search algorithm for solving the problem. Due to its complexity involved with high-dimensional matrix and dynamic nature, an adaptive search scheme is also developed using genetic algorithms. Numerical results reveal that the solutions generated by GAs are optimal in small-sized problems, e.g. in a two-period scenario, and are near optimal in median to large-sized problems, e.g. in a four-period scenario. Further analysis reveals that the decisions depend critically on the phases of product life cycle.