In single period setting, we examine the optimal policies when the acquisition cost is piecewise linear convex as well as linear. We show that a simple sorting policy exists when the acquisition cost is linear. We study the multi-period problem and prove that the unique optimal policies in multiple periods exist. While the remanufacturer may decide to keep inventory for final products only or he may decide to keep inventory for raw cores as well, we illustrate the algorithm to solve the optimization problem. For linear acquisition cost problems in both single and multiple period problems, we show that they can be solved as general inventory problems which may include setup costs, backlogging and uncertain demand.