This paper is organized as follows. In Section 2, weanalyzethe single-item (r, Q) system with limited resource under all-units discount. In Section 3, based on the cost function properties a search region for the optimal policy is obtained. Section 4 presents an algorithm with its modification based on one-dimensional search procedure to find an optimal solution efficiently. Section 5 provides numerical evaluation of the efficiency and sensitivity of the presented algorithms. Section 6 contains concluding remarks.