Approximated Optimal Solution for Economic Manufacturing Quantity Model

This study investigates the use of the bisection algorithm in inventory models to obtain an approximated optimal solution for the economic manufacturing quantity (EMQ) problem under imperfect production conditions. The objectives are threefold. First, we utilize refined estimations of exponential functions to provide tighter lower and upper bounds for the bisection algorithm. Second, we propose three analytical improvements that simplify the solution process, each supported by rigorous proofs. Third, we incorporate recent results from the literature to further enhance the accuracy of exponential function approximations within the EMQ model. Our improved bounding approach significantly reduces the search interval needed by the bisection method and yields an approximate solution that attains a total cost very close to the true optimum. In a numerical example, the proposed method shrinks the initial search range by over 99% compared to prior methods and achieves a production run length that produces a near-minimal average total cost. These findings demonstrate the effectiveness of the enhanced bounds and provide practical insights for inventory models with imperfect processes.