We develop a computational approach for an optimal base-stock policy of an inventory system with continuous demands. The system is reviewed periodically for a finite horizon. The problem is formulated into a dynamic programming. By numerical calculations for the multi-dimensional integrals in the dynamic programming, lower and upper bounds of the minimal system cost are obtained. Based on these bounds, an estimation of the minimal system cost is given. An approximation optimal policy is also obtained, with an evaluation for its quality through the relative error of the system cost. An example demonstrates the methodology.
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