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In spite of the tremendous progress that has been attained by the scientific community on the sequencing and scheduling problems that underlie the operation of many technological applications, there is a remaining gap between the analytical insights and results offered by the existing scheduling theory and the solutions to the scheduling problems that are typically adopted in the industrial practice. The work undertaken in this project seeks to bridge this gap by tapping upon recent developments in the Supervisory Control of Resource Allocation Systems and Approximate Dynamic Programming. When combined, these two areas provide high-fidelity representations of the underlying dynamics and effective tools for developing (near-)optimal scheduling policies while explicitly managing the complexity that underlies the development and implementation of these policies. This write-up outlines the basic framework that supports the proposed approach and reports upon the current progress of the work.