This grant provides funding for the development of a linear programming (LP) based approach to solving diffusion control problems, which have proven practical and effective for modeling the stochastic nature of many processes including large call centers, assemble-to-order systems, semiconductor wafer fabrication lines, etc. One of the main advantages of diffusion models is that they provide a tractable way to find approximately optimal solutions when analyzing the problem in its exact form is difficult and intractable. Further, the use of a diffusion model as an approximation of the original system is often justified through heavy traffic limit theorems. The LP approach exploits 40 years of investments in theoretical developments and computational tools for linear optimization. It produces both a near-optimal policy describing appropriate actions to take in every circumstance and a lower bound on the best possible average cost. Formulating the problem as a linear program involves a novel discetization scheme and increasing the fidelity of the discretization produces asympotically optimal policies. The proposed approach promises to bring the practical computational power of LP to bear on the pressing and challenging problems of managing variability in the supply chain. The approach will initially be developed in an idealized setting in which a single-product, single-stage process is managed via drift controls and instantaneous controls at specified boundaries. After enhancing the fidelity of the drift control model by incorporating additional constraints and control regimens like singular control and impulse control, extensions to multiple products and stages will be addressed.
If successful, the approach will allow LP formulations of individual diffusion control problems to be knitted together and integrated into the larger multi-product, multi-stage supply chain models that address the complex strategic and operational challenges facing the semiconductor and other industries today. More effective tools for planning in stochastic environments will help improve product availability, capacity utilization and return on capital in a variety of industries. The proposed work will forge a stronger bridge between the largely separate research areas of stochastic control and deterministic optimization.
