Optimal Resource Allocation under Uncertainty

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The goal of this research is to develop systematic algorithms and techniques for rapidly searching an optimal or near optimal solution of a resource allocation problem. The research method, the Nested Partitions (NP) method, will be extended and tested to solve resource allocation problems encountered by industry partners. Many resource allocation problems such as facility planning, job scheduling, pollution control, and portfolio management can be modeled as discrete stochastic optimization problems. Owing to the complexity inherent in these systems, the design of allocation and scheduling policies can be a formidable task. One key issue is the combinatorial explosion of alternatives normally leading to NP-complete optimization problems. Beyond "toy problems", computational complexity is an obstacle faced by even the most elegant and effective approaches developed for solving realistic problems. In the case of dynamic systems, the situation is exacerbated by the added elements of uncertainty, which further complicate such problems. It is expected that this development will exert both a practical and theoretical impact in the area of complex system design, control, evaluation and optimization. This research will allow the designer or manager to examine a large solution space to produce systems with predictable behavior which would prove to be cost effective and improve the quality of the systems. The research development will also provide a framework for solving many other stochastic optimization problems.