Optimal Sparse Designs for Process Flexibility (Yuan Zhou)

Abstract

We study the problem of how to design a sparse flexible process structure in a balanced and symmetrical production system to match supply with random demand more effectively. Our goal is to provide a sparsest design to achieve (1-e)-optimality relative to the fully flexible system. In a system with n plants and n products, Chou et al. proved that there exists a graph expander with O(n/e) arcs to achieve (1-e)-optimality for every demand realization.

In this paper, we introduce a new concept called probabilistic graph expanders. We prove that a probabilistic expander with O(n ln(1/e)) arcs guarantees (1-e)-optimality with high probability (w.h.p.). On the lower bound side, we show any structure needs O(n ln(1/e)) arcs to achieve (1-e)-optimality w.h.p. We also discuss how to extend our optimal design to general production systems with n plants, m products, and non-identically distributed supplies and demands.

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