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We formulate a Belief Propagation (BP) algorithm in the context of the capacitated minimum-cost network flow problem (MCF). Unlike most of the instances of BP studied in the past, the messages of BP in the context of this problem are piecewise-linear functions. We prove that BP converges to the optimal solution in pseudo-polynomial time, provided that the(More)
The MIT Faculty has made this article openly available. Please share how this access benefits you. Your story matters. Abstract Distributed, iterative algorithms operating with minimal data structure while performing little computation per iteration are popularly known as message-passing in the recent literature. Belief Propagation (BP), a prototypical(More)
The long chain has been an important concept in the design of flexible processes. This design concept, as well as other sparse designs, have been applied by the automotive and other industries as a way to increase flexibility in order to better match available capacities with variable demands. Numerous empirical studies have validated the effectiveness of(More)
We establish a convenient necessary and sufficient condition for a multiaffine real polynomial to be stable, and use it to verify that the half-plane property holds for seven small matroids that resisted the efforts of Choe, Oxley, Sokal, and Wagner [5]. In recent years, matroid theory has found connections with certain analytic properties of real(More)
We study a hybrid strategy that uses both process flexibility and inventory to mitigate risks of plant disruption. In this setting, a firm allocates inventory before disruption while facing demand uncertainties; demand is realized after disruption, and the firm schedules its production using process flexibility to minimize lost sales. This interplay between(More)
Sparse process flexibility and long chain has became an important concept in design flexible manufacturing systems since the seminal paper of Jordan and Graves (1995). In this paper, we study the performance of long chain in comparison to all designs with at most 2n edges over n supply and n demand nodes. We show that, surprisingly, long chain is not(More)