Decision Sciences Seminar
Wednesday January 30, 2013
10:00AM - 11:30AM
Massachusetts Institute of Technology
Understanding the Effectiveness of Sparse Process Flexibility
The long chain has been an important concept in the design of sparse flexible processes. This design concept has been applied by various manufacturers as a way to increase flexibility in order to better match available capacities with variable demands. While numerous empirical studies have validated the effectiveness of the long chain, there is little theory that explains this effectiveness, except when the system size goes to infinity.
In this talk, we develop a theory that explains the effectiveness of the long chain in any finite size system. We study the sales of the long chain and other sparse flexibility designs under both stochastic and worst-case demands. Under stochastic demand, we establish two fundamental properties of the long chain, a supermodularity property and a decomposition property. These properties are then used to provide the first theoretical justification for several well-known observations in the process flexibility literature, and to derive new insights into designing flexible processes in large systems. Under worst-case demand, we propose the plant cover index and establish its relation with the worst-case sales. Applying this relation, we demonstrate that the long chain compares favorably with other sparse flexibility designs. Furthermore, motivated by the plant cover index, we propose a heuristic that finds sparse flexibility designs performing well numerically in both average-case and worst-case scenarios.