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TITLE: Performance guarantees of the long chain design in resource allocation
ABSTRACT:
We consider a class of resource allocation problems in which there are n capacitated resources and n demand types. The resources are flexible, where resource j can be used to fulfill both demand type j and j+1. This is known as the long chain design proposed by Jordan and Graves (1995), which has been an important concept in the design of sparse flexible processes. In this talk, we discuss the theoretical performance of the long chain in two different settings.
In the first setting, the resource allocation decisions are made after all the demand has realized. We obtain a distribution-free bound on the ratio of the expected unit sales of the long chain relative to that of full flexibility. In a special case with i.i.d. demand and uniform capacity, we are able to derive the bound in closed form. Our bound depends only on the mean and standard deviation of the random demand, but compares very well with the ratio that uses complete information of the demand distribution.
In the second setting, the demand arrives sequentially and reveals its type upon arrival, and the allocation decisions must be made in real time. We show that the long chain is still very effective even under simple myopic online allocation policies. In particular, we show that the expected total number of lost sales only depends on the number of resources n, and is independent of how large the market size is.
Bio
Xuan Wang is a fifth year doctoral candidate in the Operations Management group at Stern School of Business, New York University. Xuan’s primary research interest lies in the field of supply chain management, optimization and business analytics. Prior to joining Stern, Xuan received her Bachelor's degree in industrial engineering and operations research from Tsinghua University in 2011. During her junior year, Xuan also spent one semester in the H. Milton Stewart School of Industrial & Systems Engineering at Georgia Institute of Technology as an exchange student.
