Prof. J. George Shanthikumar
Professor, Purdue University
Talk:
Applications of Joint Stochastic Orders in Arrangement and Allocation
Abstract:
It is common in many applications that one faces the problem of allocating limited budget, resources or effort among different options (subsystems). Example of such include but are not limited to allocation of financial asset in investment, allocation of deductibles in insurance, allocation of compensation limits in insurance policy, allocation of inventory among different locations, allocation of effort to improve reliability in performability systems, and the allocation of spare parts in maintenance. In these problems one need to understand whether a seemingly "fair", as opposed to a seemingly "unfair," allocation would result in better profitability or system performance. For example, should one allocate more inventories to a location with a larger demand or one with a lower transportation cost, or should one impose a higher deductible to a riskier insured asset? Answers to such questions boils down to understanding the joint stochastic ordering in arrangement. In this study, we provide a general framework to model a system consisting of multiple subsystems. Each subsystem's performance depends on the allocation policy and some random parameters. Our interest is in identifying the conditions on the response function of the subsystems, the system performance function and the random parameters under which the random system performance as a function of the resource allocation has stochastic arrangement increasing property. This allows one to substantially reduce the number of allocations that needs to be searched to identify an optimal allocation (or directly identify an optimal arrangement) that maximizes the expected utility derived from the system response as a result of the resource allocation (or the arrangement).
(This presentation is based on the joint work, titled "Arrangement Increasing Resource Allocation," with Qi Annabelle Feng)
Biography:
Professor Shanthikumar joined the Krannert faculty in 2009. Prior to coming to Purdue, he was a Chancellor's Professor of Industrial Engineering and Operations Research at the University of California, Berkeley. His research interests are in integrated interdisciplinary decision making, model uncertainty and learning, production systems modeling and analysis, queueing theory, reliability, scheduling, semiconductor yield management, simulation stochastic processes, and sustainable supply chain management. He has written or cowritten more than 250 papers on these topics. He is a co-author (with John A. Buzacott) of the book Stochastic Models of Manufacturing Systems and a co-author (with Moshe Shaked) of the books Stochastic Orders and Their Applications.He was a co-editor of Flexible Services & Manufacturing Journal and is (or was) a member of the editorial boards of the Asia-Pacific Journal of Operations Research, IEEE Transactions on Automation Sciences and Engineering, IIE Transactions, International Journal of Flexible Management Systems, Journal of Discrete Event Dynamic Systems, Journal of the Production and Operations Management Society, Operations Research, Operations Research Letters, OPSEARCH, Probability in the Engineering and Information Sciences, and Queueing Systems: Theory and Applications.Dr. Shanthikumar developed a data-driven production planning tool for Intel. Through this data-driven model, he discovered several shopfloor level coordination between manufacturing and maintenance, which helped to significantly improve the working process performance. This study also led to a new theory in stochastic models that inspires a new stream of academic research.
