J. George Shanthikumar

Bio: J. George Shanthikumar is an academic researcher from Purdue University. The author has contributed to research in topics: Queueing theory & Random variable. The author has an hindex of 48, co-authored 215 publications receiving 10194 citations. Previous affiliations of J. George Shanthikumar include University of California, Berkeley & University of Cambridge.

Stochastic orders and their applications

Abstract: General Theory. Applications in Statistics. Applications in Biology. Applications in Economics. Applications in Operations Research. Applications in Reliability Theory.

Stochastic models of manufacturing systems

Abstract: 1 Discrete Part Manufacturing Systems 2 Evolution of Manufacturing System Models: An Example 3 Single Stage 'Produce-to-Order' Systems 4 Single Stage 'Produce-to-Stock' Systems 5 Flow Lines 6 Transfer Lines 7 Dynamic Job Shops 8 Flexible Machining Systems 9 Flexible Assembly Systems 10 Multiple Cell Manufacturing Systems 11 Unresolved Issues: Directions for Future Research Appendix A: Standard Probability Distributions Appendix B: Some Notions of Stochastic Ordering Appendix C: Nonparametric Families of Distributions

Convex separable optimization is not much harder than linear optimization

Abstract: The polynomiality of nonlinear separable convex (concave) optimization problems, on linear constraints with a matrix with “small” subdeterminants, and the polynomiality of such integer problems, provided the inteter linear version of such problems ins polynomial, is proven. This paper presents a general-purpose algorithm for converting procedures that solves linear programming problems. The conversion is polynomial for constraint matrices with polynomially bounded subdeterminants. Among the important corollaries of the algorithm is the extension of the polynomial solvability of integer linear programming problems with totally unimodular constraint matrix, to integer-separable convex programming. An algorithm for finding a e-accurate optimal continuous solution to the nonlinear problem that is polynomial in log(1/e) and the input size and the largest subdeterminant of the constraint matrix is also presented. These developments are based on proximity results between the continuous and integral optimal solutions for problems with any nonlinear separable convex objective function. The practical feature of our algorithm is that is does not demand an explicit representation of the nonlinear function, only a polynomial number of function evaluations on a prespecified grid.

Relative Entropy, Exponential Utility, and Robust Dynamic Pricing

Abstract: In the area of dynamic revenue management, optimal pricing policies are typically computed on the basis of an underlying demand rate model. From the perspective of applications, this approach implicitly assumes that the model is an accurate representation of the real-world demand process and that the parameters characterizing this model can be accurately calibrated using data. In many situations, neither of these conditions are satisfied. Indeed, models are usually simplified for the purpose of tractability and may be difficult to calibrate because of a lack of data. Moreover, pricing policies that are computed under the assumption that the model is correct may perform badly when this is not the case. This paper presents an approach to single-product dynamic revenue management that accounts for errors in the underlying model at the optimization stage. Uncertainty in the demand rate model is represented using the notion of relative entropy, and a tractable reformulation of the “robust pricing problem” is obtained using results concerning the change of probability measure for point processes. The optimal pricing policy is obtained through a version of the so-called Isaacs' equation for stochastic differential games, and the structural properties of the optimal solution are obtained through an analysis of this equation. In particular, (i) closed-form solutions for the special case of an exponential nominal demand rate model, (ii) general conditions for the exchange of the “max” and the “min” in the differential game, and (iii) the equivalence between the robust pricing problem and that of single-product revenue management with an exponential utility function without model uncertainty, are established through the analysis of this equation.

Markov Chains and Stochastic Stability

Abstract: Meyn & Tweedie is back! The bible on Markov chains in general state spaces has been brought up to date to reflect developments in the field since 1996 - many of them sparked by publication of the first edition. The pursuit of more efficient simulation algorithms for complex Markovian models, or algorithms for computation of optimal policies for controlled Markov models, has opened new directions for research on Markov chains. As a result, new applications have emerged across a wide range of topics including optimisation, statistics, and economics. New commentary and an epilogue by Sean Meyn summarise recent developments and references have been fully updated. This second edition reflects the same discipline and style that marked out the original and helped it to become a classic: proofs are rigorous and concise, the range of applications is broad and knowledgeable, and key ideas are accessible to practitioners with limited mathematical background.

Lectures on Stochastic Programming: Modeling and Theory

Abstract: List of notations Preface to the second edition Preface to the first edition 1. Stochastic programming models 2. Two-stage problems 3. Multistage problems 4. Optimization models with probabilistic constraints 5. Statistical inference 6. Risk averse optimization 7. Background material 8. Bibliographical remarks Bibliography Index.

On the Value of Mitigation and Contingency Strategies for Managing Supply Chain Disruption Risks

Abstract: We study a single-product setting in which a firm can source from two suppliers, one that is unreliable and another that is reliable but more expensive. Suppliers are capacity constrained, but the reliable supplier may possess volume flexibility. We prove that in the special case in which the reliable supplier has no flexibility and the unreliable supplier has infinite capacity, a risk-neutral firm will pursue a single disruption-management strategy: mitigation by carrying inventory, mitigation by single-sourcing from the reliable supplier, or passive acceptance. We find that a suppliers percentage uptime and the nature of the disruptions (frequent but short versus rare but long) are key determinants of the optimal strategy. For a given percentage uptime, sourcing mitigation is increasingly favored over inventory mitigation as disruptions become less frequent but longer. Further, we show that a mixed mitigation strategy (partial sourcing from the reliable supplier and carrying inventory) can be optimal if the unreliable supplier has finite capacity or if the firm is risk averse. Contingent rerouting is a possible tactic if the reliable supplier can ramp up its processing capacity, that is, if it has volume flexibility. We find that contingent rerouting is often a component of the optimal disruption-management strategy, and that it can significantly reduce the firms costs. For a given percentage uptime, mitigation rather than contingent rerouting tends to be optimal if disruptions are rare.