2015 Informs Annual Meeting

WB12

INFORMS Philadelphia – 2015

WB12 12-Franklin 2, Marriott Optimization Stochastic II Contributed Session Chair: Ruediger Schultz, Prof., University of Duisburg-Essen, Faculty of Mathematics, Thea-Leymann-Str. 9, Essen, D-45127, Germany, ruediger.schultz@uni-due.de 1 - Sampling-based Approximation Schemes for Capacitated Stochastic Inventory Control Models Wang Chi Cheung, Graduate Student, Massachusetts Institute of Technology, 77 Massachusetts Ave, Cambridge, MA, 02139, United States of America, wangchimit@gmail.com, David Simchi-levi We study the multi-period capacitated stochastic inventory control problem in a data-driven setting, where the demand distributions can only be accessed through samples. We apply the Sample Average Approximation (SAA) method, and establish a polynomial upper bound on the number of samples needed for achieving near-optimality. However, the underlying SAA problem is #P-hard. Thus we provide a polynomial time approximation scheme, which involves a subgradient sparsification procedure. 2 - Competitive Capacity Investment under Uncertainty Xishu Li, PhD Candidate, Erasmus University, Dept. Technology&Operations Management, Burgemeester Oudlaan 50, Rotterdam, Ro, 3062 PA, Netherlands, x.li@rsm.nl, Rob Zuidwijk, Rommert Dekker, Rene De Koster Our research explores a fleet capacity investment problem under market uncertainty. We study how competition between firms affects investment strategies, and investigate the optimal investment policy. Here, we focus on a single vessel type with the intention to extend our results to also incorporate green vessels. 3 - ADMM for Two-Stage Stochastic Programs with Quadratic Objective Function Sebastian Arpon, Universidad Adolfo Ibañez, Diagonal Las Torres 2640, Peñalolen, Santiago, Chile, sebarpon@gmail.com, Tito Homem-de-mello, Bernardo Pagnoncelli We discuss a decomposition method for two-stage stochastic programs with quadratic objective functions. Our algorithm is based on the Alternating Direction Method of Multipliers (ADMM) developed in the literature, and decomposes the problem by scenarios. Some attractive features of the algorithm are the low computational cost per iteration and its suitability for parallelization. We discuss some aspects related to convergence of the method and present numerical results to illustrate the ideas. 4 - The Dynamic Multi-newsvendor Problem Zhaohu Fan, PhD Student, The Pennsylvania State University, 244 Leonhard Building, State College, PA, 1680001, United States of America, zxf109@psu.edu, Terry Friesz, Yiou Wang, Tao Yao We articulate a dynamic model of newsvendors where a set of service providers form an oligopoly that is equilibrium tending.The price setting mechanism involving the providers resembles the replicator dynamics of evolutionary game theory. We show that generalization of the news vendor problem to a Cournot- Nash differential game based on replicator dynamics in a stochastic setting takes the form of a stochastic differential variational inequality. 5 - Stochastic Programming in Gas Transportation using Symbolic Computation Ruediger Schultz, Prof., University of Duisburg-Essen, Faculty of Mathematics, Thea-Leymann-Str. 9, Essen, D-45127, Germany, ruediger.schultz@uni-due.de Nomination validation, i.e., to decide technical feasibility of a transportation order with balanced in- and output, is among the challenges in daily operation of gas networks. We address the problem in the steady-state case with uncertain orders. In particular we provide parametric solution procedures for polynomial equations resulting from Kirchhoff’s Laws based on insights and procedures from computational algebra.

1 - On the Adaptivity Gap in Two-stage Robust Linear Optimization under Constraints Vineet Goyal, Columbia University IEOR department, 500 West 120th Street, 304 Mudd, New York, NY, 10027, United States of America, vg2277@columbia.edu, Brian Lu We consider two-stage adjustable robust linear optimization problem with uncertain constraint coefficients that models many important applications including resource allocation with uncertain requirements. The adjustable problem is hard to approximate within a factor better than O(log n) in general. We show that the static solution gives a O(log^2 n)-approximation for the adjustable robust problem. Surprisingly, this is nearly the best possible approximation for the problem. 2 - A Robust Optimization Approach to Optimizing Expected Performance Nataly Youssef, MIT, 20 Palermo Street, Cambridge, MA, United States of America, youssefn@mit.edu We propose a tractable approach for optimizing the expected performance of stochastic systems via robust optimization. We model uncertainty via parameterized polyhedral sets inspired by probabilistic limit laws and characterized by variability parameters. We then cast the performance optimization problem as a robust optimization problem. We demonstrate the tractability and accuracy of our approach via an inventory management example. 3 - Resource Allocation under Coherent Distortion Risk Measures Chaitanya Bandi, Kellogg School of Management, Northwestern University, Evanston, IL, United States of America, c-bandi@kellogg.northwestern.edu, Paat Rusmevichientong We consider high dimensional resource allocation problems faced by a decision maker with a sophisticated risk attitude modeled by a fairly general risk measure known as a coherent distorted risk measure (CDRM) which encompasses many popular risk measures such as spectral risk measures and law-invariant coherent risk measures. We address the problem of tractability and obtain explicit closed form solution for the this problem while identifying new properties of the optimal solution. Risk-Averse Control of Markov Systems Sponsor: Optimization/Optimization Under Uncertainty Sponsored Session Chair: Andrzej Ruszczynski, Rutgers University, 100 Rockafeller Road, Rutgers Business School, Piscataway, NJ, 08854, United States of America, rusz@business.rutgers.edu 1 - Risk-averse Control of Markov Chains in Discrete and Continuous Time Andrzej Ruszczynski, Rutgers University, 100 Rockafeller Road, We shall consider risk-averse control problems for controlled Markov chains in discrete and continuous time. The concept of a dynamic risk measure and its of time consistency will be resined. We shall derive optimality conditions and discuss solution methods for discrete-time problems. For continuous-time problems, we shall derive the structure of time-consistent Markov risk measures and optimality conditions. 2 - Process-based Risk Measures for Observable and Partially Observable Discrete-time Controlled Systems Jingnan Fan, Rutgers University, 100 Rockafeller Road, Rutgers Business School, Piscataway, NJ, 08854, United States of America, jingnan.fan@rutgers.edu, Andrzej Ruszczynski For controlled discrete-time stochastic processes we introduce process-based dynamic risk measures to measure risk of processes. We also introduce a new concept of conditional stochastic time consistency and we derive the structure of risk measures enjoying this property. We show that they can be equivalently represented by a collection of static law-invariant risk measures on the space of functions of the state space. This structure can be applied to Markov controlled problems, including POMDP. 3 - Risk-averse Optimal Learning for Clinical Trial Design We formulate the risk-averse optimal learning problem for the exploration vs. exploitation dilemma in clinical trial design. We establish the class of logistic toxicity models leading to log-concave posteriors in the Markov model. We then offer risk-averse approximate dynamic programming methods of the resulting single- and multistage problems. Finally, we compare performance of prominent policies for this problem class in terms of multivariate stochastic dominance. Rutgers Business School, Piscataway, NJ, 08854, United States of America, rusz@business.rutgers.edu Curtis Mc Ginity, Rutgers University, Piscataway, NJ, United States of America, curtis.mcginity@rutgers.edu WB14 14-Franklin 4, Marriott

WB13 13-Franklin 3, Marriott

Robust Optimization: Theory and Applications Sponsor: Optimization/Optimization Under Uncertainty Sponsored Session Chair: Chaitanya Bandi, Kellogg School of Management, Northwestern University, Evanston, United States of America, c-bandi@kellogg.northwestern.edu

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