Title: 

Two-Stage Stochastic Multi-Objective Linear Programming

Abstract: 

We consider a two-stage stochastic multi-objective linear program (TSSMOLP) which is a natural multi-objective generalization of the well-studied two-stage stochastic linear program. The second-stage recourse decision is governed by an uncertain multi-objective linear program whose solution maps to an uncertain second-stage nondominated set. The TSSMOLP then comprises the objective function, which is the Minkowsi sum of a linear term plus the expected value of the second-stage nondominated set, and the constraints, which are linear. Since the second-stage nondominated set is a random set, its expected value is defined through the selection expectation. The global Pareto set is defined as the collection of nondominated points in the image space of the TSSMOLP. We discuss properties of TSSMOLPs and the multifunctions that arise therein, as well as the implications of these properties for the development of TSSMOLP solution methods. We illustrate the TSSMOLP and its properties through an example in disaster relief planning.

This work is joint work with Akshita Gupta, Edwardson School of Industrial Engineering, Purdue University.

Bio: 

Susan R. Hunter is an associate professor in the Edwardson School of Industrial Engineering at Purdue University. Her research interests include theoretical and algorithmic aspects of stochastic optimization in the presence of multiple performance measures with emphasis on asymptotics, computation, and application. In 2016, she received an NSF CAREER Award to work on multi-objective simulation optimization; that is, multi-objective optimization in which the objective functions can only be observed with stochastic error as the output of a black-box Monte Carlo simulation oracle. Her published works have been recognized by the INFORMS Computing Society in 2011, by IISE Transactions in 2017, and by The Operational Research Society in 2021. She currently serves as Program Chair for the 2024 Winter Simulation Conference, on the Organizing Committee for SIAM Conference on Optimization (OP26), as Vice President / President Elect of the INFORMS Simulation Society, and as an associate editor for Operations Research, Journal of Optimization Theory and Applications, and Flexible Services and Manufacturing Journal.