Stochastic user equilibrium in the presence of state dependence

We consider the following two state-dependent effects at the level of route choice: inertia to change and, as a consequence of experience, lower perception variance for the currently used route. A heteroscedastic extreme value model embodying heterogeneity across alternatives in the mean of the random terms is used. Estimations based on stated preference data confirm the presence of both state-dependent effects. We introduce a new class of stochastic user equilibrium (SUE) models that take state-dependent effects into account. The class includes conventional SUE as special case. The equilibrium conditions are formulated as fixed-point states of deterministic day-to-day assignment processes. At the equilibrium (1) no user can improve her/his utility by unilaterally changing route, and (2) if each user shifts from her/his current route to her/his newly chosen route the observed route flows do not change. The existence of the equilibrium is guaranteed under usually satisfied conditions. A modified method of successive averages is proposed for solution. Examples related to a two arc network and to the Nguyen-Dupuis network illustrate the model

Distributionally robust mixed integer linear programs: Persistency models with applications

10.1016/j.ejor.2013.07.009European Journal of Operational Research2333459-473EJOR

Choice prediction with semidefinite optimization when utilities are correlated

IEEE Transactions on Automatic Control57102450-2463IETA

Convex Optimization and Online Learning: Their Applications in Discrete Choice Modeling and Pricing

University of Minnesota Ph.D. dissertation. May 2018. Major: Industrial and Systems Engineering. Advisors: Shuzhong Zhang, Zizhuo Wang. 1 computer file (PDF); ix, 129 pages.The discrete choice model has been an important tool to model customers' demand when facing a set of substitutable choices. The random utility model, which is the most commonly used discrete choice framework, assumes that the utility of each alternative is random and follows a prescribed distribution. Due to the popularity of the random utility model, the probabilistic approach has been the major method to construct and analyze choice models. In recent years, several choice frameworks that are based on convex optimization are studied. Among them, the most widely used frameworks are the representative agent model and the semi-parametric choice model. In this dissertation, we first study a special class of the semi-parametric choice model - the cross moment model (CMM) - and reformulate it as a representative agent model. We also propose an efficient algorithm to calculate the choice probabilities in the CMM model. Then, motivated by the reformulation of the CMM model, we propose a new choice framework - the welfare-based choice model - and establish the equivalence between this framework and the other two choice frameworks: the representative agent model and the semi-parametric choice model. Lastly, motivated by the multi-product pricing problem, which is an important application of discrete choice models, we develop an online learning framework where the learning problem shares some similarities with the multi-product pricing problem. We propose efficient online learning algorithms and establish convergence rate results for these algorithms. The main techniques underlying our studies are continuous optimization and convex analysis