Modeling User Responses to Pricing: Simultaneous Route and Departure Time Network Equilibrium with Heterogeneous Users

In a previous contribution, the authors showed how to incorporate user heterogeneity in determining equilibrium route choices in a network in response to pricing. Presented here is a generalization of that framework to incorporate joint consideration of route and departure time as well as heterogeneity in a wider range of behavioral characteristics. A multicriterion simultaneous route and departure time user equilibrium (MSRDUE) model is presented, along with a simulation-based algorithm intended for practical network applications. The model explicitly considers heterogeneous users with different values of time (VOTs) and values of (early or late) schedule delay (VOESDs or VOLSDs) in their joint choice of departure times and paths characterized by a set of trip attributes that include travel time, out-of-pocket cost, and schedule delay cost. The problem is formulated as an infinite-dimensional variational inequality problem and solved by a column generation-based algorithmic framework that embeds (a) an extreme nondominated alternative-finding algorithm to obtain the VOT, VOESD, and VOLSD breakpoints that define multiple user classes and the associated least trip cost (joint departure time and path) alternative for each user class; (b) a traffic simulator to capture traffic flow dynamics and determine travel costs experienced; and (c) a path-swapping multiclass alternative flow-updating scheme to solve the restricted multiclass SRDUE problem defined by a subset of feasible alternatives. Application to an actual network illustrates the properties of the algorithm and underscores the importance of capturing user heterogeneity and temporal shifts in the appraisal of dynamic pricing schemes.