In a world of ever-changing travel behavior and ever-increasing modal options, is vital to have integrated models that could capture the interactions between supply and demand layers of travel. Addressing this need, we propose three different versions of network representation and mathematical models for the activity-based vehicle routing problem to connect activity-travel graphs of passengers (demand layer) to spatio-temporal networks of vehicles (supply layer). Versions I and II are arc-based, while version III is path-based. In version I, we introduce the concept of activity-travel graphs for passengers. For vehicles, we construct space–time networks and add a new dimension, called “under-service state”, to track the execution status of trip requests at any location and time. In version II, we reduce the complexity of the network structure by eliminating the state dimension and some other modifications in the structure of the passengers’ and vehicles’ network. Although both versions can capture various behavioral constraints of the activity-based vehicle routing problem (e.g., mandatory and optimal activities, duration of activities, chain of activities, preferred starting and ending times of activities), due to the high level of complexity of the network structure, both versions can only solve small-sized problems. To tackle the computational complexity, we propose a path-based network representation in version III, and to make a balance between the disutility of passengers and vehicles, we present a tolled user equilibrium problem. Mathematical models are coded in C and GAMS and implemented on real-world Phoenix regional transportation network with more than 39 million trip requests, which demonstrate the effectiveness of the proposed solution for the original and restricted master problems.

在一个不断变化的旅行行为和不断增加的模式选择的世界中，拥有能够捕获旅行的供需层之间相互作用的集成模型至关重要。为满足此需求，我们针对基于活动的车辆路线选择问题提出了三种不同版本的网络表示形式和数学模型，以将乘客的活动行程图（需求层）连接到车辆的时空网络（供应层）。版本I和II是基于弧的，而版本III是基于路径的。在版本I中，我们介绍了乘客活动旅行图的概念。对于车辆，我们构建了时空网络，并添加了一个新的维度，称为“服务不足状态”，以跟踪在任何位置和时间的旅行请求的执行状态。在第二版中 我们通过消除乘客和车辆网络的状态维度和其他一些修改来降低网络结构的复杂性。尽管两个版本都可以捕获基于活动的车辆路径问题的各种行为约束（例如，强制性活动和最佳活动，活动持续时间，活动链，活动的首选开始和结束时间），因为网络结构，这两个版本只能解决小型问题。为了解决计算的复杂性，我们在版本III中提出了基于路径的网络表示形式，并且为了平衡乘客和车辆的无用性，我们提出了收费用户均衡问题。