Constructing the feasible space–time region of the Household Activity Pattern Problem

In this paper, a method of constructing the feasible region in space–time dimension of the well-known Household Activity Pattern Problem (HAPP) is developed. HAPP is an optimization model that generates an optimal set of full-day activity-travel decisions. Based on the definition of an activity and its spatial and temporal constraints, feasible space–time region for the completion of one activity is derived. Then, a full-day feasible space–time region is determined as an intersection of a set of feasible regions for activities to be performed on a given travel day. This feasible space–time region is shown to be consistent with the concept of space–time prism. An algorithm is developed for the construction of an activity-specific feasible space–time region for a network-based travel environment. The algorithm generates a set of time windows for each activity and for each node that later converts to link-based time windows of accessibility.