A multi-day activity-based inventory routing model with space–time–needs constraints

We extend activity routing problems to consider ‘needs’ satisfaction over multiple days using an inventory routing problem concept. The resulting inventory-based selective household activity routing problem allows activity type choice, duration choice, activity destination choice, departure time, and scheduling of activities, all within space–time–needs constraints. A Lagrangian relaxation-based algorithm is proposed to solve the model for multiple days. A computational study is conducted. The model can measure several effects: heterogeneity in impacts of travel time changes on different days; the use of dual price as a threshold when needs play a role in the utility maximisation objectives; the possibility for activity participation consolidation due to increased travel time; and non-uniform impacts of travel time increase on utilities across a heterogeneous population. Comparison of the algorithm's performance against a commercial package showed average objective values that differed by only 1.8% or less.