A Periodic Traveling Politician Problem with Time-Dependent Rewards

Abstract

The Periodic Traveling Politician Problem (PTPP) deals with determining daily routes for a party leader who holds meetings in various cities during a campaign period of $\tau$ days. On a graph with static edge costs and time-dependent vertex profits, PTPP seeks a closed or open tour for each day. The objective is the maximization of the net benefit defined as the sum of rewards collected from meetings in the visited cities minus the traveling costs normalized into a compatible unit. The reward of a meeting in a city are linearly depreciated according to the meeting date and recency of the preceding meeting in the same city. We propose a MILP formulation in which we capture many real-world aspects of the PTPP.