Optimizing election logistics: A multi-period routing problem embedding time-dependent reward functions

With the 2024 US Presidential Election now concluded, the growing complexity of designing effective election campaigns has become clearer. Motivated by the logistical challenges associated with US election campaigns, we introduce the Reward-driven Multi-period Politician Routing Problem. It involves diverse politicians planning their campaigns over multiple days, considering constraints such as clustered locations, time-and location-dependent rewards, budget limits, mandatory rest days, and flexible daily routes that can be either open or closed, with starting and ending locations not known in advance. We model the problem as a mixed-integer linear program, complemented with several valid inequalities, and innovate by designing new subtour elimination techniques that jointly deal with open and closed paths. We developed 36 new benchmark instances tailored to the US presidential elections. To tackle large-sized instances, we develop a Sequential Route Construction Matheuristic that exploits the multi-period structure of the problem to provide efficient and effective solutions. We incorporate time-dependent reward profiles (concave, convex, linearly decreasing, linearly increasing, and periodic) into the objective function to capture diverse decision-making perspectives. Experimental results show interesting computational issues on the different tested models and the impact of the chosen reward profile on their performance.