Stochastic Multi-Objective Multi-Trip AMR Routing Problem with Time Windows

In recent years, with the rapidly aging population, alleviating the pressure on medical staff has become a critical issue. To improve the work efficiency of medical staff and reduce the risk of infection, we consider the multi-trip autonomous mobile robot (AMR) routing problem in a stochastic environment. Our goal is to minimize the total expected operating cost and maximize the total service quality for patients, ensuring that each route violates the vehicle capacity and the time window with only a minimal probability. The travel time of AMRs is stochastically affected by the surrounding environment; the demand for each ward is unknown until the AMR reaches the ward, and the service time is linearly related to the actual demand. We developed a population-based tabu search algorithm (PTS) that combines the genetic algorithm with the tabu search algorithm to solve this problem. Extensive numerical experiments were conducted on the modified Solomon instances to demonstrate the efficiency of the PTS algorithm and reveal the impacts of the confidence level on the optimal solution, providing insights for decision-makers to devise delivery schemes that balance operating costs with patient satisfaction.