The field of AI has been a topic of interest for the better part of a century, where the goal is to have computers mimic human behaviour. Researchers have incorporated AI in different problem domains, such as autonomous driving, game playing, diagnosis and security. This paper concentrates on a subfield of AI, i.e., the field of Learning Automata (LA), and to use its tools to tackle a problem that has not been tackled before using AI, namely the problem of the optimally scheduling and parking of elevators. In particular, we are concerned with determining the Elevators’ optimal “parking” location. In this paper, we specifically work with the Single (We consider the more complicated multi-elevator problem in a forthcoming paper.) Elevator Problem (SEP), and show how it can be extended to the solution to Elevator-like Problems (ELPs), which are a family of problems with similar characteristics. Here, the objective is to find the optimal parking floors for the single elevator scenario so as to minimize the passengers’ Average Waiting Time (AWT). Apart from proposing benchmark solutions, we have provided two different novel LA-based solutions for the single-elevator scenario. The first solution is based on the well-known $$L_{RI}$$ scheme, and the second solution incorporates the Pursuit concept to improve the performance and the convergence speed of the former, leading to the $$PL_{RI}$$ scheme. The simulation results presented demonstrate that our solutions performed much better than those used in modern-day elevators, and provided results that are near-optimal, yielding a performance increase of up to 80%.