Artificial intelligence is increasingly being used in various fields, including the management of hazardous medical waste. Medical waste poses an economic burden and a risk to public health, and it should be disposed of with care, preferably in areas far from residential areas. Data was collected on waste generated by 15 government hospitals in Menoufia Governorate and a single disposal site in Kafr Dawood, along with a central collection point for waste transport vehicles. This study addresses the issue of limited-capacity vehicle routing, which is considered a complex problem (NP-hard). Specific vehicles are designated to collect waste from hospitals and transport it to the disposal center, with the goal of finding the shortest route while maximizing the vehicle's capacity, which is limited to three tons. Reinforcement learning techniques were developed, treating the vehicle as an agent trained to choose the shortest, least costly route between hospitals. The SARSA algorithm was implemented and improved. Solutions include SARSA, Dijkstra, knapsack dynamic programming, and hybrid approaches that combine SARSA with Dijkstra and SARSA with knapsack dynamic programming. The result shows that the hybrid approach between SARSA and knapsack dynamic programming is the most effective, as it reduces the number of vehicles used for waste transport and maximizes the vehicle's capacity, determining the shortest routes between all hospitals. Finally, transportation costs were calculated to complete the mathematical model for medical waste management.