In recent years, due to the globalization of the market and the expansion of e-commerce, logistics optimization attracts keen interest from manufacturing companies and service providers. The service area expands wider and the number of customers increases rapidly, thus logistics service providers need to determine the customer assignments and the routes for their trucks considering not only the efficiency of logistics but also the balance of workload for each truck. Therefore, in this study, we propose a customer assignment and vehicle routing algorithm based on the saving method and the simulated annealing. The algorithm first determines the customer assignment and initial route for each truck based on the saving method to balance the workload consisting of the number of customers, the demand of the customers, and distance. Then the initial route is improved by applying the simulated annealing. To evaluate the effectiveness of the proposed method, we conducted computational experiments. In experiments, we solved the waste collection vehicle routing problem in a Japanese city where the wastes generated from over 1000 customers are collected by 10 trucks starting from 1 depot. We evaluated the total cost consisting of the number of waste collecting points, the amount of waste, and the distance for this case study.