Production scheduling is one of the issues in the field of planning in production systems that has a significant impact on reducing costs, increasing productivity, customer satisfaction, and other competitive advantages. Orders are received instantly based on the planned schedule, and all customers expect to receive their orders as soon as possible. In a situation where the volume of orders is high, and there are limited product manufacturers, manufacturing companies tend to prioritize their customers. The purpose of this study is to prioritize the customers of a medical equipment company, and customers are prioritized based on some criteria such as deprivation, urgency of orders, purchase volume, good pay, and participation in a regional exhibition. In this research, a two-objective production flow scheduling problem is presented. The first objective function is related to minimizing the weighted delay at the time of delivery. The second objective function is related to minimizing the total program time changes of the devices or setting them. Due to the complexity of the problem, a multi-objective particle swarm optimization algorithm is proposed to solve the problem. In order to evaluate the efficiency of the proposed model, the one-month orders of the manufacturer in question have been examined, and the stated results show the efficiency of the scheduling.