A multi-objective lead time control problem based on the failure rate of multi-style of products

In this paper a new queueing system based on the arrival of multi-style of products and failure rate of products for optimal design of single-stage assembly systems is developed, in which the server has many kinds of styles with different service rate to different style of product and the products may have quality problems and need to be repaired in each service station. The service times and maintenance times of manufacturing and assembly operations are exponentially distributed. By using the total probability decomposition and Markov process method, queue length distribution, the recursion expression of the equilibrium distribution and the mean waiting time are obtained. Then, we develop a multi-objective optimal control problem, in which the average lead time, the operating costs of the system and the maintenance costs per period are minimized using goal attainment method.