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

In this paper, we develop a multi-objective model to optimally control the lead time of a manufacturing system, using goal attainment method. The manufacturing system is modelled as a new queueing system based on the failure rate of products, in which the products may have quality problems and need to be repaired in each service station. It is assumed that the product order arrives according to a Poisson process. In each service station, there is only one server (machines) with exponentially distributed processing time, in which the service rate (capacity) is controllable. The maintenance time of manufacturing and assembly operations is exponentially distributed. By using the total probability decomposition and Markov process method, the 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 maintenance costs and the operating costs of the system per period are minimized using goal attainment method.