A multi-objective lead time control problem in multistage assembly systems using an interactive method

In this paper, we develop a multi-objective model to optimally control the lead time of a multistage assembly system, using an interactive method. The multistage assembly system is modelled as an open queueing network, whose service stations represent manufacturing or assembly operations. It is assumed that the product order arrives according to a Poisson process. In each service station, there is either one or infinite number of servers (machines) with exponentially distributed processing time, in which the service rate (capacity) is controllable. The transport times between the service stations are independent random variables with generalized Erlang distributions. The problem is formulated as a multi-objective optimal control problem that involves four conflicting objective functions. The objective functions are the total operating costs of the system per period (to be minimized), the average lead time (min), the variance of the lead time (min) and the probability that the manufacturing lead time does not exceed a certain threshold (max). Finally, the STEM method is used to solve a discrete-time approximation of the original problem. We also investigate the trade-off between the accuracy (correctness) and the computational time of the proposed approximation technique.