Multi-Objective Lead Time Control in Multistage Assembly Systems (TECHNICAL NOTE)

In this paper we develop a multi-objective model to optimally control the lead time of a multistage assembly system. The multistage assembly system is modeled as an open queueing network, whose service stations represent manufacturing or assembly operations. The arrival processes of the individual parts of the product, which should be assembled to each other in assembly stations, are assumed to be independent Poisson processes with equal rates. In each service station, there is one machine with exponentially distributed processing time, such that the service rate is controllable. The transport times between the service stations are independent random variables with exponential distributions. By applying the longest path analysis in queueing networks, we obtain the distribution function of time spend by a product in the system or the manufacturing lead time. The decision variables of the model are the number of servers in the service stations. The problem is formulated as a multi-objective optimal control problem that involves three conflicting objective functions. The objective functions are the total operating costs of the system per period (to be minimized), the average lead time (min), and the probability that the manufacturing lead time does not exceed a certain threshold (max). The goal programming method is used to solve a discrete-time approximation of the original problem.