A multi-objective lead time control problem in multi-stage assembly systems using genetic algorithms

• Published in: European journal of operational research Vol. 180; no. 1; pp. 292 - 308
• Main Authors: Perkgoz, Cahit, Azaron, Amir, Katagiri, Hideki, Kato, Kosuke, Sakawa, Masatoshi
• Format: Journal Article
• Language: English
• Published: Amsterdam Elsevier B.V 01.07.2007; Elsevier; Elsevier Sequoia S.A
• Series: European Journal of Operational Research
• Subjects: Applied sciences; Exact sciences and technology; Genetic algorithms; Multiple objective programming; Operational research and scientific management; Operational research. Management science; Poisson distribution; Production; Queueing; Queuing; Queuing theory. Traffic theory; Random variables; Studies; Queueing; Multiple objective programming; Production; Genetic algorithms; Multiobjective programming; Processing time; Queueing network; Modeling; Poisson process; Service station; Minimum time; Distributed processing; Character string; Queue; Assembly; Operating system; Probabilistic approach; Operating cost; Independent variable; Lead time; Service time; Multiserver queue; Genetic algorithm; Time average; Optimal control; Erlang distribution; Discrete time; Objective function
• ISSN: 0377-2217; 1872-6860
• DOI: 10.1016/j.ejor.2006.04.024

In this paper, we develop a multi-objective model to optimally control the lead time of a multi-stage assembly system, using genetic algorithms. The multi-stage assembly system is modelled as an open queueing network. 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 optimal service control is decided at the beginning of the time horizon. 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, we apply a genetic algorithm with double strings using continuous relaxation based on reference solution updating (GADSCRRSU) to solve this multi-objective problem, using goal attainment formulation. The results are also compared against the results of a discrete-time approximation technique to show the efficiency of the proposed genetic algorithm approach.