Proactive maintenance scheduling in a re-entrant flow shop using Lagrangian decomposition coordination method T. Kaihara a, *, N. Fujii a , A. Tsujibe a , Y. Nonaka b a Department of Computer Science and Systems Engineering, Kobe University, Japan b Production Engineering Research Laboratory, Hitachi, Ltd., Japan Submitted by Kazuaki Iwata (1), Osaka, Japan. 1. Introduction As the size and complexity of manufacturing systems have increased, agent-based approaches are increasingly regarded as sophisticated means to cope with such difficulties [1]. Social contract-based resource allocation mechanisms, such as market- oriented programming [2], combinatorial auctions [3], Lagrangian decomposition coordination method [4], and so on are mostly constructed as multi-agent systems. They have become promising approaches to achieve efficient management in manufacturing systems or supply chains [5] because they can metaphorically represent the complexity and effectiveness of our social systems with their characteristic efficiency and robustness. They also must have strong applicability to real shop floors because social contract-based mechanisms are easily accepted for shop floor operators. On the other hand, process flows of products become complex in re-entrant flow shops, where the same machines are used recursively in single-product process flow. Typical examples of re- entrant flow shops are semiconductor production floors, in which hundreds of machines and products demand hundreds of processes. For that reason, scheduling processes in such re-entrant flow shops have difficulty achieving high productivity and low production costs. Furthermore, the complexity and uncertainty of modern production environments [6] exacerbate problems of production scheduling. Maintenance scheduling is also important to achieve high productivity. Maintenance of several kinds for machines must be conducted on the production floor daily, weekly, and monthly. Certain maintenance tasks can require several days in re-entrant flow shops used for semiconductor production. Proper main- tenance scheduling must maintain both productivity and a high level of product quality. However, the mere use of maintenance scheduling is usually insufficient to obtain feasible solutions based on traditional combinatorial optimization methods because of the complexity of production processes. Consequently, heuristic approaches based on the know-how of human experts are usually adopted in real fabrication facilities. This paper describes a new approach to proactive main- tenance scheduling to achieve both high productivity and prevention of malfunctions of machines, which employs the Lagrangian decomposition coordination method as a social contract-based mechanism. The Lagrangian decomposition coordination method relaxes the constraint conditions of a problem by adopting Lagrangian multipliers. It then solves the problem quickly by decomposing the problem to sub-problems. Finally, it coordinates solutions of sub-problems to obtain feasible solutions. This method has been applied to production scheduling problems [7] and optimization problems of the supply chain [8]. Each reports the effectiveness of applying the Lagrangian decomposition coordination method; however, no application exists for maintenance scheduling. This study proposes a method for realizing maintenance scheduling based on Lagrangian decomposition coordination by regarding main- tenance tasks as jobs with a constraint of a special type: limitation of execution. The proposed method is applied to a hypothetical semiconductor fabrication factory to the minimiz- ing total tardiness problem. The effectiveness of the proposal is discussed using computer simulation results. Investment in the semiconductor industry is becoming huge. Therefore, the achievement of higher productivity using the proposed methodology is expected to be impactful and to affect the whole economy considerably. CIRP Annals - Manufacturing Technology 59 (2010) 453–456 ARTICLE INFO Keywords: Scheduling Optimization Equipment maintenance ABSTRACT Proactive maintenance scheduling is necessary to prevent facility trouble and to ensure high productivity in semiconductor production systems. For such systems, it is usually difficult to determine a proper plan because of complex process flows, which necessitate that jobs often re-enter a facility. This paper presents a method for re-entrant production floor optimization using Lagrangian decomposition coordination. By regarding maintenance as jobs that are limited by a starting and finishing time, the proposed approach produces a schedule that can facilitate proper maintenance. Feasibility is discussed using computer simulation results: the proposed method produces feasible solutions for minimizing overall tardiness problems. ß 2010 CIRP. * Corresponding author. Contents lists available at ScienceDirect CIRP Annals - Manufacturing Technology journal homepage: http://ees.elsevier.com/cirp/default.asp 0007-8506/$ – see front matter ß 2010 CIRP. doi:10.1016/j.cirp.2010.03.031