Opportunistic preventive maintenance scheduling for a multi-unit series system based on dynamic programming Xiaojun Zhou a,Ã , Lifeng Xi a , Jay Lee b a Department of Industrial Engineering, School of Mechanical Engineering, Shanghai Jiao Tong University, No. 800 Dong Chuan Road, Shanghai 200240, PR China b University of Cincinnati, Cincinnati OH 45221-0072, OH, USA article info Article history: Received 14 March 2006 Accepted 30 September 2008 Available online 22 October 2008 Keywords: Preventive maintenance Imperfect Opportunistic Dynamic Scheduling abstract It is understood that for a multi-unit series system, whenever one of the units stops to perform a preventive maintenance (PM) action, the whole series system must be stopped. At that time PM opportunities arise for the other units in the system. This paper proposes an opportunistic PM scheduling algorithm for the multi-unit series system based on dynamic programming with the integration of the imperfect effect into maintenance actions. An optimal maintenance practice is determined by maximizing the short-term cumulative opportunistic maintenance cost savings for the whole system. Matlab is considered for the optimization which is based on numerical simulation. Numerical examples are given throughout to show how this approach works. Finally, a comparison between the proposed PM model and other models is given. & 2008 Elsevier B.V. All rights reserved. 1. Introduction It is understood that conducting proper maintenance is an effective way to keep manufacturing systems in good condition. Since Barlow and Hunter gave the minimal repair model in 1960 (Barlow and Hunter, 1960), a lot of efforts have been made on maintenance scheduling which play great roles in improving operational safety, minimi- zing maintenance costs, and reducing the frequency and severity of in-service system failures. Traditionally, preventive maintenance (PM) is sched- uled periodically based on a technician’s experience and it often hold a same time interval for PM activities (Nakagawa, 1984; Canfield, 1986; Sheu et al., 1995). In practice however, PM activity is generally imperfect and it cannot restore the system to as good as new. Even though some degraded components are replaced during PM activities, the cumulative wear on adjacent components may go unnoticed and worsen the condition of the relative parts, and the system as a whole. Therefore, the age-T policy will give unavoidably decreasing reliabilities to the deteriorating systems with imperfect maintenance effect. Fortunately, many imperfect PM models have been developed which pay much attention to the system reliability (Pham and Wang, 1996). In fact, under an imperfect circumstance, a system will be preventive maintained at a decreasing sequence of time intervals, which could be more practical since most systems need more frequent maintenance with increased usage and age. On the other hand, with the increasing demand from industry, more and more research efforts are being directed toward multi-unit system modeling. In term of the different system configurations (i.e., series, parallel, k-out-of-n), different maintenance models for multi-unit systems have been proposed (Berg, 1978; Zheng and Fard, 1992; Pham and Wang, 2000; Jhang and Sheu, 2000; Marseguerra et al., 2002; Bris et al., 2003; Karin et al., 2007; Allaoui et al., 2008; Rachaniotis and Pappis, 2008). However, two issues still need to be addressed. First, the majority of these models that appear in the literature Contents lists available at ScienceDirect journal homepage: www.elsevier.com/locate/ijpe Int. J. Production Economics ARTICLE IN PRESS 0925-5273/$ - see front matter & 2008 Elsevier B.V. All rights reserved. doi:10.1016/j.ijpe.2008.09.012 Ã Corresponding author. Tel./fax: +86 2134206782. E-mail address: zzhou745@sjtu.edu.cn (X. Zhou). Int. J. Production Economics 118 (2009) 361–366