International Journal of Production Research Vol. 51, No. 3, 1 February 2013, 847–868 A branch and bound algorithm for single-machine production scheduling integrated with preventive maintenance planning Shijin Wang * and Ming Liu Department of Management Science and Engineering, School of Economics and Management, Tongji University, Shanghai, China (Received 24 September 2011; final version received 9 March 2012) This paper deals with an integrated optimisation model for production scheduling and preventive maintenance (PM) in a single machine with its time to failure subject to a Weibull probability distribution. The objective is to minimise the total expected weighted completion time of jobs. To solve this problem, we develop a branch and bound (B&B) algorithm (hereafter called the B&BA). Several lower bounds, dominance rules and upper bounds are developed to enhance the performance of the B&BA. Extensive computational experiments on randomly generated problems with different configurations are conducted and the results show that the proposed method can find optimal solutions for problems with up to 18 jobs in a reasonable amount of computation time. Keywords: branch and bound algorithm; preventive maintenance; single machine; production scheduling 1. Introduction As the importance of applications in industry has been increasingly recognised, scheduling problems integrated with preventive maintenance has received more and more attention from both practitioners and management scientists since the beginning of the 1990s. Unlike traditional scheduling problems with the assumption of continuously available machines, this stream of research has more practical relevance as it considers deterministic machine unavailability due to preventive maintenance and/or stochastic unavailability due to unforeseen breakdown. There is a considerable amount of literature on the scheduling problem integrated with machine availability constraints especially at the operational (scheduling) level, which feature different machine environments settings, including single machine, parallel machine (e.g. Lee and Chen 2000, Sun and Li 2010), flow shop (e.g. Ruiz et al. 2007), job shop (e.g. Kubzin and Strusevich 2006, Ben Ali et al. 2011) and flexible job shop (e.g. Gao et al. 2006). Different job processing characteristics after repair or PM (i.e. resumable, semi-resumable and non-resumable) and different optimality criteria are considered. This paper falls into the single machine setting. Single machine problems are of a fundamental nature and could be interpreted as building blocks for more complex problems (Ma et al. 2010). Moreover, a complicated machine environment with a single bottleneck (Gagne et al. 2002, Liao and Juan 2007), and even a group of machines, e.g. high-tech manufacturing facilities (computer- controlled machining centres and robotic cells), are often treated as a single machine scheduling problem (Lin and Ying 2007). Therefore, the scheduling problem with PM in the context of a single machine has attracted tremendous attention, which could fall into the following three categories according to the feature of machine unavailability: (1) Unavailability periods are fixed (deterministic) when the start of an interval and its duration are known in advance. (2) Unavailability constraints are also decision variables (flexible), in which the start time and/or the maintenance duration are flexible. (3) Unavailability periods are due to machine breakdown with stochastic features. Most prior research has concentrated on the deterministic machine unavailability constraint, which can serve as a modelling tool for planned breaks (lunch breaks, days off, holidays, etc.) (Kubzin and Strusevich 2006). Lee et al. (1997), Sanlaville and Schmidt (1998) and Schmidt (2000) provide earlier surveys of this topic and Ma et al. (2010) provides recent comprehensive reviews. *Corresponding author. Email: shijinwang0223@yahoo.com.cn ISSN 0020–7543 print/ISSN 1366–588X online ß 2013 Taylor & Francis http://dx.doi.org/10.1080/00207543.2012.676683 http://www.tandfonline.com Downloaded by [HKUST Library] at 00:49 09 October 2013