Effective dynamic dispatching rule and constructive heuristic for solving single-machine scheduling problems with a common due window Kuo-Ching Ying a,1 , Shih-Wei Lin b,c,d,1 and Chung-Cheng Lu e * ,1 a Department of Industrial Engineering and Management, National Taipei University of Technology, Taipei, Taiwan; b Department of Information Management, Chang Gung University, Taoyuan, Taiwan; c Department of Neurology, Linkou Chang Gung Memorial Hospital, Taoyuan, Taiwan; d Department of Industrial Engineering and Management, Ming Chi University of Technology, New Taipei City, Taiwan; e Department of Transportation and Logistics Management, National Chiao Tung University, Taipei, Taiwan (Received 13 October 2015; accepted 9 August 2016) This study addresses the single-machine scheduling problem with a common due window (CDW) that has a constant size and position. The objective is to minimise the total weighted earliness–tardiness penalties for jobs completed out of the CDW. To determine a schedule as close to optimum as possible, this study develops a dynamic dispatching rule and an effective constructive heuristic. The better performance of the proposed heuristic is demonstrated by comparing the results of it with those of a state-of-the-art greedy heuristic on a well-known benchmark problem set. In addition, we incorporate the constructive heuristic into a best-so-far meta-heuristic to examine the benefit of the proposed heuristic. The results show that the best known solutions in 144 out of the 250 benchmark instances are improved. Keywords: scheduling; heuristics; common due window; dispatching rule 1. Introduction Single-machine scheduling problems (SMSPs) are common in numerous real-world production systems that require effective scheduling of jobs performed on a unique machine. In the last few decades, various studies have targeted SMSPs with different scheduling criteria (e.g. Chen, Potts, and Woeginger 1999; Senthilkumar and Narayanan 2010; Liu, Wang, and Wang 2016; Wang et al. 2016), dispatching rules (e.g. Panwalkar and Iskander 1977; Blackstone, Phillips, and Hogg 1982), and efficient heuristics (e.g. Lin and Ying 2008; Lu, Lin, and Ying 2012; Lu, Ying, and Lin 2014). In customised or just-in-time production systems, specifying due dates of job operations is necessary for firms to achieve greater flexibilities (Lin, Chou, and Ying 2007; Lin, Lu, and Ying 2011; Sun et al. 2016; Lin et al. forthcoming). To meet job due dates, many SMSPs focus on minimising the total tardiness and earliness penalty of jobs. Sidney (1977) addressed the SMSP, with an aim to minimise the penalty of earliness and tardiness of jobs. Gens and Levner (1981) followed up with the SMSP minimising the total penalty of delayed jobs and proposed a range- and-bound method for finding a tight bound of objective values. Yurtkuran and Emel ( forthcoming) presented a discrete artificial bee colony algorithm for a single-machine earliness–tardiness scheduling problem, which can produce solutions better than other compared algorithms. Unlike these SMSPs that designate different due dates to different jobs, Kanet (1981) considered a common due date for all jobs in the SMSP, in order to minimise the average deviation of job completion times. Hall, Kubiak, and Sethi (1991) and Hall and Posner (1991) showed that the SMSP with a common due date is NP-Complete. Their problem minimises the weighted penalty costs of earliness and tardiness, and they proposed dynamic programming algorithms and a fully polynomial approximation scheme for finding optimal solutions. Chen (1996) further looked at the common due date to be determined by the SMSP that minimises the earliness–tardiness penalties and batch delivery costs. A polynomial-time dynamic programming algorithm was presented to solve the problem. Gordon, Proth, and Chu (2002) provided a comprehensive review of SMSPs with a common due date. Moslehi et al. (2010) developed an efficient branch-and-bound algorithm to obtain lower and upper bounds of the sum of maximum earliness and tardiness. The algorithm was shown to outperform the algorithms presented in previous works. *Corresponding author. Email: jasoncclu@gmail.com 1 All authors contributed equally to this work. © 2016 Informa UK Limited, trading as Taylor & Francis Group International Journal of Production Research, 2017 Vol. 55, No. 6, 1707–1719, http://dx.doi.org/10.1080/00207543.2016.1224949