“…Although scheduling with machine maintenance has attracted many researchers' attentions in the last three decades, most of the past research mainly focuses on prefixed maintenance durations, see, e.g., Qi et al (1999), Liao and Chen (2003), Chen (2006aChen ( , b, 2008aChen ( , 2007aChen ( , b, 2009, Qi (2007), Sheen and Liao (2007), Ji et al (2007), Sbihi and Varnier (2008), Xu et al (2008Xu et al ( , 2009Xu et al ( , 2014, Sun and Li (2010), Xu and Yin (2011), Xu and Yang (2013), Shi and Xu (2014). However, as can be seen in many production systems, the time needed to perform a maintenance activity is not usually prefixed but depends on many factors such as the degree of tool wear, the amount of fuel to be filled, and the proficiency level of the maintenance workers.…”