“…This raises a challenge on how the lot size can be optimised to improve the economic benefit of the manufacturer, which has been widely studied for a long time (Ben-Daya et al, 2008;Lamas & Chevalier, 2018;Kilic & Tunc, 2019;Ou & Feng, 2019;Taş et al, 2019). In most cases, the optimal lot sizing is obtained by minimising the sum of inventory holding and set-up costs (Liu et al, 2019). In practice, a production system may fail and maintenance may therefore be carried out (Barata et al, 2002;Garbatov & Soares, 2001;Xiao & Peng, 2014;Levitin & Lisnianski, 2000;Cha et al, 2017;Cha et al, 2018;Yang, et al, 2018;Yang et al, 2019;Zhang et al, 2014;Li et al, 2016).…”