“…Exact solution methods such as Branch-and-Bound (BB) for integer and mixed-integer programming models, and Generalized Reduced Gradient (GRG2) algorithm for nonlinear programming models have been employed in the literature mostly for single-machine models or for smallscale multi-machine situations (Cassady and Kutanoglu, 2003;Aghezzaf et al, 2007;Aghezzaf and Najid, 2008;Nourelfath and Chatelet, 2012;Portioli-Staudacher and Tantardini, 2012;Bajestani et al, 2014;Yalaoui et al, 2014;Kumar and Lad, 2017;Ao et al, 2019;and Polotski et al, 2019). It has been reported that most integrated production and maintenance scheduling problems, with availability constraints, under different machine configurations and various objective functions are NP-hard problems (Kubiak et al, 2002).…”