In this study, we consider stochastic single machine scheduling problem. We assume that setup times are both sequence dependent and uncertain while processing times and due dates are deterministic. In the literature, most of the studies consider the uncertainty on processing times or due dates. However, in the real-world applications (i.e. plastic moulding industry, appliance assembly, etc.), it is common to see varying setup times due to labour or setup tools availability. In order to cover this fact in machine scheduling, we set our objective as to minimise the total expected tardiness under uncertain sequence-dependent setup times. For the solution of this NP-hard problem, several heuristics and some dynamic programming algorithms have been developed. However, none of these approaches provide an exact solution for the problem. In this study, a two-stage stochastic-programming method is utilised for the optimal solution of the problem. In addition, a Genetic Algorithm approach is proposed to solve the large-size problems approximately. Finally, the results of the stochastic approach are compared with the deterministic one to demonstrate the value of the stochastic solution.

The integration of renewable energy sources into the manufacturing sector is a recent development, which is prompting companies to explore innovative approaches to enhance their production systems through efficient renewable energy utilization. Within this context, renewable energy-aware machine scheduling has emerged as a pivotal area requiring novel strategies for sustainability. This study aims to evaluate the effect of intermittent renewable energy supply on sustainable machine scheduling by incorporating the option of machine speed for the first time in the literature. A two-stage stochastic program is developed to model the problem and examine the value of the stochastic solution. Additionally, an efficient genetic algorithm is proposed for approximate problem solving. Extensive test study is conducted to explore and generalize the sustainable operational policies derived from the proposed method. The results reveal key scheduling strategies that promote sustainability in production by reducing non-renewable dependence. Notably, the study underlines the importance of considering uncertainties in renewable supply in scheduling, especially under conditions of substantial job and machine scales, high-capacity but variable renewable supply, and flexible job deadlines. As an illustration, in the context of a test case involving 20 jobs and 3 machines, the value of the stochastic solution amounts to 68.72 units. This finding implies that failing to account for the stochastic nature of the renewable energy supply would result in an additional energy expenditure of 68.72 units from the grid. These findings offer valuable insights for corporate management and scheduling operations, particularly as they navigate the transition towards green manufacturing practices.