A simheuristic approach to optimize energy consumption in the single-machine scheduling problem with stochastic processing times

This paper addresses a stochastic single-machine scheduling problem with energy consumption. In this problem, job processing times are random variables, and total energy consumption depends on job scheduling, as each job has its own energy use and each period follows a Time-Of-Use tariff policy. To solve the problem, we propose a simheuristic algorithm that combines the metaheuristics Simulated Annealing and Greedy Randomized Adaptive Search Procedure to explore the solution space, along with Monte Carlo Simulation to better evaluate the solutions during the search. The solutions obtained are compared with those derived from a deterministic approach, and the results show that the simheuristic outperforms the deterministic method in terms of Average, Value at Risk, and Conditional Value at Risk, emphasizing the importance of incorporating uncertainty into the solution methods.