Mathematical programming formulations for single-machine scheduling problems while considering renewable energy uncertainty

Carbon dioxide (CO2) in particular is by far the primary driver of global warming. One of the most effective ways to reduce CO2 emissions is to increase the amount of power from renewable energy. A key challenge in utilising renewable energies, such as wind and solar, is their uncertainty in terms of when and to what degree and force renewable energies will become available next time. This study uses interval number theory for renewable energy in uncertainty modelling and proposes two novel interval single-machine scheduling problems, 1 vertical bar Q, T, (RE) over bar (j)vertical bar TWFT, CO2 and 1 vertical bar Q, T, (RE) over bar (j), R, U vertical bar TWFT. A solution procedure is formulated to optimise these problems with interval numbers using interval arithmetic. Additionally, this study derives Pareto-optimal solutions of the bi-objective optimisation problem, 1 vertical bar Q, T, (RE) over bar (j)vertical bar TWFT, CO2, using the lexicographic-weighted Tchebycheff method. Some managerial implications are obtained by parameter analysis. Analytical results offer decision-makers an intuitive view of how these factors impact scheduling results and provide practical guidelines for real-life production.