Exact method to optimize the total electricity cost in two-machine permutation flow shop scheduling problem under Time-of-use tariff - Ho, Minh Hung; Hnaien, Faicel; Dugardin, Frederic (Computers & operations research, 2022)
This study investigates the minimization of total electricity cost in a two-machine permutation flow shop scheduling problem under the most common electricity tariff, Time-of-Use (ToU). We provide a new property and solution approach to enhance existing methods in the literature. First, we provide an overview of the optimal cases for some specific ToU pricing structures that consist of only two pricing intervals. When the electricity price decreases, Johnson’s rule and dynamic programming give rise to an optimal solution. On the other hand, when the electricity price increases, we provide a condition of optimality for Johnson’s rule. Second, we develop a property based on Johnson’s rule to determine the optimal sequence for general ToU pricing structures. Third, we propose a new mixed-integer linear programming. Then, we design an exact method based on “Logic-based Benders decomposition” to solve the problem. Finally, the numerical tests show that our proposed approach significantly improves the quality of existing results in the literature. •We give the optimal cases for some specific Time-of-Use pricing structures that consist of only two pricing intervals.•We develop a property based on Johnson’s rule to determine the optimal sequence for general Time-of-Use pricing structures.•We propose a new mixed-integer linear programming for two-machine permutation flow shop scheduling problem with electricity costs.•We apply an exact method by Logic-based Benders decomposition to solve the problem.•Our proposed solutions approaches outperform other approaches in the literature in terms of electricity cost in computational experiments.