Energy Conscious Bi-objective Job Shop Scheduling: A New Formulation and Augmented e-Constraint Method

This paper addresses a job shop scheduling problem in which machines can operate at varying speeds and different energy efficient strategies known as speed scaling and switching on/off are incorporated as well. When a machine runs at high-speed, the amount of time to complete the job shortens but energy consumed by the machine increases. Selection of different speed modes of machines for different jobs (i.e. speed scaling) generates compromise solutions. To save energy further, one must decide whether to shut down the machine during idle periods of consecutive jobs. One option is to turn off the machine whenever the idle period occurs regardless of its duration, which may result in machine breakdown due to excessive opening and closing. Alternatively, a threshold or time limit can be determined below which the machine is kept in standby mode by consuming very little energy. We aim to minimize two conflicting objectives, energy consumption resulting from usage while the machine runs at a particular speed or in standby state and total tardiness emanating from late completions. To this end, we developed a MILP formulation for the problem and Augmented epsilon-Constraint (Augmecon) method is implemented to find pareto optimal solutions. The experimental result reveals that energy consumption and total tardiness objectives are conflicting. Based on payoff table, while the total energy consumed is 25000, total tardiness is 270. When energy consumption increases to 32186, total tardiness reduces to 36. Between the two, Augmented epsilon-Constraint (Augmecon) method provides non-dominated optimal solutions based on 11 grid points.