Operations scheduling under electricity time-varying prices

Global climate change requires stakeholders to consider energy elements in their decision-making. Electricity costs, in particular, constitute a significant portion of operational costs in most manufacturing systems. The electricity bills can be lowered if electricity-consuming operations are correctly scheduled. We consider a manufacturing operations control problem with known time-varying electricity prices in a finite planning horizon. Each operation is unique and has its own concave electricity consumption function. Pre-emptions of operations are allowed, yet postponing an operation incurs a cumulative penalty for each time period. In addition, each pre-emption is considered a new operation. The electricity cost in each time period is exogenous and there exists a capacity constraint on the total electricity amount consumed in each period due to infrastructure and providers limitations. There is a fixed start-up cost incurred for switching on the machine and a fixed reservation cost incurred for keeping the machine On. The system also includes a rechargeable battery. The customer has to determine when to process each operation within the time horizon so as to minimise total electricity consumption and operations postponement penalty costs. A dynamic programming solution is proposed and the complexity of the models is analysed. After examining several special cases of the model, the optimum times to charge and discharge the rechargeable battery are determined. A polynomial time algorithm for a special case of a single operation with uniform capacity is proposed.