Parallel Machine Scheduling Under Time-of-Use Electricity Prices: New Models and Optimization Approaches

The industrial sector is one of the largest energy consumers in the world. To alleviate the grid's burden during peak hours, time-of-use (TOU) electricity pricing has been implemented in many countries around the globe to encourage manufacturers to shift their electricity usage from peak periods to off-peak periods. In this paper, we study the unrelated parallel machine scheduling problem under a TOU pricing scheme. The objective is to minimize the total electricity cost by appropriately scheduling the jobs such that the overall completion time does not exceed a predetermined production deadline. To solve this problem, two solution approaches are presented. The first approach models the problem with a new time-interval-based mixed integer linear programming formulation. In the second approach, we reformulate the problem using Dantzig-Wolfe decomposition and propose a column generation heuristic to solve it. Computational experiments are conducted under different TOU settings and the results confirm the effectiveness of the proposed methods. Based on the numerical results, we provide some practical suggestions for decision makers to help them in achieving a good balance between the productivity objective and the energy cost objective.