Parallel machine scheduling with linearly increasing energy consumption cost

This paper deals with a parallel machine scheduling problem with linearly increasing energy consumption cost. Maintenance activities are considered in the problem. After maintenance, the machine energy consumption cost returns to the normal level. Thus, an important decision is how to determine a reasonable number of maintenance activities to enable a significant tradeoff between the maintenance cost and the energy consumption cost. We define the jobs processed between two adjacent maintenance activities as a batch since the job processing cannot be interrupted. A further decision is how to batch the jobs. To solve the investigated problem, we first study a special case where there is only one single machine. A heuristic approach is proposed to solve the single machine scheduling problem. Then, we present a variable neighborhood search (VNS) algorithm for general cases, where the heuristic approach for the single machine case is intergrated. Extensive computational experiments are conducted and the results show that the proposed VNS algorithm is superior to artificial bee colony (ABC) algorithm, genetic algorithm (GA), ant colony optimization (ACO) algorithm, Tabu search (TS)algorithm, and greedy randomized adaptive search procedure (GRASP) algorithm.