A Production Plan Considering Parallel Machines and Deteriorating Effects: Minimizing the Makespan in the Section of Steel Box Girder Processing

Abstract

With the popularization of energy conservation and emission reduction, amounts of industrial production has taken energy conservation as a goal to achieve. The paper considers an online parallel-batch scheduling problem with deteriorating and incompatible families on identical machines to minimize the makespan, which minimizes the maximum energy consumption of machines. Specifically, the processing time of job [Formula: see text] is defined by an increasing function of its starting time [Formula: see text], i.e., [Formula: see text], where [Formula: see text] is the deterioration rate of job [Formula: see text]. For the problem, we propose an online algorithm with a competitive ratio of [Formula: see text], where [Formula: see text] is the largest deterioration rate in an instance. Furthermore, the paper presents a concise computational study of the numerical experiment to show that our algorithm performs very well in practice of this model.