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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 $J_j$ is defined by an increasing function of its starting time $t$, i.e., $p_j={\alpha }_j(A+Bt)$, where ${\alpha }_j>0$ is the deterioration rate of job $J_j$. For the problem, we propose an online algorithm with a competitive ratio of $2+B{\alpha }_{max}$, where ${\alpha }_{max}$ 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.

In this paper, the single machine total weighted completion time scheduling problem is studied. The jobs have nonzero release time and processing time increases during the production due to the effect of deterioration on the machine. An operator sets up the machine and manually loads the job in the machine and unloads it at the end of the working time. The setup time and the removal time are influenced by the ability of the worker due to his work experience and learning capacity. Heuristic algorithms are proposed to solve the scheduling problem, and their efficiency is evaluated on a wide benchmark.