A single-machine scheduling with preventive periodic maintenance activities in a remanufacturing system including resumable and non-resumable jobs is studied.The objective is to find a schedule to minimize the makespan and an LPT-LS algorithm is proposed.Non-resumable jobs are first scheduled in a machine by the longest processing time（LPT） rule,and then resumable jobs are scheduled by the list scheduling（LS） rule.And the worst-case ratios of this algorithm in three different cases in terms of the value of the total processing time of the resumable jobs（denoted as S2） are discussed.When S2 is longer than the spare time of the machine after the non-resumable jobs are assigned by the LPT rule,it is equal to 1.When S2 falls in between the spare time of the machine by the LPT rule and the optimal schedule rule,it is less than 2.When S2 is less than the spare time of the machine by the optimal schedule rule,it is less than 2.Finally,numerical examples are presented for verification.
An operating schedule of the parallel electric arc furnaces(EAFs)considering both productivity and energy related criteria is investigated.A mathematical model is established to minimize the total completion time and the total electricity cost.This problem is proved to be an NP-hard problem,and an effective solution algorithm,longest processing time-genetic(LPT-gene)algorithm,is proposed.The impacts of varied processing energy consumption and electricity price on the optimal schedules are analyzed.The integrated influence of the different weight values and the variation between the peak price and the trough price on the optimal solution is studied.Computational experiments illustrate that considering the energy consumption costs in production has little influence on makespan;the computational performance of the proposed longest processing time-genetic algorithm is better than the genetic algorithm(GA)in the issue to be studied;considerable reductions in the energy consumption costs can be achieved by avoiding producing during high-energy price periods and reducing the machining energy consumption difference.The results can be a guidance for managers to improve productivity and to save energy costs under the time-of-use tariffs.
