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.
在只知道需求分布部分信息条件下,研究三种碳排放政策(碳限额、碳税和碳权交易)下零部件再制造决策问题.首先根据销售收入、再制造成本、废弃处理成本、库存持有成本和缺货成本等构建总利润最大化的基本模型,并在此基础上分别扩展建立三种碳排放政策情形下包括碳排放成本的生产决策优化模型;然后将它转化为REVD(relative expected value distribution)模型进行求解,在具有相同一阶矩、二阶矩的分布集合中,以最小化相对后悔值为鲁棒标准,寻找使得最坏分布下期望利润最大的最优再制造数;最后通过算例分析再制造率、有无碳排放政策以及三种不同碳排放政策的严惩程度对再制造数和总利润的影响,以期为再制造商和碳排放政策制定方在制定决策时提供帮助.
