重加工具有退化与学习现象的单机批排序问题

本文对同一台机器下次品工件可重加工生产的问题进行研究。工件要求成批加工，每批包括连续加工的两个子批。第一子批的工件加工后，一部分工件是按照要求得到的优良品，另一部分工件是次品。次品的工件接着在第二子批重加工，而次品工件在等待重加工时会产生退化与学习现象，加工完成后得到的工件是优良品。同一子批的工件同时完工，工件的完工时间是该子批中最后一个工件的完工时间。假设每批生产的工件次品率是相同的。每一批工件开始加工和重加工时都有安装时间。目标函数是使总安装时间，重加工和库存持续费用最小，并且优良品工件的需求得到满足。对于该问题的一般情形给出了动态规划算法。接着当批工件的完工时间和批的规模满足一致关系，给出多项时间算法。

Batch Scheduling for Deteriorating and Learning Reworkable in Single Machine

The problem of scheduling the production of new and reworkable defective jobs in the single machine is studied. Jobs are processed in batches. Each batch comprises two sub--batch processed consecutively. In the first sub--batch, all the jobs are newly manufactured. Some of the jobs are of the required good quality and some are defective. The defective jobs are reworked in the sec- ond sub--batch. They deteriorate and learn while waiting for reworking, each reworkahle defective job is of the required good quali ty. All the jobs in the same sub--batch complete at the same time, which is completed time of the last job in the sub--batch. It is assumed that the percentage of defective jobs in each batch is the same. A setup time is of required to start batch processing and to switch from working and reworking. The objective is to find batch size such as the total setup, rework and inventory holding cost is minimized and all the demands are satisfied. Dynamic programming algorithm is presented for the general problem. Then we give a polynomial time algorithm if processing time of the batch and its size are agreeable.