公共交货期窗口下提前／拖期惩罚不同的单机调度问题

单机作业下有一系列等待加工的彼此独立的任务需要确定最优交货期及最优加工顺序，运用公共交货期（ＣＯＮ）的方法确定了最优公共交货期，并假设如果任务在交货期窗口内完成，则不受惩罚；否则，将导致提前或拖期惩罚，且惩罚值与该任务是提前完工还是拖期完工有关。三个定理及一个多项式时间算法确定了最优交货期和最优排序，一个数值例子解释了如何运用定理来找到最优解。

Optimal Single Machine Scheduling with a Common Due Window

This paper concernes with the optimal due dates and the optimal sequencing to a set of jobs to be processed by a single machine. The common due date assignment method is usded through which all jobs are assigned a common flow allawance. It is assumed that penalty will occur if a job completion times deviate from the common due window, and it is differently penalized depending on its being early or tardy; otherwise, penalty will not occur. Four lemmas are presented to find the optimal common due date and the optimal sequencing, a numerical example is given to illustrate how the results of the lemmas can be used to find the optimal solution.