The problem of scheduling optimally a given set of jobs on a single machine is studied. The lower and upper bounds on the admissible duration of each job are known. The optimality criterion of the schedule is the minimum total completion time of a given set of jobs. Some properties of the optimality region for a job permutation are investigated. Polynomial algorithms for constructing the optimality region for a job permutation and also for calculating the volume of this region are developed. The existence conditions of an empty optimality region for a job permutation are determined. A criterion for the existence of a job permutation with the maximum possible volume of the optimality region is established.

研究了在单台机器上最佳调度给定一组作业的问题。每个作业的允许持续时间的上下限是已知的。计划的最佳标准是给定一组工作的最小总完成时间。研究了用于工作置换的最优区域的一些属性。开发了用于构造作业置换的最优区域并计算该区域的体积的多项式算法。确定用于作业置换的空的最优区域的存在条件。建立具有最佳区域的最大可能体积的工作置换的存在的标准。