具有学习效应且加工时间可控的单机排序问题

讨论一类加工时间可控的单机排序问题.在这一问题的模型中,机器具有学习效应,工件的实际加工时间为同时依赖于所排位置和所分配的资源量的资源消耗函数,其中资源消耗函数又分为线性资源消耗函数和凸资源消耗函数这两种函数.考虑共同工期分派方法和松弛工期分派方法这两种工期分派方法.极小化一个包含加权总误工数的费用、工期分派的费用、最大完工时间的费用和总资源消耗的费用的目标函数.对于工件加工时间的两种资源消耗函数与工期分派方法的不同组合,算法复杂性为O（n4）的多项式时间算法相应地被给出.创新之处是：在Shabtay研究的基础上增加考虑了学习效应后,计算相关问题的算法复杂性仍保持不变.

Single-machine scheduling problem with controllable processing times and learning effect

This paper studies scheduling problem on a single machine with controllable processing times. In this model, the machine has learning effect. The actual processing time of a job is a resource consumption function depending on its position in a sequence and its related resource consumption, which contains linear resource consumption and convex resource consumption. The due date assignment methods studied include the common due date and the slack due date. For each combination of the different resource consumption function and due date assignment methods, a polynomial-time algorithm is given accordingly, and algorithmic complexity is O（n4 ）. The innovation of this paper is the algorithm complexity of issues related is remain unchanged on the basis of research of Shabtay considering learning effect.