单机供应链排序及流水作业的反问题模型

Inverse Problems of Supply Chain Scheduling and Flowshop Scheduling

最优化问题是在给定参数情况下,对某个目标函数,如费用、容量等,寻找问题的最优解。然而在许多现实生活中,有时只能知道问题的参数近似值和一个可行解,需要最小程度地调整参数,使得给定的可行解成为最优,这就是最优化问题的反问题。本文研究单台机器供应链排序和流水作业排序的反问题。根据调整参数的不同,本文利用排序理论把这些反问题表示为相应的数学规划形式。

Optimization problems are concerned to find optimal solutions with respect to some objective function, e. g. , costs, capacities, etc, given problem parameters. However, in many real- life situations only approxi- mate values of the parameters are known, and a feasible solution is required. In such cases we may need to ＂minimally＂ adjust the parameters, i. e. , minimize the ＂cost＂ of parameter adjustments, so that the feasible solution becomes an optimal solution under the new parameter values. This is called inverse optimization. The purpose of this paper is to study inverse problems of single - machine supply chain scheduling and flowshop scheduling. It will be shown that, by the theories of scheduling, these problems can be formulated as respective mathematical programmings in accordance with different parameter adjustments.