单台机器总完工时间随机排序问题的反问题

运筹学和最优化的种种问题(“正问题”)是在已知各有关参数或者数据的条件下,找出最优(最快、成本最省或者效益最大)的方案。所谓的“反问题”,是指已经有一个方案,但在目前的情况下,该方案并非最优,需要考虑如何最小限度地改变现有参数,使这个方案成为最优的方案。如果说“正问题”的研究有助于一个新系统的设计和确定,那么“反问题”的研究对改善现有系统的性能具有重要的意义。文章以数学规划为工具,研究单台机器以带权总完工时间为优化目标的随机排序问题1‖∑E(wjCj)关于加工时间分布参数的反问题,并给出不带权的情况1‖E(∑Cj)的反问题及其最优解。

Inverse Scheduling Problem on a Single Machine Stochastic Scheduling to Minimize the Total Completion Time

Many(obverse) problems considered in Operational Research and Optimization are to find an optimal solution under some known parameters or data.Given a feasible solution to a problem,its inverse is to find values of the parameters which make the known solutions optimum and which differ from the given estimates as little as possible.Moreover,if the obverse problem is said to be useful for the design of a new system,then the inverse problem will be considered to have very important signification for improving the efficient of an existed system.This paper employs the mathematical programming tool to study the inverse problem of a single machine stochastic scheduling with total weighted completion times,i.e.,1‖E(∑w_jC_j),and the corresponding optimal solutions are obtained under different norms.Furthermore,the inverse problems of the special case of 1‖E(∑C_j) and its related optimal solutions have been also investigated.