求解广义优先关系下的项目最小费用问题

发布时间：2018-09-12 15:05

【摘要】：在项目调度中,求解与费用相关的问题时,需要先求得项目的最小费用,然后以此为起点进行优化,例如时间费用权衡问题.当工序之间只存在单一优先关系时,各工序只需选用费用最小的工期就能得到项目最小费用.但是当工序之间存在广义优先关系(GPRs)时,各工序若都选用费用最小的工期通常无法满足既定的优先关系,导致项目不可行.针对GPRs下的项目最小费用问题,首先,通过分析GPRs的特点,建立了其数学模型;其次,对该模型进行对偶变换,将其等效转化为特殊的最小费用最大流模型.该模型能够运用现有算法求解,并跟据初始对偶关系求得GPRs下的项目最小费用.
[Abstract]:In the process of project scheduling, the minimum cost of the project should be obtained first, and then optimized from this point of view, such as the time and cost tradeoff problem. When there is only a single priority relationship between the processes, the minimum cost can be obtained by selecting the minimum cost duration. However, when there is a generalized priority relationship (GPRs) between the processes, if each process chooses the minimum cost time limit, it is usually unable to satisfy the established priority relationship, which leads to the infeasibility of the project. Aiming at the problem of minimum cost of project under GPRs, firstly, the mathematical model of GPRs is established by analyzing the characteristics of GPRs; secondly, the model is transformed into a special maximum flow model of minimum cost by dual transformation. The model can be solved by using the existing algorithms, and the minimum project cost under GPRs can be obtained according to the initial duality relationship.
【作者单位】：华北电力大学经济与管理学院;
【基金】：国家自然科学基金资助项目(70671040;71171079)
【分类号】：F062.4

【参考文献】