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在项目管理中,最低成本是主要目标之一,也是求解诸如时间-费用权衡等相关问题时必备的起始点,通常只需令各工序选用费用最低的工期即可.但是当工序之间存在一般优先关系(简称GPRs)时,各工序选用费用最低的工期往往无法满足时间约束,使得项目不可行,因此需要考虑其它费用较高的工期.针对如何在满足GPRs条件下使项目成本最低,首先,通过分析GPRs网络的特点,建立了GPRs网络的最小费用模型;其次,对模型进行对偶变换,等效转化为最小费用流模型,其特点是,除了与起点或终点连接的弧,其余均没有容量限制.当前已有的算法能够有效求解该模型,并跟据其最优解可求得原问题的最优解.
In project management, the minimum cost is one of the main goals and the necessary starting point for solving related issues such as time-expense balances, which usually require only the least-cost timeframe for each process, but when there are processes In the case of GPRs, the project with the lowest cost can not meet the time constraint, which makes the project unfeasible and therefore needs to consider other projects with higher costs.Aiming at how to minimize the project cost under the condition of meeting GPRs, , By analyzing the characteristics of GPRs network, the minimum cost model of GPRs network is established. Secondly, the model is transformed into the minimum cost flow model, which is characterized by that except the arc connected with the starting point or the ending point, none Capacity limitation.At present, the existing algorithm can solve the model effectively and get the optimal solution of the original problem according to its optimal solution.