GERT网络时间──费用优化数学模型（Ⅰ）

A Mathematics Model(I)to Optimize Time-Cost Tade-off in GERT

对于肯定型网络或是随机型网络在时间—费用线性关系条件下，网络的时间一费用最优化问题已得到较好地解决；但在ＧＥＲＴ网络中，当时间—费用为非线性关系时，优化问题至今尚未有完善的解决方法。本文旨在对于ＧＥＲＴ网络中时间—费用为非线性关系时，阐述了追加费用与缩短作业时间的一般性关系，进而建立了一个多目标数学规划模型。该模型主要研究如何在各活动中分配追加费用，求出最佳方案，使得总追加费用最省并且缩短工期方差最大。该模型的建立对网络理论的基础研究和实际应用方法有一定的现实意义和参考价值。

Optimal time─cost trade-off problems with either deterministic network or stochastic metwork under the linear relationships between the time and the cost of activities have been neatly solved. But such problems with the GERT network under the nonlinear relationships between the time and cost of activities have not been well studied.To such problems,the gen-eral relationships between the additional cost and the reduced duration are described,a multiobjective programming is presented in the activities such that we can minimize the total additional cost and maximize the reduced variance。