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中文摘要：
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．
英文摘要：
For project scheduling, when solving a cost problem, such as the time-cost tradeoff problem, we need to obtain the minimum cost of the project as a starting point of the optimization process. If only a single precedence relation exists between activities, we can obtain the minimum cost of a project by letting all activities choose their minimum cost durations. If generalized precedence relations （GPRs） exist between activities, letting all activities choose their minimum cost durations may not meet the given precedence relations and result in a unfeasible project. Aiming at the minimum cost problem of projects under GPRs, we found a mathematical model, and then transform it into an equivalent and special minimum cost maximum flow model by u- sing primal-dual theory. Thus, we can calculate the optimal solution of the special minimum cost maximum flow model by using a current algorithm, and then obtain the minimum cost of a project under GPRs based on the primal-dual relation.
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