We propose a model to solve a project scheduling problem where resource assignments and activity schedules need to be determined to achieve a set of due-date requirements as well as possible. The concept of activity duration tolerance levels is introduced to describe the longest activity durations over which the due-dates are guaranteed to be achieved. Based on this, we propose a due-date achievement model using a proposed performance measure termed as the activities exposure level, which accounts for the total amount of durations exceeding tolerance levels for a given scheduling solution. We describe various properties and characteristics of the proposed scheduling optimization model and its practical implications. We show that the associated stochastic scheduling problem with resource constraints can be equivalently computed as the solution of a modest-sized mixed-integer linear program using the sample average approximation approach. Computational results show that our proposed models perform well when compared to different standard approaches across various performance measures.

我们提出一个模型来解决项目计划问题，在该模型中，需要确定资源分配和活动计划，以尽可能地达到一组到期日期要求。引入活动持续时间容忍度级别的概念来描述可保证达到到期日期的最长活动持续时间。基于此，我们提出了一个到期日成就模型，该模型使用一种拟议的绩效指标（称为活动暴露水平）来解决，该模型考虑了给定计划解决方案超出容忍度水平的持续时间总量。我们描述了所提出的调度优化模型的各种特性和特征及其实际意义。我们表明，可以使用样本平均近似方法等效地计算与资源约束相关的随机调度问题，作为中等大小的混合整数线性程序的解。计算结果表明，与跨各种性能指标的不同标准方法相比，我们提出的模型具有良好的性能。