The discrete time/cost trade-off problem (DTCTP) optimizes the project duration and/or cost while considering the trade-off between activity durations and their direct costs. The complete and non-dominated time-cost profile over the set of feasible project durations is achieved within the framework of Pareto front problem. Despite the importance of Pareto front optimization in project and portfolio management, exact procedures have achieved very limited success in solving the problem for large size instances. This study develops exact procedures based on combinations of mixed-integer linear programming (MILP), ε-constraint method, network and problem reduction techniques, and present new bounding strategies to solve the Pareto problem for large size instances. This study also provides new large size benchmark problem instances aiming to represent the size of real-life projects for the DTCTP. The new instances, therefore, are generated to include up to 990 activities and nine execution modes. Computational experiments reveal that the procedures presented herein can remarkably outperform the state-of-the-art exact methods. The new exact procedures enabled obtaining the optimal Pareto front for instances with serial networks that include more than 200 activities for the first time.

中文翻译：

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大尺寸离散时间/成本权衡问题的 Pareto 前沿优化的 ε 约束过程


离散时间/成本权衡问题 （DTCTP） 优化了项目持续时间和/或成本，同时考虑了活动持续时间与其直接成本之间的权衡。在一组可行的项目持续时间内，完整且非主导的时间成本概况是在帕累托前沿问题的框架内实现的。尽管 Pareto 前沿优化在项目和项目组合管理中很重要，但确切的过程在解决大型实例的问题方面取得的成功非常有限。本研究基于混合整数线性规划 （MILP）、ε约束方法、网络和问题减少技术的组合开发了精确的程序，并提出了新的边界策略来解决大型实例的帕累托问题。本研究还提供了新的大型基准问题实例，旨在表示 DTCTP 的实际项目的大小。因此，生成的新实例最多包含 990 个 activity 和 9 种执行模式。计算实验表明，本文提出的程序可以显着优于最先进的精确方法。新的精确程序首次为具有包含 200 多个活动的串行网络的实例提供了最佳 Pareto 前沿。