In the past decades, the resource on the resource-constrained project scheduling problem (RCPSP) has grown rapidly, resulting in an overwhelming amount of solution procedures that provide (near)-optimal solutions in a reasonable time. Despite the rapid progress, little is still known what makes a project instance hard to solve. Inspired by a previous research study that has shown that even small instances with only up to 30 activities is sometimes hard to solve, the current study provides an analysis of the project data used in the academic literature. More precisely, it investigates the ability of four well-known resource indicators to predict the hardness of an RCPSP instance.

The study introduces a new instance equivalence concept to show that instances might have very different values for their resource indicators without changing any possible solution for this instance. The concept is based on four theorems and a search algorithm that transforms existing instances into new equivalent instances with more compact resources. This algorithm illustrates that the use of resource indicators to predict the hardness of an instance is sometimes misleading.

In a set of computational experiment on more than 10,000 instances, it is shown that the newly constructed equivalent instances have values for the resource indicators that are not only different than the values of the original instances, but also often are better in predicting the hardness the project instances. It is suggested that the new equivalent instances are used for further research to compare results on the new instances with results obtained from the original dataset.

在过去的几十年中，用于资源受限的项目计划问题（RCPSP）的资源迅速增长，导致大量的解决方案过程可以在合理的时间内提供（接近）最佳解决方案。尽管取得了快速的进展，但很少有人知道导致项目实例难以解决的原因。受先前的研究启发，该研究表明即使只有最多30个活动的小实例有时也难以解决，当前的研究提供了对学术文献中使用的项目数据的分析。更准确地说，它研究了四个众所周知的资源指标预测RCPSP实例硬度的能力。

该研究引入了新的实例等效概念，以表明实例的资源指标可能具有非常不同的值，而无需更改该实例的任何可能解决方案。该概念基于四个定理和一个搜索算法，该算法将现有实例转换为具有更紧凑资源的新等效实例。该算法说明，使用资源指示器预测实例的硬度有时会产生误导。

在超过10,000个实例的一组计算实验中，结果表明，新构造的等效实例具有的资源指标值不仅与原始实例的值不同，而且通常在预测硬度方面更佳。项目实例。建议将新的等效实例用于进一步研究，以将新实例的结果与从原始数据集获得的结果进行比较。