An analysis of network and resource indicators for resource-constrained project scheduling problem instances

Abstract

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.