Characterization and Generation of a General Class of Resource-Constrained Project Scheduling Problems

TLDR

The study focuses on precedence‑ and resource‑constrained project scheduling problems, with potential applicability to other network optimization problems. The paper aims to generate problem instances of controlled difficulty. The authors construct networks by incorporating topology constraints, a resource factor reflecting coefficient‑matrix density, and a resource‑strength measure, then benchmark single‑ and multi‑mode resource‑constrained project scheduling instances using state‑of‑the‑art branch‑and‑bound procedures. Computational experiments show that the parametric characterization strongly influences difficulty, revealing that long‑used benchmark instances are very easy while hard instances are smaller than expected and often unsolvable to optimality within reasonable time.

Abstract

This paper addresses the issue of how to generate problem instances of controlled difficulty. It focuses on precedence- and resource-constrained (project) scheduling problems, but similar ideas may be applied to other network optimization problems. It describes a network construction procedure that takes into account a) constraints on the network topology, b) a resource factor that reflects the density of the coefficient matrix, and c) a resource strength, which measures the availability of resources. The strong impact of the chosen parametric characterization of the problems is shown via an in depth computational study. Instances for the single- and multi-mode resource-constrained project scheduling problem are benchmarked by using the state of the art (branch and bound) procedures. The results provided, demonstrate that the classical benchmark instances used by several researchers over decades belong to the subset of the very easy ones. In addition, it is shown that hard instances, being far more smaller in size than presumed in the literature, may not be solved to optimality even within a large amount of computation time.