This paper looks at the contribution that mathematical modelling has made to project management over the past 50 years, and the contribution it is currently making and can make in the future. Project Management started with well-defined foundations posing precise, well-defined problems. In its growing phase, modellers played an essential role in taking the problems defined by the project-management world and offering solutions, from the original PERT, through resource allocation and levelling procedures, Monte Carlo simulation models, criticality analyses and so on. Since then, however, while the project management field itself has tried to establish its procedures, keeping to its philosophical stance, much of the mathematical-modelling world has continued along its trajectory, producing ever more complex solutions to ever more complex models, motivated by mathematical impressiveness rather than the need to solve real-world problems. This paper outlines much of this work, some of which does find its way into project-network software but much of which languishes in journals. However, over the last decade or so, Operational Researchers have begun to build models of projects that are systemic and dynamic and explain many of the behaviours of projects that conventional decomposition models do not; and at the same time, some of the Project Management world has started to realize the limitations of its philosophical stance and started looking to build new theory for modern, complex, dynamic projects. As these two trends come together, it is essential that modellers are at the forefront of building this new theory
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