The contribution of mathematical modelling to the practice of project management

This paper looks at the contribution that mathematical modellinghas made to project management over the past 50 years, and thecontribution it is currently making and can make in the future.Project Management started with well-defined foundations posingprecise, well-defined problems. In its growing phase, modellersplayed an essential role in taking the problems defined by theproject-management world and offering solutions, from the originalPERT, through resource allocation and levelling procedures,Monte Carlo simulation models, criticality analyses and so on.Since then, however, while the project management field itselfhas tried to establish its procedures, keeping to its philosophicalstance, much of the mathematical-modelling world has continuedalong its trajectory, producing ever more complex solutionsto ever more complex models, motivated by mathematical impressivenessrather than the need to solve real-world problems. This paperoutlines much of this work, some of which does find its wayinto project-network software but much of which languishes injournals. However, over the last decade or so, Operational Researchershave begun to build models of projects that are systemic anddynamic and explain many of the behaviours of projects thatconventional decomposition models do not; and at the same time,some of the Project Management world has started to realizethe limitations of its philosophical stance and started lookingto build new theory for modern, complex, dynamic projects. Asthese two trends come together, it is essential that modellersare at the forefront of building this new theory.