A grey mathematical model for crashing of projects by considering time, cost, quality, risk and law of diminishing returns

The purpose of this paper is to examine projects crashing based on the factors including cost, time, quality, risk and the law of diminishing returns.

The paper first investigated effective factors on project crashing then proposed a grey linear programming model. In the proposed grey linear programming model, the costs of quality of works that include the cost of conformance and non-conformance of deliverables in the project were studied. The results are presented for considering the existing uncertainties using positioned programming under the sensitivity analysis table and graphs.

The lack of consideration of project risks will reduce the project success probability in future. The proposed model reduces the existing uncertainties to a significant extent by covering the project risks completely. Based on the law of diminishing returns, after a certain point technically known as saturation point, the increase of resources does not lead to the reduction of time and may even have negative impacts. Finding the saturation point for each activity prevents the excessive allocation of resources that can lead to reduction of productivity.

The main duty of each project manager is finishing the project in the framework of the determined objectives. In most of the cases, after the preparation of the initial project schedule by the project team, it is seen that there is a need for the time reduction. This study has used a grey linear programming model for optimum crashing of project activities. In order to make the model more realistic and applicable, the authors endeavoured to consider most of the factors that are involved in doing a project.

In the present study, to the best of the authors’ knowledge the factors of time, cost, quality, risk and the law of diminishing returns are simultaneously considered in project crashing for the first time and the grey theory was used for considering the uncertainties of project parameters. Also, “the law of diminishing returns” has not been considered during crashing in the studies conducted so far.