PERT-type projects: time–cost tradeoffs under uncertainty

Factual and anecdotal evidence confirms that investments in projects are inherently risky, as most large projects fail to meet their on-time and on-budget objectives. In one KPMG survey, 67% of the companies said that their project management function was in need of improvement. To address this issue, we examine two currently used procedures for crashing the project completion time by additional budget and develop a new stochastic procedure for this purpose. We consider projects with various patterns of activities, where the randomness of their duration derives from external uncertainty, internal uncertainty or both and where the correlation between their actual cost and random duration is known. The objective is to optimize the budget allocation among project activities, i.e. to determine the optimized activity execution speeds. We aim to minimize the project budget or any chance-constrained project cost, subject to any chance-constrained project completion time. We conduct Monte Carlo comparisons of the relative efficiency of the alternative procedures for crashing the project completion time on PERT-type projects. Broad Monte Carlo simulations confirm that the newly developed procedure can be an efficient tool for project management.

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