Time-cost trade-off model in GERT-type network with characteristic function for project management

Abstract

Activity crashing is an efficient way for project acceleration but always leads to time–cost trade-off issues. The current study proposes an optimal time–cost trade-off model in GERT (Graphical Evaluation and Review Technique) with consideration to both the probability of on-time delivery and under-budget. Firstly, the hypothesis in the previous literature that the minimization of expected completion time is equivalent to the maximization of the on-time completion probability is proven to be invalid. Secondly, to ensure successful project completion, the constraints on the probability of on-time delivery and under-budget are added in the trade-off model. Furthermore, the characteristic function-enhanced GERT is designed to derive the probability density function of project time and cost, thereby yielding the on-time probability and under-budget probability. Consequently, the stochastic programming model for time–cost trade-offs is presented to minimize the mean duration while ensuring a desired on-time completion probability and under-budget probability. To solve the proposed stochastic programming, a genetic algorithm-based solution procedure is designed. Finally, a numerical example is employed to demonstrate the effectiveness of the proposed model. The study contributes to our understanding that minimizing mean duration cannot necessarily maximize on-time project completion. It also helps us reduce the mean project duration and guarantee high on-time delivery and under-budget performance simultaneously, which are two critical success factors in project management.