Statistics

Duration (music)

Literature

Mathematical optimization

Neoclassical economics

Stochastic programming

Function (biology)

Minification

Economics

Microeconomics

Total cost

Probability density function

Maximization

Mathematics

Computer science

Operations research

Evolutionary biology

Budget constraint

Biology

Computers & Industrial Engineering

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.

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