Completing on time, within the estimated budget and at the desired quality are three main constraints of construction projects. However, construction projects become nowadays more complex than ever, so they are subjected to uncertainties and changes throughout the project life cycles. These uncertainties and changes may lead to severe delays in project duration. Therefore, project managers desire to reduce the project duration without changing scope of the project. Crashing a project is an advanced project management strategy, which aims to achieve the maximum reduction in project duration with the minimum additional cost without changing the scope. However, project crashing is a difficult task and should be used if it is necessarily needed. This paper proposes a model that considers crash duration consumption rates of activities for solving the project crashing problem. The crash duration consumption rate is the percentage that is set to determine the maximum amount of crash duration that an activity can consume with safety margin. The proposed model enables the schedulers to assign crash duration consumption rates to each activity that can be used during the project crashing procedure. Having applied the proposed model, the Monte Carlo simulation is also performed to determine the probability of completion of the project at the latest in crashed project duration. The applicability of the proposed model is presented along with an illustrative example. The proposed model is supposed to minimize the likelihood of delays, while maintaining schedule flexibility. In addition, the proposed model provides schedulers a new perspective in solving project crashing problems.