Activity time–cost tradeoffs under time and cost chance constraints

We describe a stochastic extension of the critical path method time–cost tradeoff model. This extension includes four fundamental formulations of time–cost tradeoff models that represent different assumptions of the effect of the changing performance speed on the frequency distribution parameters of the activity duration, as well as the effect of the random activity duration on the activity cost. The formulations are based on clean fractile methods and therefore avoid the unfeasible necessity for additional groups of experts' estimates for each possible performance speed. Our formulations also enable us to consider both stochastic time and cost parameters. We developed several ideas for formulating the relationships between time–cost tradeoffs and two chance constraints for a single activity, the time chance constraint and the cost chance constraint. The developed formulas for multi-objective models can easily be incorporated into time–cost optimization procedures, thus enabling the procedures to optimize cost risks as well as time risks.