Time–cost tradeoff analysis considering funding variability and time uncertainty

This paper presents a linear programming model for solution of the time–cost tradeoff problem. Although several analytical models have been developed for time–cost optimization (TCO), some of them mainly focused on projects where the contract duration is fixed. The optimization objective is therefore restricted to identify the minimum total cost only. Another group have primarily focused on project duration minimization. The model presented here considers scheduling characteristics that were ignored simultaneously in prior research. In the new formulation, variability of funding and uncertainty of project duration are considered simultaneously. A chance-constrained programming is used to incorporate the variability of funding, which is quantified by the coefficient of variation. The financial feasibility expressed as a stochastic constraint, which transformed into a deterministic equivalent at a pre-specified confidence level. Also, the project duration uncertainty incorporated into the model by applying PERT in scheduling and then the uncertainty is quantified by the coefficient of variation at a pre-specified confidence level. A system of objective function, which is minimizing direct cost and the group of constraints are solved by means of Lindo software. Two examples are conducted to demonstrate the model performance and its contributions. Four scenarios were adopted in solving the example problems to reflect the effect of each of funding variability and time uncertainty on project cost and duration. The results revealed that with 95% confidence level: 10% variability in funding versus neglecting it, would increase direct cost with 20% approximately for a pre-specified project deadline. Also, 10% variability in time versus neglecting it, would increase duration in range from 16.5% to 30% approximately, for a pre-specified direct cost. Also, considering 10% variability in funding and time would increase direct cost with more than 25% for a pre-specified project deadline. In parallel, an increase in project duration, more than 30% will occur for a pre-specified direct cost.