A mathematical model for controlling the budget and variable cost of project activities in the status of time-cost tradeoff with consideration of delay penalty

In this paper, an integer linear programming model is proposed to examine the effect of the project's uncertain budget on its performance. Although much research has been done in the past to optimize the time-cost trade off problem (TCT), in this paper, the project accounting approach has been used in the uncertain terms of receiving the allocated budget, the uncertainty associated with the cost of project activities and its duration. From the innovations of this research, the combination of generalized prerequisite relationships (GPRs) with the various modes of implementation of the activities and scenarios is continuous, discrete and combined (continuous / discrete). Chance constraint programming (CCP) has been used to terminate the variable budget. Stochastic budget limitations are at a predetermined level of confidence. Program evaluation review technique (PERT) has been used to estimate uncertain times, and to calculate the uncertain costs of the operating modes of activities; the triangulation method has been used. The mathematical model, which is to minimize the total time of the project, was solved by software (GAMS), taking into account the early remuneration at the completion of the project and the late delinquency, and was implemented on a real numeric sample to prove the function and validation of the model. Different scenarios have been proposed that the effect of each of them on budget changes and uncertainty over time on direct, indirect, total and project costs are reviewed.