Designing a Robust Multi-objective Model for Project Scheduling with Limited Resources and Time-cost Balance

One of the important issues in project management is project scheduling. Since projects are faced with high uncertainty, project scheduling is of high importance under uncertain conditions. The purpose of this research is to present a robust multi-objective model to optimize project scheduling with limited resources by considering uncertainty, in which activities have several execution modes with uncertain duration, costs, and resources.
After reviewing the extant theoretical literature on project scheduling, the assumptions, parameters, and variables of the mathematical model were determined. Then, considering the goals and limitations of the project scheduling problem in deterministic conditions, a mathematical model was developed. This model was transformed into a single-objective model by the epsilon constraint method. To consider the uncertainty in the parameters of the problem, robust optimization, and Bertsimas and Sim's approach were used. Also, Robust optimization of the single-objective model was developed to consider the uncertainty.
According to the obtained results, while the duration of the project increases with the increase in the tolerance of non-deterministic parameters; the percentage of project duration changes decreases for higher values ​​of robust parameters.
The robust parameters are with negative coefficient in the objective function, so their increase leads to a decrease in the objective function value. The highest reduction of the objective function is when the robust parameter is changed from two to one. This coefficient decreases with the increasing value of the corresponding parameter i.e., as the value of stability parameters increases, its effect on changing the value of the objective function decreases. The cost parameter was changed between -40% to +40% for the value of gamma 10 (the state where 10 activities of the project are non-deterministic) for different variation values of parameters of non-deterministic activities. Its effect on the values of the objective function indicated that the variation of the cost parameter in the range of 0 to +40% turns it into an unnecessary constraint and that its change has no effect on the value of the objective function (project duration). Also, in the range of 0 to -40%, the cost reduction caused a decrease in the value of the objective function (increasing the project duration) and the maximum impact of the reduction of the project budget related to the situation where the uncertain parameters of time and cost change by 40% and 50%.