New continuous-time and discrete-time mathematical formulations for resource-constrained project scheduling problems

Two binary integer programming discrete-time models and two precedence-based mixed integer programming continuous-time formulations are developed for the resource-constrained project scheduling problem. The discrete-time models are based on the definition of binary variables that describe the processing state of every activity between two consecutive time points, while the continuous-time models are based on the concept of overlapping of activities, and the definition of a number of newly introduced sets. Our four mathematical formulations are compared with six representative literature models in 3240 benchmark problem instances. A detailed computational comparison assesses the performance of the mathematical models considered.