A Continuous-Time Unit-Based MILP Formulation for the Resource-Constrained Project Scheduling Problem

Abstract

In the basic resource-constrained project scheduling problem RCPSP, one aims at selecting starting times for the tasks of a project such that the project makespan is minimized and the project schedule is precedence- and resource-feasible. There is a considerable body of literature about problem-specific solution methods; recently, mixed-integer linear programming (MILP) formulations for the RCPSP have received increasing attention. We suggest a new MILP formulation that utilizes a set of continuous variables indicating the starting times of the project tasks, and three sets of binary variables indicating the assignment of resource units to the project tasks, the potential overlapping of the project tasks, and the sequencing of the project tasks. In a comparison with ten reference formulations from the literature, it is found that the advantages of this new formulation are its simple structure, enhanced flexibility, and superior or comparable performance, particularly when the range of the tasks’ durations is relatively high.