Resource constraint scheduling with a fractional shared resource

► We present a scheduling problem with a single shared resource. ► We compare ILP and Lagrangian methods with simulated annealing and genetic algorithms. ► Computational results show that ILP could only solve very small size instances. ► The Lagrange relaxation method was better than the metaheuristics for large instances. ► In small instances, the metaheuristics were found close to optimum solutions.