Makespan optimization in a single-machine scheduling problem with dynamic job ready times—Complexity and algorithms

An industrial problem encountered in steel mills is considered in the paper. The problem is formulated as a single-processor scheduling problem with a dynamic model of the task release date. In this model, a task is released for processing when its preprocessing is in the final state. The instantaneous rate of the change of the preprocessing state (from the initial to the final one) depends on the amount of resource allotted to the task. The resource available for task preprocessing is renewable and upper bounded. The problem consists in establishing the task sequence and the resource allocation that minimize the makespan. This problem has already been considered in the literature, but its complexity has not been formally proved. The proof of NP-hardness by polynomial reduction from the partition problem is presented in this paper. Two metaheuristics (simulated annealing and tabu search) are proposed to solve the problem. Both are tested, and the results are analyzed.