Um estudo sobre formulações matemáticas e estratégias algorítmicas para problemas de escalonamento em máquinas paralelas com penalidades de antecipação e atraso

Abstract

This dissertation presents a study on scheduling problems with earliness and tardiness penalties on identical parallel machines, considering independent and weighted jobs with arbitrary processing times. An analysis of the major mathematical formulations in integer programming is given, and presented the main results from the literature. An integer mathematical formulation based on network flow model was also proposed for the problem, which can be applied on single and parallel machines without idle time. Exact methods of implicit enumeration were studied and applied for the problem through the integer linear programming solver CPLEX and the UFFLP library and, mainly, algorithmic strategies of global optimization based on local search heuristic and path-relinking technique were developed. The computational experiments shows that the proposed algorithmic strategies are competitive in relation to existing results from the literature for single-machine scheduling, involving instances based on OR-Library benchmark for 40, 50, 100, 150, 200 and 300 jobs, where all the optimal values were found, and, mainly, being the best algorithmic strategy for multiprocessor environments, involving 2, 4 and 10 identical parallel machines.