Computations for the Capacitated Planned Maintenance Problem

Abstract

Computational experiments evaluate the optimization approaches for the Capacitated Planned Maintenance Problem (CPMP). Since the CPMP is a novel problem, an instance generation scheme and test-sets are presented. The evaluation includes the absolute strength of all relevant lower bounds obtained from Lagrangean relaxation, decomposition and by neglecting constraints completely. Pseudo-subgradient optimization solves the Lagrangean relaxation heuristically, whereas many approaches in literature prefer an optimal solution to derive subgradients from. A computational study empirically shows that this approach is more successful if the better the lower and upper bounds to the Lagrangean relaxation are. The best construction heuristic provides an average relative error of 6 % to the optimum but the Lagrangean and tabu search heuristics provide ¡1 %. The Lagrangean heuristics evolve the upper bounds in the first seconds and find a good solution. The tabu search heuristic slowly but constantly improves the upper bound and outperforms the Lagrangean heuristics when the capacity availability is low.