Final Remarks and Future Perspectives

Abstract

This chapter summarizes the presented work for Capacitated Planned Maintenance Problem (CPMP) and the Weighted Uncapacitated Planned Maintenance Problem (WUPMP) that are both strongly $\mathcal{N}\mathcal{P}$-hard. The main computational complexity results and the running time of optimal algorithms are given. The WUPMP has the single-assignment property and the polytope is quasi-integral. A generalized period covering constraint has an integral polytope. The CPMP is solved via construction heuristics, Lagrangean heuristics, a novel Lagrangean hybrid approach that links two Lagrangean relaxations and tabu search. The performance of these approaches is described. It is advantageous to derive valid subgradients from heuristically derived feasible solutions, whereas many approaches in literature solve the Lagrangean relaxation to optimality.