Lagrangian relaxation based heuristic for an integrated production and maintenance planning problem

In this paper, an approach is developed to solve the joint production planning and maintenance problem. Moreover, some propositions and mathematical properties were suggested and applied in the proposed heuristic to solve this integrated problem. It is based on Lagrangian relaxation (Fisher, M.L., 1981 Fisher, M.L. 1981. Lagrangian relaxation method for solving integer programming problem. Management Science, 27(1): 1–18. [Crossref], [Web of Science ®] , [Google Scholar]. Lagrangian relaxation method for solving integer programming problem. Management Science, 27 (1), 1–18) of the capacity constraints and sub-gradient optimisation. At every step of the sub-gradient method, a smoothing procedure is applied to the solution of the Lagrangian problem to ensure the feasibility of solution and to improve it. Computational experiments are carried out to show the results obtained by our approaches and are compared to those of a commercial solver.