Solving the integrated production and imperfect preventive maintenance planning problem

This paper considers the integrated production and imperfect preventive maintenance planning problem. The article provides more details on how Relax-and-Fix/Fix-and-Optimize as well as Dantzig-Wolfe Decomposition and Lagrangian Relaxation techniques were applied and implemented for solving the integrated production and imperfect preventive maintenance planning problem. More experiments were also carried out. The objective of this planning problem is to determine an optimal integrated production and preventive maintenance plan that concurrently minimizes production as well as preventive maintenance costs during a given finite planning horizon. Three solution approaches were investigated and applied to the reformulated version of the problem, and their performances are compared and discussed. The Relax-and-Fix/Fix-and-Optimize method (RFFO) determines first an initial feasible solution, generated by the relax-and-fix heuristic step, which is further improved in the fix-and-optimize step. Dantzig-Wolfe Decomposition (DWD) and Lagrangian Relaxation (LR) techniques are also applied to the same reformulation of the problem and the results of these three approaches are compared in terms of the solution quality as well as CPU time. The computational results obtained for different instances of the integrated production planning and imperfect preventive maintenance planning problem, show that the RFFO method is very efficient and is competitive in term of the solutions quality. It provides quite good solutions to the tested instances with a noticeable improvement in computational time. Dantzig-Wolfe Decomposition (DWD) and Lagrangian Relaxation (LR) methods, on the other hand, exhibit a good enhancement in terms of computational time especially for large instances, however, the quality of solution still requires some more improvements