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

Abstract

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 1981) of the capacity constraints and sub-gradient optimization. At every step of 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.

Modelling maintenance effects on manufacturing equipment performance: results from simulation analysis

“…Tsarouhas (2012) also proposes a framework based on OEE for analysing the performance of a beverage plant. Alaoui-Selsouli, Mohafid, and Najid (2012) propose the use of a mixed-integer mathematical model incorporating a relaxed Lagrangian heuristic to investigate the conflicting interaction between production demand on the one hand and an unreliable equipment on the other hand.…”

Integration of maintenance and production strategies under subcontracting constraint: Classification and opportunity

“…The work by [34] focused on an integrated modelling method that simultaneously determined production planning and maintenance planning in the machining system, considering the replacement of the machine's failure tool, as well as the constant demand and possible shortage. Based on a linear mixed number programming model, the authors of reference [35] jointly planned the production and maintenance activities. The model considered the reliability (expected number of failures) of production costs, maintenance, shortages and demand.…”

“…Several approaches have been developed to solve the problem of planning and maintenance of joint production. Moreover, some mathematical propositions and properties have been suggested and applied in the proposed heuristic to solve this integrated problem based on the Lagrangian relaxation of the capacity constraints and the optimisation of the sub-gradient [35]. In addition, heuristics based on genetic algorithms have been used to solve an integrated optimisation model for production scheduling and preventive maintenance planning [61].…”