Abstract
Problem statement: In this article we address the multi-objective Per iodic Maintenance Scheduling Problem (PMSP) of scheduling a set of cyclic maintenance operations for a given set of machines through a specified planning period to min imize the total variance of workforce levels measured in man-hours and maintenance costs with equal weights. Approach: The article proposed a mixed integer non-linear math programming model and a linearised model for the PMSP. Also, we proposed a Genetic Algorithm (GA) for solving the p roblem using a new genome representation considered as a new addition to the maintenance sch eduling literature. The algorithms were compared on a set of representative test problems. Results: The developed GA proves its capability and superiority to find good solutions for the PMSP and outperforms solutions found by the commercial optimization package CPLEX. The results indicated that the developed algorithms were able to identify optimal solutions for small size problems up to 5 machines and 6 planning periods.The GAs defined solutions in 22 seconds con suming less than two kilobytes with a reliability of 0.84 while the nonlinear and linear models consumes on average 705 and 37 kilobytes respectively. Conclusion: The developed GA could define solutions of averag e performance of 0.34 and 0.8 for the linearized algorithm compared with lower bound defined by the nonlinear math programming model. We hope to expand the developed algorithms for integrating maintenance planning and aggregate production planning problems.
Highlights
The preventive maintenance scheduling is among the most important problems faced by productive/service organizations
Based on the definitions of indexes, parameters and decision variables we formulate the multi-objective mixed-integer non-linear math programming model for the PSMP as follows: The math programming models: We develop a mixed-integer non-linear math programming model for Periodic Maintenance Scheduling Problem (PMSP) as a standard time-indexed formulation and linearise it to find the global optimal solution
The problem had a predefined sequence of maintenance operations on a set of machines for a definite planning period
Summary
The preventive maintenance scheduling is among the most important problems faced by productive/service organizations. The preventive maintenance applied by servicing the equipment on regular intervals is for the purpose of increasing its reliability as much as possible. The problem has attracted researchers due to its economical importance and complexity, see for example Dekker (1996). These articles and others contained therein were interested in modeling and solving the problem to minimize the cost or maximize the machine lifetime. Extensive research treated the problem as a stochastic model whereas the machine failures described by probability distributions (see for instance Gertsbakh and Gertsbakh (2000) while a little was concerned with the deterministic case where the failures described by constant parameters
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