Integrated production and preventive maintenance scheduling for a single machine with failure uncertainty

We propose a joint model of production scheduling and PM planning for single machine.Proactive buffer times are planned considering unexpected breakdowns.Genetic algorithm is developed based on the analysis on problem properties.Both robustness and stability of the obtained initial plan are demonstrated. This paper addresses the problem of finding a robust and stable schedule for a single machine with availability constraints. The machine suffers unexpected breakdowns and follows the Weibull failure function. A joint model for integrating run-based preventive maintenance (PM) into the production scheduling problem is proposed, in which the sequence of jobs, the PM times and the planned completion times of jobs are proactively determined simultaneously. Aiming at optimizing the bi-objective of system robustness and stability, a genetic algorithm based on the properties of the optimal schedule is proposed. The experimental results demonstrate that the proposed algorithm is efficient and effective under practical problem sizes. In addition, the impact of degree of uncertainty on the performance and the tradeoff between robustness and stability are explored in detail.

[1]  Chen-Hua Chung,et al.  Integrating maintenance and production decisions in a hierarchical production planning environment , 1999, Comput. Oper. Res..

[2]  Alexander H. G. Rinnooy Kan,et al.  Single machine flow-time scheduling with a single breakdown , 1989, Acta Informatica.

[3]  Panos Kouvelis,et al.  Robust scheduling of a two-machine flow shop with uncertain processing times , 2000 .

[4]  Panagiotis Kouvelis,et al.  Robust scheduling to hedge against processing time uncertainty in single-stage production , 1995 .

[5]  Xiangtong Qi,et al.  A note on worst-case performance of heuristics for maintenance scheduling problems , 2007, Discret. Appl. Math..

[6]  George L. Vairaktarakis,et al.  Robust scheduling of a two-machine flow shop with uncertain processing times , 2000 .

[7]  Xiangtong Qi,et al.  Scheduling the maintenance on a single machine , 1999, J. Oper. Res. Soc..

[8]  K. Arrow,et al.  Optimal Inventory Policy. , 1951 .

[9]  Henri Pierreval,et al.  Analysis of robustness in proactive scheduling: A graphical approach , 2010, Comput. Ind. Eng..

[10]  Robert H. Storer,et al.  Robustness Measures and Robust Scheduling for Job Shops , 1994 .

[11]  Adam Kurpisz,et al.  Approximating a two-machine flow shop scheduling under discrete scenario uncertainty , 2012, Eur. J. Oper. Res..

[12]  Ihsan Sabuncuoglu,et al.  Robustness and stability measures for scheduling: single-machine environment , 2008 .

[13]  Jacek Blazewicz,et al.  An improved approximation algorithm for the single machine total completion time scheduling problem with availability constraints , 2005, Eur. J. Oper. Res..

[14]  Sanjay Mehta,et al.  Predictable scheduling of a single machine subject to breakdowns , 1999, Int. J. Comput. Integr. Manuf..

[15]  Christophe Varnier,et al.  Single-machine scheduling with periodic and flexible periodic maintenance to minimize maximum tardiness , 2008, Comput. Ind. Eng..

[16]  Charles E Ebeling,et al.  An Introduction to Reliability and Maintainability Engineering , 1996 .

[17]  Reha Uzsoy,et al.  Predictable scheduling of a job shop subject to breakdowns , 1998, IEEE Trans. Robotics Autom..