A branch and bound algorithm for single-machine production scheduling integrated with preventive maintenance planning

This paper deals with an integrated optimisation model for production scheduling and preventive maintenance (PM) in a single machine with its time to failure subject to a Weibull probability distribution. The objective is to minimise the total expected weighted completion time of jobs. To solve this problem, we develop a branch and bound (B&B) algorithm (hereafter called the B&BA). Several lower bounds, dominance rules and upper bounds are developed to enhance the performance of the B&BA. Extensive computational experiments on randomly generated problems with different configurations are conducted and the results show that the proposed method can find optimal solutions for problems with up to 18 jobs in a reasonable amount of computation time.

[1]  Jian-Bo Yang,et al.  Minimizing total completion time on a single machine with a flexible maintenance activity , 2011, Comput. Oper. Res..

[2]  J. S. Chen,et al.  Single-machine scheduling with flexible and periodic maintenance , 2006, J. Oper. Res. Soc..

[3]  Wen-Jinn Chen,et al.  Minimizing number of tardy jobs on a single machine subject to periodic maintenance , 2009 .

[4]  C. Richard Cassady,et al.  Integrating preventive maintenance planning and production scheduling for a single machine , 2005, IEEE Transactions on Reliability.

[5]  Ching-Jong Liao,et al.  An ant colony optimization for single-machine tardiness scheduling with sequence-dependent setups , 2007, Comput. Oper. Res..

[6]  Chung-Yee Lee,et al.  Single-machine scheduling with maintenance and repair rate-modifying activities , 2001, Eur. J. Oper. Res..

[7]  Jen-Shiang Chen,et al.  Scheduling of nonresumable jobs and flexible maintenance activities on a single machine to minimize makespan , 2008, Eur. J. Oper. Res..

[8]  Jiang Zuhua,et al.  Multi-objective integrated optimization research on preventive maintenance planning and production scheduling for a single machine , 2008 .

[9]  C. Richard Cassady,et al.  Minimizing Job Tardiness Using Integrated Preventive Maintenance Planning and Production Scheduling , 2003 .

[10]  M. Gossa,et al.  Simultaneous scheduling of production and maintenance tasks in the job shop , 2011 .

[11]  Min Ji,et al.  Minimizing the makespan in a single machine scheduling problems with flexible and periodic maintenance , 2010 .

[12]  J. George Shanthikumar,et al.  COMBINED PRODUCTION AND MAINTENANCE SCHEDULING FOR A MULTIPLE‐PRODUCT, SINGLE‐ MACHINE PRODUCTION SYSTEM , 2009 .

[13]  Nidhal Rezg,et al.  No-wait scheduling of a two-machine flow-shop to minimise the makespan under non-availability constraints and different release dates , 2011 .

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

[15]  M. Azizoglu,et al.  Single machine scheduling with preventive maintenances , 2009 .

[16]  C. Richard Cassady,et al.  Genetic algorithms for integrated preventive maintenance planning and production scheduling for a single machine , 2005, Comput. Ind..

[17]  Shih-Wei Lin,et al.  Solving single-machine total weighted tardiness problems with sequence-dependent setup times by meta-heuristics , 2007 .

[18]  Maw-Sheng Chern,et al.  MINIMIZING THE MAKESPAN IN A SINGLE MACHINE SCHEDULING PROBLEM WITH A FLEXIBLE MAINTENANCE , 2002 .

[19]  Günter Schmidt,et al.  Scheduling with limited machine availability , 2000, Eur. J. Oper. Res..

[20]  Rubén Ruiz,et al.  Considering scheduling and preventive maintenance in the flowshop sequencing problem , 2007, Comput. Oper. Res..

[21]  Kevin D. Glazebrook,et al.  Scheduling stochastic jobs on a single machine subject to breakdowns , 1984 .

[22]  Michael Pinedo,et al.  Scheduling: Theory, Algorithms, and Systems , 1994 .

[23]  Michael Pinedo,et al.  Current trends in deterministic scheduling , 1997, Ann. Oper. Res..

[24]  Marc Gravel,et al.  Comparing an ACO algorithm with other heuristics for the single machine scheduling problem with sequence-dependent setup times , 2002, J. Oper. Res. Soc..

[25]  Chung-Yee Lee,et al.  Machine scheduling with an availability constraint , 1996, J. Glob. Optim..

[26]  Jen-Shiang Chen,et al.  Optimization models for the machine scheduling problem with a single flexible maintenance activity , 2006 .

[27]  Eric Sanlaville,et al.  Machine scheduling with availability constraints , 1998, Acta Informatica.

[28]  Chengbin Chu,et al.  A survey of scheduling with deterministic machine availability constraints , 2010, Comput. Ind. Eng..

[29]  Vitaly A. Strusevich,et al.  Planning Machine Maintenance in Two-Machine Shop Scheduling , 2006, Oper. Res..

[30]  Wen‐Jinn Chen,et al.  Scheduling with different maintenance policies in a textile company , 2005 .

[31]  Mitsuo Gen,et al.  Scheduling jobs and maintenances in flexible job shop with a hybrid genetic algorithm , 2006, J. Intell. Manuf..

[32]  Chung Yee Lee,et al.  Scheduling maintenance and semiresumable jobs on a single machine , 1999 .

[33]  Gang Yu,et al.  Single machine scheduling under potential disruption , 2007, Oper. Res. Lett..

[34]  Lifeng Xi,et al.  Single-machine-based production scheduling model integrated preventive maintenance planning , 2010 .

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

[36]  Hongxing Li,et al.  Scheduling problems with multiple maintenance activities and non-preemptive jobs on two identical parallel machines , 2010 .

[37]  Maher Rebai,et al.  Scheduling jobs and maintenance activities on parallel machines , 2013, Oper. Res..