Parallel branch-and-bound and parallel PSO algorithms for job shop scheduling problem with blocking

In this paper, we deal with the resolution of the scheduling problem with blocking which is known to be non-polynomial-hard. The nature of the workshop defines the type of issue to treat: flow shop problem and job shop problem (JSP). A lot of researches are dedicated in the literature to the resolution of the flow shop problem, whereas not enough works are found concerning JSP. We have oriented our efforts in this paper to the resolution of JSP with blocking. For that, we propose three methods: a parallel version of a branch-and-bound method based on an implicit enumeration, a sequential particle swarm optimisation (PSO) and a parallel PSO. The first one is an exact method but the complexity of the problem makes it useless for more than 10 jobs × 10 machines. For that, we investigate in meta-heuristics which procure good scheduling in real time. A comparison of these methods is presented at the end of this paper.

[1]  Débora P. Ronconi,et al.  Some heuristic algorithms for total tardiness minimization in a flowshop with blocking , 2009 .

[2]  Ameur Soukhal,et al.  Complexity of flow shop scheduling problems with transportation constraints , 2005, Eur. J. Oper. Res..

[3]  Martina Gorges-Schleuter,et al.  ASPARAGOS An Asynchronous Parallel Genetic Optimization Strategy , 1989, ICGA.

[4]  Chin-Chia Wu,et al.  A two-machine flowshop scheduling problem with deteriorating jobs and blocking , 2010 .

[5]  Andreas Klinkert,et al.  Surgical case scheduling as a generalized job shop scheduling problem , 2008, Eur. J. Oper. Res..

[6]  Chelliah Sriskandarajah,et al.  A Survey of Machine Scheduling Problems with Blocking and No-Wait in Process , 1996, Oper. Res..

[7]  Heinz Gröflin,et al.  A new neighborhood and tabu search for the Blocking Job Shop , 2009, Discret. Appl. Math..

[8]  P. Shahabudeen,et al.  GA based static scheduling of multilevel assembly job shops , 2009 .

[9]  Heinz Mühlenbein,et al.  Parallel Genetic Algorithms, Population Genetics, and Combinatorial Optimization , 1989, Parallelism, Learning, Evolution.

[10]  Xianpeng Wang,et al.  A tabu search heuristic for the hybrid flowshop scheduling with finite intermediate buffers , 2009, Comput. Oper. Res..

[11]  Erwin Pesch,et al.  Evolution based learning in a job shop scheduling environment , 1995, Comput. Oper. Res..

[12]  Ling Wang,et al.  An effective hybrid particle swarm optimization for no-wait flow shop scheduling , 2007 .

[13]  J. Grabowski,et al.  The permutation flow shop problem with blocking. A tabu search approach , 2007 .

[14]  John L. Hunsucker,et al.  A new heuristic for minimal makespan in flow shops with multiple processors and no intermediate storage , 2004, Eur. J. Oper. Res..

[15]  E.L. Lawler,et al.  Optimization and Approximation in Deterministic Sequencing and Scheduling: a Survey , 1977 .

[16]  T. C. Edwin Cheng,et al.  The three-machine flowshop scheduling problem to minimise maximum lateness with separate setup times , 2007 .

[17]  R. Gomory,et al.  Multistage Cutting Stock Problems of Two and More Dimensions , 1965 .

[18]  Jens Clausen,et al.  Parallel branch-and-bound methods for thejob-shop scheduling problem , 1998, Ann. Oper. Res..

[19]  Ling Wang,et al.  An Effective Hybrid Heuristic for Flow Shop Scheduling , 2003 .

[20]  Débora P. Ronconi,et al.  A note on constructive heuristics for the flowshop problem with blocking , 2004 .

[21]  Zaher Mahjoub,et al.  On a parallel genetic-tabu search based algorithm for solving the graph colouring problem , 2009, Eur. J. Oper. Res..

[22]  Ameur Soukhal,et al.  Resolution of a scheduling problem in a flowshop robotic cell , 2005, Eur. J. Oper. Res..

[23]  Peter Brucker,et al.  A Branch and Bound Algorithm for the Job-Shop Scheduling Problem , 1994, Discret. Appl. Math..

[24]  Nidhal Rezg,et al.  Scheduling Problem of Job-Shop with Blocking: A Taboo Search Approach , 2001 .

[25]  Imma Ribas,et al.  An iterated greedy algorithm for the flowshop scheduling problem with blocking , 2011 .

[26]  J. Carlier,et al.  Adjustment of heads and tails for the job-shop problem , 1994 .

[27]  Yazid Mati,et al.  Complexity of flowshop scheduling problems with a new blocking constraint , 2003, Eur. J. Oper. Res..

[28]  C. V. Ramamoorthy,et al.  On the Flow-Shop Sequencing Problem with No Wait in Process † , 1972 .

[29]  J. Carlier,et al.  An algorithm for solving the job-shop problem , 1989 .

[30]  Tapan P. Bagchi,et al.  Minimizing makespan in a blocking flowshop using genetic algorithms , 2001 .

[31]  Dario Pacciarelli,et al.  Job-shop scheduling with blocking and no-wait constraints , 2002, Eur. J. Oper. Res..

[32]  Tarek Y. ElMekkawy,et al.  Mathematical formulations for scheduling in manufacturing cells with limited capacity buffers , 2010 .

[33]  Ravi Sethi,et al.  The Complexity of Flowshop and Jobshop Scheduling , 1976, Math. Oper. Res..

[34]  Bernard Manderick,et al.  Fine-Grained Parallel Genetic Algorithms , 1989, ICGA.

[35]  Ponnuthurai N. Suganthan,et al.  A novel hybrid discrete differential evolution algorithm for blocking flow shop scheduling problems , 2010, Comput. Oper. Res..

[36]  Erhan Kozan,et al.  Scheduling a flow-shop with combined buffer conditions , 2009 .