Exact and heuristic methods to solve the parallel machine scheduling problem with multi-processor tasks

Abstract This paper studies a special parallel machine scheduling problem where some tasks require more than one machine to process, known as the Parallel Machine Scheduling Problem with Multi-processor Tasks. Two mathematical models and several theoretical properties are proposed for the studied problem. To solve this problem, this paper develops an exact branch and bound algorithm and a heuristic tabu search algorithm. A series of numerical experiments are conducted to test the performance of these solution methods. The computational results show that the solution methods are effective and efficient in solving the problem with different sizes.

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

[2]  Maciej Drozdowski,et al.  On contiguous and non-contiguous parallel task scheduling , 2015, J. Sched..

[3]  Chung-Yee Lee,et al.  Parallel machines scheduling with nonsimultaneous machine available time , 1991, Discret. Appl. Math..

[4]  Maciej Drozdowski,et al.  Scheduling multiprocessor tasks -- An overview , 1996 .

[5]  Lotfi Hidri.  Note on the Hybrid Flowshop Scheduling Problem with Multiprocessor Tasks , 2016 .

[6]  Errol L. Lloyd,et al.  Concurrent Task Systems , 1981, Oper. Res..

[7]  Berit Johannes,et al.  Scheduling parallel jobs to minimize the makespan , 2006, J. Sched..

[8]  Joseph Y.-T. Leung,et al.  Complexity of Scheduling Parallel Task Systems , 1989, SIAM J. Discret. Math..

[9]  Fuh-Der Chou,et al.  PARTICLE SWARM OPTIMIZATION WITH COCKTAIL DECODING METHOD FOR HYBRID FLOW SHOP SCHEDULING PROBLEMS WITH MULTIPROCESSOR TASKS , 2013 .

[10]  M. F. Monaco,et al.  A tabu search heuristic for the quay crane scheduling problem , 2007 .

[11]  Fred W. Glover,et al.  Future paths for integer programming and links to artificial intelligence , 1986, Comput. Oper. Res..

[12]  Jianer Chen,et al.  General Multiprocessor Task Scheduling , 1999 .

[13]  Maghsud Solimanpur,et al.  A tabu search approach for cell scheduling problem with makespan criterion , 2013 .

[14]  Jatinder N. D. Gupta,et al.  Scheduling identical parallel machines with fixed delivery dates to minimize total tardiness , 2015, Eur. J. Oper. Res..

[15]  Sao-Jie Chen,et al.  Scheduling algorithm for nonpreemptive multiprocessor tasks , 1994 .

[16]  Henryk Krawczyk,et al.  An Approximation Algorithm for Diagnostic Test Scheduling in Multicomputer Systems , 1985, IEEE Transactions on Computers.

[17]  Joseph Y.-T. Leung,et al.  Handbook of Scheduling: Algorithms, Models, and Performance Analysis , 2004 .

[18]  Franciszek Seredynski,et al.  Scheduling parallel batch jobs in grids with evolutionary metaheuristics , 2014, Journal of Scheduling.

[19]  Anatoliy O. Buda.  Multiprocessor Automata , 1987, Inf. Process. Lett..

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

[21]  Jan Karel Lenstra,et al.  Scheduling subject to resource constraints: classification and complexity , 1983, Discret. Appl. Math..

[22]  Michel Gendreau,et al.  A tabu search heuristic for the multiprocessor scheduling problem with sequence dependent setup times , 1996 .

[23]  S. Webster.  A general lower bound for the makespan problem , 1996 .

[24]  Evripidis Bampis,et al.  Scheduling Independent Multiprocessor Tasks , 2002, Algorithmica.

[25]  Jacek Blazewicz,et al.  Scheduling Multiprocessor Tasks to Minimize Schedule Length , 1986, IEEE Transactions on Computers.

[26]  Keqin Li.  Analysis of an Approximation Algorithm for Scheduling Independent Parallel Tasks , 1999, Discret. Math. Theor. Comput. Sci..

[27]  Jacek Blazewicz,et al.  Scheduling multiprocessor tasks on parallel processors with limited availability , 2003, Eur. J. Oper. Res..

[28]  Z. Caner Taskin,et al.  Optimal berth allocation and time-invariant quay crane assignment in container terminals , 2014, Eur. J. Oper. Res..

[29]  J. M. J. Schutten,et al.  List scheduling revisited , 1996, Oper. Res. Lett..

[30]  G. Laporte,et al.  A tabu search heuristic for periodic and multi-depot vehicle routing problems , 1997, Networks.