Scheduling on parallel processors with varying processing times

The parallel processor makespan minimization with general position dependent models is considered.An exact parallel fast dynamic programing algorithm is constructed.Fully polynomial time approximation schemes are provided. In this paper, we construct the pseudopolynomial dynamic programming algorithm that optimally solves the parallel identical processor scheduling problem to minimize the maximum job completion times (makespan) under varying processing times. They can be described by an arbitrary monotonic function dependent on the number of previously processed jobs, which can model learning or aging effects. Beside the canonical dynamic programming algorithm, we provide its efficient parallel fast version, which solves moderate problem instances of the problem within reasonable time and memory usage. Additionally, on the basis of the constructed algorithm, a fully polynomial time approximation scheme for the considered problem is provided.

[1]  Tamer Eren,et al.  A note on minimizing maximum lateness in an m-machine scheduling problem with a learning effect , 2009, Appl. Math. Comput..

[2]  Bart De Schutter,et al.  A Comprehensive Survey of Multiagent Reinforcement Learning , 2008, IEEE Transactions on Systems, Man, and Cybernetics, Part C (Applications and Reviews).

[3]  Gur Mosheiov,et al.  Parallel machine scheduling with a learning effect , 2001, J. Oper. Res. Soc..

[4]  Dirk Biskup,et al.  Single-machine scheduling with learning considerations , 1999, Eur. J. Oper. Res..

[5]  Dehua Xu,et al.  Comments on "A note on minimizing maximum lateness in an m-machine scheduling problem with a learning effect" , 2010, Appl. Math. Comput..

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

[7]  Stanislaw Gawiejnowicz,et al.  Exact and heuristic algorithms for parallel-machine scheduling with DeJong's learning effect , 2010, Comput. Ind. Eng..

[8]  T. C. Edwin Cheng,et al.  Unrelated parallel-machine scheduling with aging effects and multi-maintenance activities , 2012, Comput. Oper. Res..

[9]  Alessandro Agnetis,et al.  Multiagent Scheduling - Models and Algorithms , 2014 .

[10]  Wei-Chang Yeh,et al.  Uniform parallel-machine scheduling to minimize makespan with position-based learning curves , 2012, Comput. Ind. Eng..

[11]  Xi Zhang,et al.  Several flow shop scheduling problems with truncated position-based learning effect , 2013, Comput. Oper. Res..

[12]  Stanislaw Gawiejnowicz,et al.  A Note on Scheduling on a Single Processor with Speed Dependent on a Number of Executed Jobs , 1996, Inf. Process. Lett..

[13]  Dirk Biskup,et al.  A state-of-the-art review on scheduling with learning effects , 2008, Eur. J. Oper. Res..