Generating efficient schedules for identical parallel machines involving flow-time and tardy jobs

This paper considers the problem of generating a set of efficient (non-dominated) schedules on identical parallel machines involving total flow-time and total number of tardy jobs. In view of the NP-hard nature of this problem, heuristic algorithms are proposed for its solution. Two evaluation methods that provide a scheme by which multiple non-dominated sets can be compared are described and used to compare the performance of the proposed algorithms. Results of several experiments demonstrate the capability of the proposed algorithms and evaluation methodologies to address the problem at hand.

[1]  Jacques Teghem,et al.  Efficiency of interactive multi-objective simulated annealing through a case study , 1998, J. Oper. Res. Soc..

[2]  R. Barton,et al.  Simulated annealing heuristics for the average flow-time and the number of tardy jobs bi-criteria identical parallel machine problem , 1997 .

[3]  Johnny C. Ho,et al.  Minimizing the number of tardy jobs for m parallel machines , 1995 .

[4]  George L. Vairaktarakis,et al.  Complexity of Single Machine Hierarchical Scheduling: A Survey , 1993 .

[5]  C. D. Gelatt,et al.  Optimization by Simulated Annealing , 1983, Science.

[6]  Gerhard J. Woeginger,et al.  A Review of Machine Scheduling: Complexity, Algorithms and Approximability , 1998 .

[7]  E. L. Ulungu,et al.  MOSA method: a tool for solving multiobjective combinatorial optimization problems , 1999 .

[8]  P. Pardalos.  Complexity in numerical optimization , 1993 .

[9]  David S. Johnson,et al.  Complexity Results for Multiprocessor Scheduling under Resource Constraints , 1975, SIAM J. Comput..

[10]  Joseph Y.-T. Leung,et al.  Heuristic for Minimizing the Number of Late Jobs on Two Processors , 1994, Int. J. Found. Comput. Sci..

[11]  Wayne E. Smith.  Various optimizers for single‐stage production , 1956 .

[12]  P. Pardalos,et al.  Handbook of Combinatorial Optimization , 1998 .

[13]  Jatinder N. D. Gupta,et al.  Minimizing maximum tardiness and number of tardy jobs on parallel machines subject to minimum flow-time , 2003, J. Oper. Res. Soc..

[14]  Gürsel A. Süer,et al.  Minimizing the number of tardy jobs in identical machine scheduling , 1993 .

[15]  William L. Maxwell,et al.  Theory of scheduling , 1967 .

[16]  A. Nagar,et al.  Multiple and bicriteria scheduling : A literature survey , 1995 .

[17]  Jean-Charles Billaut,et al.  Multicriteria scheduling , 2005, Eur. J. Oper. Res..

[18]  Warren B. Powell,et al.  Solving Parallel Machine Scheduling Problems by Column Generation , 1999, INFORMS J. Comput..

[19]  R. Bulfin,et al.  Complexity of single machine, multi-criteria scheduling problems , 1993 .