Scheduling identical parallel machines to minimize total tardiness

Abstract This paper considers the problem of scheduling a given number of jobs on a specified number of identical parallel machines to minimize total tardiness. In view of its NP-hard nature, we propose a new heuristic approach which is general enough for solving several important types of parallel-machine scheduling problems. Consequently, we develop and evaluate an efficient heuristic algorithms for finding optimal or near-optimal schedules for the identical parallel-machine problem to minimize total tardiness. Computational results of empirical experiments involving the proposed and the three best available heuristics are used to identify the most effective heuristic algorithms for minimizing total tardiness.

[1]  John W. Fowler,et al.  A SURVEY OF ALGORITHMS FOR SINGLE AND MULTI-OBJECTIVE UNRELATED PARALLEL-MACHINE DETERMINISTIC SCHEDULING PROBLEMS , 2004 .

[2]  Jwm Will Bertrand,et al.  A dynamic priority rule for scheduling against due-dates , 1982 .

[3]  Christos Koulamas.  Decomposition and hybrid simulated annealing heuristics for the parallel-machine total tardiness problem , 1997 .

[4]  Inyong Ham,et al.  A heuristic algorithm for the m-machine, n-job flow-shop sequencing problem , 1983 .

[5]  Julius Surkis,et al.  Evaluation of a Heuristic for Scheduling Independent Jobs on Parallel Identical Processors , 1979 .

[6]  J. D. Irwin,et al.  An Improved Method for Scheduling Independent Tasks , 1971 .

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

[8]  Christos Koulamas,et al.  The Total Tardiness Problem: Review and Extensions , 1994, Oper. Res..

[9]  Warren B. Powell,et al.  A column generation based decomposition algorithm for a parallel machine just-in-time scheduling problem , 1999, Eur. J. Oper. Res..

[10]  M. Azizoglu,et al.  Tardiness minimization on parallel machines , 1998 .

[11]  Shunji Tanaka,et al.  A branch-and-bound algorithm with Lagrangian relaxation to minimize total tardiness on identical parallel machines , 2008 .

[12]  Chris N. Potts,et al.  A branch and bound algorithm to minimize the number of late jobs in a permutation flow-shop , 1989 .

[13]  Gilbert Laporte,et al.  Integer programming formulations for the multi-depot vehicle routing problem: Comments on a paper by Kulkarni and Bhave , 1989 .

[14]  Christos Koulamas,et al.  A heuristic for the single machine tardiness problem , 1993 .

[15]  Jatinder N. D. Gupta,et al.  SCHEDULING JOBS ON PARALLEL PROCESSORS WITH DYNAMIC PROGRAMMING , 1973 .

[16]  Han Hoogeveen,et al.  Parallel Machine Scheduling by Column Generation , 1999, Oper. Res..

[17]  Joseph Y.-T. Leung,et al.  Minimizing Total Tardiness on One Machine is NP-Hard , 1990, Math. Oper. Res..

[18]  Yih-Long Chang,et al.  Heuristics for minimizing mean tardiness form parallel machines , 1991 .

[19]  Bahram Alidaee,et al.  Scheduling parallel machines to minimize total weighted and unweighted tardiness , 1997, Comput. Oper. Res..

[20]  Eugene L. Lawler,et al.  Sequencing and scheduling: algorithms and complexity , 1989 .

[21]  James G. Root.  Scheduling with Deadlines and Loss Functions on k Parallel Machines , 1965 .

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

[23]  Eugene L. Lawler.  On Scheduling Problems with Deferral Costs , 1964 .

[24]  G. L. Thompson,et al.  A Heuristic Approach to Solving Travelling Salesman Problems , 1964 .

[25]  Chengbin Chu,et al.  Parallel machine scheduling to minimize total tardiness , 2002 .

[26]  Yeong-Dae Kim,et al.  Scheduling on parallel identical machines to minimize total tardiness , 2007, Eur. J. Oper. Res..

[27]  Tapan Sen,et al.  Static scheduling research to minimize weighted and unweighted tardiness: A state-of-the-art survey , 2003 .