Parallel machine earliness and tardiness scheduling with proportional weights

In this paper we study the problem of scheduling n jobs with a common due date and proportional early and tardy penalties on m identical parallel machines. We show that the problem is NP-hard and propose a dynamic programming algorithm to solve it. We also propose two heuristics to tackle the problem and analyze their worst-case error bounds.

[1]  David S. Johnson,et al.  Computers and Intractability: A Guide to the Theory of NP-Completeness , 1978 .

[2]  S. Sethi,et al.  Equivalence of Mean Flow Time Problems and Mean Absolute Deviation Problems , 1990 .

[3]  J. A. Hoogeveen,et al.  Scheduling around a small common due date , 1991 .

[4]  Ram Rachamadugu.  Scheduling jobs with proportionate early/tardy penalties , 1995 .

[5]  Hamilton Emmons,et al.  Scheduling to a common due date on parallel uniform processors , 1987 .

[6]  W. Szwarc,et al.  Weighted Tardiness Single Machine Scheduling with Proportional Weights , 1993 .

[7]  Gur Mosheiov,et al.  Heuristics for multimachine scheduling problems with earliness and tardiness costs , 1996 .

[8]  Marc E. Posner,et al.  Earliness-Tardiness Scheduling Problems, I: Weighted Deviation of Completion Times About a Common Due Date , 1991, Oper. Res..

[9]  Mesbah U. Ahmed,et al.  Minimizing the Weighted Sum of Late and Early Completion Penalties in a Single Machine , 1990 .

[10]  Gary D. Scudder,et al.  Sequencing with Earliness and Tardiness Penalties: A Review , 1990, Oper. Res..

[11]  Mesbah U. Ahmed,et al.  Minimizing the sum of absolute lateness in single‐machine and multimachine scheduling , 1984 .

[12]  Esther M. Arkin,et al.  Weighted-Tardiness Scheduling on Parallel Machines with Proportional Weights , 1991, Oper. Res..

[13]  B. Alidaee,et al.  A note on minimizing the weighted sum of tardy and early completion penalties in a single machine: A case of small common due date , 1997 .

[14]  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..

[15]  Chak-Kuen Wong,et al.  Worst-Case Analysis of a Placement Algorithm Related to Storage Allocation , 1975, SIAM J. Comput..

[16]  Nicholas G. Hall.  Single- and multiple-processor models for minimizing completion time variance , 1986 .

[17]  R. Heady,et al.  Minimizing the sum of job earliness and tardiness in a multimachine system , 1998 .