Scheduling equal length jobs with eligibility restrictions

We consider the problem of scheduling independent jobs on identical parallel machines to minimize the total completion time. Each job has a set of eligible machines and a given release date, and all jobs have equal processing times. For the problem with a fixed number of machines, we determine its computational complexity by providing a polynomial time dynamic programming algorithm. We also present two polynomial time approximation algorithms along with their worst case analyses. Experiments with randomly generated instances show that the proposed algorithms consistently generate schedules that are very close to optimal.

[1]  Jan Karel Lenstra,et al.  Complexity of machine scheduling problems , 1975 .

[2]  Celia A. Glass,et al.  Scheduling unit length jobs with parallel nested machine processing set restrictions , 2006, Comput. Oper. Res..

[3]  Ahmet B. Keha,et al.  Mixed integer programming formulations for single machine scheduling problems , 2009, Comput. Ind. Eng..

[4]  Dorit S. Hochbaum,et al.  Approximation Algorithms for NP-Hard Problems , 1996 .

[5]  Peter Brucker,et al.  Scheduling jobs with equal processing times and time windows on identical parallel machines , 2008, J. Sched..

[6]  Barbara B. Simons,et al.  Multiprocessor Scheduling of Unit-Time Jobs with Arbitrary Release Times and Deadlines , 1983, SIAM J. Comput..

[7]  Edward G. Coffman,et al.  Scheduling independent tasks to reduce mean finishing time , 1974, CACM.

[8]  Philippe Baptiste,et al.  Ten notes on equal-processing-time scheduling , 2004, 4OR.

[9]  Chung-Lun Li,et al.  Scheduling unit-length jobs with machine eligibility restrictions , 2006, Eur. J. Oper. Res..

[10]  Chung-Lun Li,et al.  Scheduling with processing set restrictions: A survey , 2008 .

[11]  Michael Pinedo,et al.  Scheduling: Theory, Algorithms, and Systems , 1994 .

[12]  Joseph Y.-T. Leung,et al.  Scheduling jobs with equal processing times subject to machine eligibility constraints , 2010, J. Sched..

[13]  Martin Skutella,et al.  Convex quadratic and semidefinite programming relaxations in scheduling , 2001, JACM.

[14]  Kangbok Lee,et al.  Parallel machine scheduling under a grade of service provision , 2004, Comput. Oper. Res..

[15]  W. A. Horn.  Technical Note - Minimizing Average Flow Time with Parallel Machines , 1973, Oper. Res..

[16]  Shi Li,et al.  Scheduling to Minimize Total Weighted Completion Time via Time-Indexed Linear Programming Relaxations , 2017, 2017 IEEE 58th Annual Symposium on Foundations of Computer Science (FOCS).

[17]  Peter Brucker,et al.  Complexity of scheduling problems with multi-purpose machines , 1997, Ann. Oper. Res..

[18]  Shi Li,et al.  Better Unrelated Machine Scheduling for Weighted Completion Time via Random Offsets from Non-uniform Distributions , 2016, 2016 IEEE 57th Annual Symposium on Foundations of Computer Science (FOCS).

[19]  Frank Werner,et al.  Parallel machine problems with equal processing times: a survey , 2011, J. Sched..

[20]  Evripidis Bampis,et al.  Approximation schemes for minimizing average weighted completion time with release dates , 1999, 40th Annual Symposium on Foundations of Computer Science (Cat. No.99CB37039).