A SURVEY OF ALGORITHMS FOR SINGLE AND MULTI-OBJECTIVE UNRELATED PARALLEL-MACHINE DETERMINISTIC SCHEDULING PROBLEMS

ABSTRACT This paper surveys the literature related to solving traditional unrelated parallel-machine scheduling problems. It compiles algorithms for the makespan, total weighted sum of completion times, maximum tardiness, total tardiness, total earliness and tardiness, and multiple criteria performance measures. The review of the existing algorithms is restricted to the deterministic problems without setups, preemptions, or side conditions on the problem. Even for such traditional problems, this survey reveals that while makespan minimization has been fairly widely studied, problems that include processing characteristics such as release times, sequence dependent setups, and preemptions remain largely unstudied. Research in solving unrelated parallel-machine scheduling problems involving the minimization of the number of tardy jobs, weighted number of tardy jobs, total tardiness, and total weighted tardiness is quite limited.

[1]  V. Suresh,et al.  Minimizing maximum tardiness for unrelated parallel machines , 1994 .

[2]  Costas P. Pappis,et al.  Scheduling under a common due-data on parallel unrelated machines , 1998, Eur. J. Oper. Res..

[3]  Ellis Horowitz,et al.  Exact and Approximate Algorithms for Scheduling Nonidentical Processors , 1976, JACM.

[4]  Dipak Chaudhuri,et al.  Bicriteria scheduling problem for unrelated parallel machines , 1996 .

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

[6]  T.C.E. Cheng,et al.  A state-of-the-art review of parallel-machine scheduling research , 1990 .

[7]  John W. Fowler,et al.  The impacts of variability on scheduling approaches for a printed wiring board assembly operation , 2002 .

[8]  Klaus Jansen,et al.  Grouping Techniques for Scheduling Problems: Simpler and Faster , 2001, Algorithmica.

[9]  Chris N. Potts,et al.  Heuristics for scheduling unrelated parallel machines , 1991, Comput. Oper. Res..

[10]  Jan Karel Lenstra,et al.  Recent developments in deterministic sequencing and scheduling: a survey : (preprint) , 1981 .

[11]  Martin Skutella,et al.  Scheduling Unrelated Machines by Randomized Rounding , 2002, SIAM J. Discret. Math..

[12]  Lawrence B. Evans,et al.  An approximate method for the production scheduling of industrial batch processes with parallel units , 1989 .

[13]  Philippe Chrétienne,et al.  A cutting plane algorithm for the unrelated parallel machine scheduling problem , 2002, Eur. J. Oper. Res..

[14]  Éva Tardos,et al.  Scheduling unrelated machines with costs , 1993, SODA '93.

[15]  Chris N. Potts,et al.  Unrelated parallel machine scheduling using local search , 1994 .

[16]  Gerhard J. Woeginger,et al.  Polynomial time approximation algorithms for machine scheduling: ten open problems , 1999 .

[17]  Klaus Jansen,et al.  Improved approximation schemes for scheduling unrelated parallel machines , 1999, STOC '99.

[18]  Kai-Chi Pang Algorithmic analysis of the unrelated parallel machines scheduling problem to minimize mean weighted flowtime , 1995 .

[19]  N. Metropolis,et al.  Equation of State Calculations by Fast Computing Machines , 1953, Resonance.

[20]  C. N. Potts,et al.  Analysis of a linear programming heuristic for scheduling unrelated parallel machines , 1985, Discret. Appl. Math..

[21]  Nathalie Sauer,et al.  Heuristics for unrelated machine scheduling with precedence constraints , 1997 .

[22]  Jan Karel Lenstra,et al.  Approximation algorithms for scheduling unrelated parallel machines , 1987, 28th Annual Symposium on Foundations of Computer Science (sfcs 1987).

[23]  Prabuddha De,et al.  SCHEDULING TO MINIMIZE MAKESPAN ON UNEQUAL PARALLEL PROCESSORS , 1980 .

[24]  Giuseppe Lancia,et al.  Scheduling jobs with release dates and tails on two unrelated parallel machines to minimize the makespan , 2000, Eur. J. Oper. Res..

[25]  Bharatendu Srivastava,et al.  An effective heuristic for minimising makespan on unrelated parallel machines , 1998, J. Oper. Res. Soc..

[26]  Paolo Toth,et al.  Exact and Approximation Algorithms for Makespan Minimization on Unrelated Parallel Machines , 1997, Discret. Appl. Math..

[27]  Ehl Emile Aarts,et al.  Statistical cooling : a general approach to combinatorial optimization problems , 1985 .

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

[29]  Linet Özdamar,et al.  Hybrid heuristics for the capacitated lot sizing and loading problem with setup times and overtime decisions , 1998, Eur. J. Oper. Res..

[30]  Sudipto Guha,et al.  Approximating the Throughput of Multiple Machines in Real-Time Scheduling , 2002, SIAM J. Comput..

[31]  Fabián A. Chudak A min‐sum 3/2‐approximation algorithm for scheduling unrelated parallel machines , 1999 .

[32]  Peter T. Cummings,et al.  Scheduling of multiple products on parallel units with tardiness penalties using simulated annealing , 1995 .

[33]  Oscar H. Ibarra,et al.  Heuristic Algorithms for Scheduling Independent Tasks on Nonidentical Processors , 1977, JACM.

[34]  Maria J. Serna,et al.  Approximating Scheduling Unrelated Parallel Machines in Parallel , 2002, Comput. Optim. Appl..

[35]  Jeffrey M. Jaffe,et al.  Algorithms for Scheduling Tasks on Unrelated Processors , 1981, JACM.

[36]  Frank Werner,et al.  Heuristic algorithms for unrelated parallel machine scheduling with a common due date, release dates, and linear earliness and tardiness penalties , 2001 .

[37]  Leo Kroon,et al.  On the computational complexity of (maximum) class scheduling , 1991 .

[38]  Meral Azizoglu,et al.  Scheduling jobs on unrelated parallel machines to minimize regular total cost functions , 1999 .

[39]  S. S. Panwalkar,et al.  Common Due Date Assignment to Minimize Total Penalty for the One Machine Scheduling Problem , 1982, Oper. Res..

[40]  Evripidis Bampis,et al.  A PTAS for the average weighted completion time problem on unrelated machines , 2000 .

[41]  John W. Fowler,et al.  Scheduling of unrelated parallel machines: an application to PWB manufacturing , 2002 .

[42]  Steef L. van de Velde Duality-Based Algorithms for Scheduling Unrelated Parallel Machines , 1993, INFORMS J. Comput..