Stable Scheduling with Random Processing Times

In this work stability of solutions determined by algorithms based on tabu search method for a certain (NP-hard) one-machine arrangement problem was examined. The times of tasks performance are deterministic and they also constitute random variables of the standard or the Erlang’s schedule. The best results were obtained when as a criterion to choose an element from the neighborhood convex combinations of the first and the second moments of the random goal function were accepted. In this way determined solutions are stable, i.e. little sensitive to parameters random changes.

[1]  Clyde L. Monma,et al.  Linear-Time Algorithms for Scheduling on Parallel Processors , 1982, Oper. Res..

[2]  H. Ishii,et al.  Fuzzy due-date scheduling problem with fuzzy processing time , 1999 .

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

[4]  Ching-Fang Liaw,et al.  A branch-and-bound algorithm for the single machine earliness and tardiness scheduling problem , 1999, Comput. Oper. Res..

[5]  Michael O. Rabin.  Complexity of computations , 1977, CACM.

[6]  Safia Kedad-Sidhoum,et al.  A faster branch-and-bound algorithm for the earliness-tardiness scheduling problem , 2008, J. Sched..

[7]  Richard M. Karp,et al.  Reducibility Among Combinatorial Problems , 1972, 50 Years of Integer Programming.

[8]  J. Vondrák.  Probabilistic Methods in Combinatorial and Stochastic Optimization , 2005 .

[9]  Jan Karel Lenstra,et al.  Complexity results for scheduling chains on a single machine : (preprint) , 1980 .

[10]  Sartaj Sahni,et al.  Algorithms for Scheduling Independent Tasks , 1976, J. ACM.

[11]  David S. Johnson,et al.  Scheduling Tasks with Nonuniform Deadlines on Two Processors , 1976, J. ACM.

[12]  J. M. Moore,et al.  A Functional Equation and its Application to Resource Allocation and Sequencing Problems , 1969 .

[13]  H. Prade.  Using fuzzy set theory in a scheduling problem: A case study , 1979 .

[14]  Xian Zhou,et al.  Single-Machine Scheduling with Exponential Processing Times and General Stochastic Cost Functions , 2005, J. Glob. Optim..

[15]  Brian C. Dean,et al.  Approximation algorithms for stochastic scheduling problems , 2005 .

[16]  Robert L. Bulfin,et al.  Scheduling a Single Machine to Minimize the Weighted Number of Tardy Jobs , 1983 .

[17]  Michael Pinedo,et al.  Stochastic Scheduling with Release Dates and Due Dates , 1983, Oper. Res..

[18]  Mieczysław Wodecki,et al.  A very fast tabu search algorithm for the permutation flow shop problem with makespan criterion , 2004, Comput. Oper. Res..

[19]  John E. Beasley,et al.  OR-Library: Distributing Test Problems by Electronic Mail , 1990 .

[20]  Mieczysław Wodecki.  A block approach to earliness-tardiness scheduling problems , 2009 .

[21]  Wojciech Bozejko,et al.  Block approach - tabu search algorithm for single machine total weighted tardiness problem , 2006, Comput. Ind. Eng..

[22]  E.L. Lawler,et al.  Optimization and Approximation in Deterministic Sequencing and Scheduling: a Survey , 1977 .

[23]  Mieczysław Wodecki,et al.  A Very Fast Tabu Search Algorithm for Job Shop Problem , 2005 .

[24]  L. V. Wassenhove,et al.  Algorithms for scheduling a single machine to minimize the weighted number of late jobs , 1988 .

[25]  Han Hoogeveen,et al.  Minimizing the number of late jobs in a stochastic setting using a chance constraint , 2008, J. Sched..

[26]  E. Lawler.  A “Pseudopolynomial” Algorithm for Sequencing Jobs to Minimize Total Tardiness , 1977 .

[27]  Chris N. Potts,et al.  A Branch and Bound Algorithm for the Total Weighted Tardiness Problem , 1985, Oper. Res..

[28]  Toshihide Ibaraki,et al.  A Solvable Case of the One-Machine Scheduling Problem with Ready and Due Times , 1978, Oper. Res..

[29]  Bahram Alidaee,et al.  Metaheuristic Optimization via Memory and Evolution: Tabu Search and Scatter Search (Operations Research/Computer Science Interfaces Series) , 2005 .

[30]  J. M. Moore.  An n Job, One Machine Sequencing Algorithm for Minimizing the Number of Late Jobs , 1968 .

[31]  Hugo De Man,et al.  Just in time scheduling , 1992, Proceedings 1992 IEEE International Conference on Computer Design: VLSI in Computers & Processors.

[32]  Mieczysław Wodecki.  A branch-and-bound parallel algorithm for single-machine total weighted tardiness problem , 2008 .