Stable scheduling of single machine with probabilistic parameters

*e-mail: wojciech.bozejko@pwr.edu.pl Abstract. We consider a stochastic variant of the single machine total weighted tardiness problem jobs parameters are independent random variables with normal or Erlang distributions. Since even deterministic problem is NP-hard, it is difficult to find global optimum for large instances in the reasonable run time. Therefore, we propose tabu search metaheuristics in this work. Computational experiments show that solutions obtained by the stochastic version of metaheuristics are more stable (i.e. resistant to data disturbance) than solutions generated by classic, deterministic version of the algorithm.

[1]  Mitsuo Gen,et al.  A new model for single machine scheduling with uncertain processing time , 2017, J. Intell. Manuf..

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

[3]  Chris N. Potts,et al.  Local Search Heuristics for the Single Machine Total Weighted Tardiness Scheduling Problem , 1998, INFORMS J. Comput..

[4]  W. John Braun,et al.  Stochastic scheduling on a repairable machine with Erlang uptime distribution , 1998, Advances in Applied Probability.

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

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

[7]  Chris N. Potts,et al.  Single Machine Tardiness Sequencing Heuristics , 1991 .

[8]  Yang Li,et al.  Stochastic Single Machine Scheduling to Minimize the Weighted Number of Tardy Jobs , 2010, ACFIE.

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

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

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

[12]  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 .

[13]  M. Dorigo,et al.  Design of Iterated Local Search Algorithms An Example Application to the Single Machine Total Weighted Tardiness Problem , 2001 .

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

[15]  H. M. Soroush,et al.  Minimizing the weighted number of early and tardy jobs in a stochastic single machine scheduling problem , 2007, Eur. J. Oper. Res..

[16]  Matthijs den Besten,et al.  Design of Iterated Local Search Algorithms , 2001, EvoWorkshops.

[17]  Xian Zhou,et al.  Optimal Stochastic Scheduling , 2014 .

[18]  Gur Mosheiov,et al.  Single machine scheduling to minimize the number of early and tardy jobs , 1996, Comput. Oper. Res..

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

[20]  Wooseung Jang,et al.  Dynamic scheduling of stochastic jobs on a single machine , 2002, Eur. J. Oper. Res..

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

[22]  Wojciech Bozejko,et al.  Parallel path relinking method for the single machine total weighted tardiness problem with sequence-dependent setups , 2010, J. Intell. Manuf..

[23]  H. M. Soroush,et al.  Single Machine Scheduling with Stochastic Processing Times or Stochastic Due-Dates to Minimize the Number of Early and Tardy Jobs , 2006 .

[24]  Ceyda Oguz,et al.  A variable neighborhood search for minimizing total weighted tardiness with sequence dependent setup times on a single machine , 2012, Comput. Oper. Res..

[25]  Nasser Salmasi,et al.  Stochastic scheduling with minimizing the number of tardy jobs using chance constrained programming , 2013, Math. Comput. Model..

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

[27]  Mohammad Mahdavi Mazdeh,et al.  Solving a single machine stochastic scheduling problem using a branch and bound algorithm and simulated annealing , 2012 .

[28]  Wojciech Bozejko,et al.  On the theoretical properties of swap multimoves , 2007, Oper. Res. Lett..

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