Minimizing makespan subject to minimum total absolute deviation of completion time on identical parallel machines

This study addresses the identical parallel machine scheduling problem with the objective of minimizing makespan subject to minimum total absolute deviation of job completion time (TADC). An optimization algorithm is first proposed to solve TADC on an identical parallel machine and an iterative procedure based on a polynomial binary integer programming model is then proposed to minimize makespan. Computational experiments show that the proposed algorithm is efficient. The worst case performance, which refers to the largest average execution for each scenario of the experiments, is 229.10 seconds for the problem with n=200, m=30 and p j from a uniform [1, 100].

[1]  John J. Kanet,et al.  Minimizing Variation of Flow Time in Single Machine Systems , 1981 .

[2]  Prabuddha De,et al.  On the Minimization of Completion Time Variance with a Bicriteria Extension , 1992, Oper. Res..

[3]  Michael Pinedo,et al.  On the Minimization of the Makespan Subject to Flowtime Optimality , 1993, Oper. Res..

[4]  Xiaoqiang Cai,et al.  A tight lower bound for the completion time variance problem , 1996 .

[5]  Xiaoqiang Cai,et al.  V-shape property for job sequences that minimize the expected completion time variance , 1996 .

[6]  Jatinder N. D. Gupta,et al.  Minimizing makespan subject to minimum flowtime on two identical parallel machines , 2001, Comput. Oper. Res..

[7]  G. Srinivasan,et al.  A branch and bound algorithm to minimize completion time variance on a single processor , 2003, Comput. Oper. Res..

[8]  Gur Mosheiov,et al.  Simultaneous minimization of total completion time and total deviation of job completion times , 2004, Eur. J. Oper. Res..

[9]  Gur Mosheiov.  Minimizing total completion time and total deviation of job completion times from a restrictive due-date , 2005, Eur. J. Oper. Res..

[10]  Appa Iyer Sivakumar,et al.  Hierarchical minimization of completion time variance and makespan in jobshops , 2006, Comput. Oper. Res..

[11]  Daniel Oron,et al.  Single machine scheduling with simple linear deterioration to minimize total absolute deviation of completion times , 2008, Comput. Oper. Res..

[12]  Gur Mosheiov,et al.  Minimizing total absolute deviation of job completion times: extensions to position-dependent processing times and parallel identical machines , 2008, J. Oper. Res. Soc..

[13]  Jinjiang Yuan,et al.  A DP algorithm for minimizing makespan and total completion time on a series-batching machine , 2009, Inf. Process. Lett..

[14]  Abbas Afshar,et al.  Fuzzy multi-objective optimization of finance-based scheduling for construction projects with uncertainties in cost , 2009 .

[15]  Ling-Huey Su,et al.  Minimizing earliness and tardiness subject to total completion time in an identical parallel machine system , 2009, Comput. Oper. Res..

[16]  Linyan Sun,et al.  Single machine scheduling of deteriorating jobs to minimize total absolute differences in completion times , 2009 .

[17]  Chengbin Chu,et al.  A lower bound for weighted completion time variance , 2010, Eur. J. Oper. Res..

[18]  B. Srirangacharyulu,et al.  Completion time variance minimization in single machine and multi-machine systems , 2010, Comput. Oper. Res..

[19]  Xue Huang,et al.  Parallel identical machines scheduling with deteriorating jobs and total absolute differences penalties , 2011 .