Minimizing the weighted number of tardy jobs on a two-machine flow shop

In this paper, we describe an exact algorithm to solve the weighted number of tardy jobs two-machine flow shop scheduling problem. The algorithm uses branch-and-bound; a surrogate relaxation resulting in a multiple-choice knapsack provides the bounds. Extensive computational experiments indicate problems with 100 jobs can be solved quickly.

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

[2]  Bertrand M. T. Lin,et al.  Scheduling in the two-machine flowshop with due date constraints ☆ , 2001 .

[3]  Chris N. Potts,et al.  An adaptive branching rule for the permutation flow-shop problem , 1980 .

[4]  T. Cheng,et al.  Solvable cases of permutation flowshop scheduling with dominating machines , 2000 .

[5]  Chris N. Potts,et al.  A branch and bound algorithm to minimize the number of late jobs in a permutation flow-shop , 1989 .

[6]  B. J. Lageweg,et al.  A General Bounding Scheme for the Permutation Flow-Shop Problem , 1978, Oper. Res..

[7]  E. Ignall,et al.  Application of the Branch and Bound Technique to Some Flow-Shop Scheduling Problems , 1965 .

[8]  Martin Dyer,et al.  AN O(n) ALGORITHM FOR THE MULTIPLE-CHOICE , 2007 .

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

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

[11]  W. Townsend.  A Branch-and-Bound Method for Sequencing Problems with Linear and Exponential Penalty Functions , 1977 .

[12]  Jatinder N. D. Gupta,et al.  Two-machine flowshop scheduling to minimize the number of tardy jobs , 1997 .

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

[14]  Gilbert Laporte,et al.  Integer programming formulations for the multi-depot vehicle routing problem: Comments on a paper by Kulkarni and Bhave , 1989 .

[15]  Jatinder N. D. Gupta,et al.  Flowshop scheduling with dominant machines , 1995, Comput. Oper. Res..

[16]  Jatinder N. D. Gupta,et al.  Minimizing tardy jobs in a flowshop with common due date , 2000, Eur. J. Oper. Res..