The two-machine flowshop total completion time problem: Branch-and-bound algorithms based on network-flow formulation

We consider the flowshop problem on two machines with sequence-independent setup times to minimize total completion time. Large scale network flow formulations of the problem are suggested together with strong Lagrangian bounds based on these formulations. To cope with their size, filtering procedures are developed. To solve the problem to optimality, we embed the Lagrangian bounds into two branch-and-bound algorithms. The best algorithm is able to solve all 100-job instances of our testbed with setup times and all 140-job instances without setup times, thus significantly outperforming the best algorithms in the literature.

[1]  Mehdi Serairi,et al.  The two-machine flowshop scheduling problem with sequence-independent setup times: New lower bounding strategies , 2013, Eur. J. Oper. Res..

[2]  Mohamed Haouari,et al.  An assignment-based lower bound for a class of two-machine flow shop problems , 2013, Comput. Oper. Res..

[3]  Han Hoogeveen,et al.  Minimizing Total Completion Time in a Two-Machine Flowshop: Analysis of Special Cases , 1999, Math. Oper. Res..

[4]  Shunji Tanaka.  Extension of the Dynasearch to the Two-Machine Permutation Flowshop Scheduling Problem , 2011 .

[5]  R. Ahmadi,et al.  Improved lower bounds for minimizing the sum of completion times of n jobs over m machines in a flow shop , 1990 .

[6]  Can Akkan,et al.  The two-machine flowshop total completion time problem: Improved lower bounds and a branch-and-bound algorithm , 2004, Eur. J. Oper. Res..

[7]  Vincent T'Kindt,et al.  Revisiting Branch and Bound Search Strategies for Machine Scheduling Problems , 2004, J. Sched..

[8]  Sheldon H. Jacobson,et al.  A branch, bound, and remember algorithm for the 1|ri|∑ti scheduling problem , 2009, J. Sched..

[9]  Ravi Sethi,et al.  The Complexity of Flowshop and Jobshop Scheduling , 1976, Math. Oper. Res..

[10]  F. D. Croce,et al.  The two-machine total completion time flow shop problem , 1996 .

[11]  H. Sherali,et al.  A primal-dual conjugate subgradient algorithm for specially structured linear and convex programming problems , 1989 .

[12]  Shunji Tanaka,et al.  An exact algorithm for single-machine scheduling without machine idle time , 2009, J. Sched..

[13]  Stéphane Dauzère-Pérès,et al.  An exact approach for scheduling jobs with regular step cost functions on a single machine , 2012, Comput. Oper. Res..

[14]  Jatinder N. D. Gupta,et al.  A review of scheduling research involving setup considerations , 1999 .

[15]  William L. Maxwell,et al.  Theory of scheduling , 1967 .

[16]  T. Ibaraki,et al.  A dynamic programming method for single machine scheduling , 1994 .

[17]  Ali Allahverdi,et al.  Minimizing mean flowtime in a two-machine flowshop with sequence-independent setup times , 2000, Comput. Oper. Res..

[18]  S. L. Velde.  Minimizing the sum of the job completion times in the two-machine flow shop by Lagrangian relaxation , 1991 .

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

[20]  Laurent Péridy,et al.  Using short-term memory to minimize the weighted number of late jobs on a single machine , 2003, Eur. J. Oper. Res..

[21]  Hanif D. Sherali,et al.  Enhancing Lagrangian Dual Optimization for Linear Programs by Obviating Nondifferentiability , 2007, INFORMS J. Comput..

[22]  Han Hoogeveen,et al.  Stronger Lagrangian bounds by use of slack variables: Applications to machine scheduling problems , 1992, Math. Program..

[23]  Philippe Baptiste,et al.  A Branch-and-Bound procedure to minimize total tardiness on one machine with arbitrary release dates , 2004, Eur. J. Oper. Res..

[24]  Roberto Tadei,et al.  An improved branch-and-bound algorithm for the two machine total completion time flow shop problem , 2002, Eur. J. Oper. Res..

[25]  Han Hoogeveen,et al.  Minimizing Total Completion Time in a Two-Machine Flowshop: Analysis of Special Cases , 1996, Math. Oper. Res..

[26]  T. S. Abdul-Razaq,et al.  Dynamic Programming State-Space Relaxation for Single-Machine Scheduling , 1988 .

[27]  Han Hoogeveen,et al.  Lower bounds for minimizing total completion time in a two-machine flow shop , 2006, J. Sched..