Minimizing the sum of the job completion times in the two-machine flow shop by Lagrangian relaxation
Annals of Operations Research
Local search heuristics for two-stage flow shop problems with secondary criterion
Computers and Operations Research
Best compromise solution for a new multiobjective scheduling problem
Computers and Operations Research
Data & Knowledge Engineering
A multi-objective ant colony system algorithm for flow shop scheduling problem
Expert Systems with Applications: An International Journal
Flexible solutions in disjunctive scheduling: General formulation and study of the flow-shop case
Computers and Operations Research
Ant colony optimization algorithm for a Bi-criteria 2-stage hybrid flowshop scheduling problem
Journal of Intelligent Manufacturing
Mixed integer formulation to minimize makespan in a flow shop with batch processing machines
Mathematical and Computer Modelling: An International Journal
Complete characterization of near-optimal sequences for the two-machine flow shop scheduling problem
CPAIOR'12 Proceedings of the 9th international conference on Integration of AI and OR Techniques in Constraint Programming for Combinatorial Optimization Problems
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This paper develops mathematical programming formulations, a branch-and-bound algorithm, and a heuristic algorithm for solving the two-machine flowshop scheduling problem with the objective of minimizing total completion time, subject to the constraint that the makespan is minimum. The proposed branch-and-bound algorithm uses several lower bounding schemes, which are based on problem relaxations. Several dominance conditions are used in the algorithm to limit the size of the search tree. Results of extensive computational tests show that the proposed branch-and-bound algorithm is effective in solving problems with up to 35 jobs. For problems containing larger number of jobs, the proposed heuristic algorithm, which is also used as an upper bound in the proposed branch-and-bound algorithm, is quite effective in finding an optimal or near-optimal schedule.