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We treats a job scheduling in a 2-machine flow-shop problem with outsourcing strategy allowed. Jobs in the first machine are processed in-house or outsourced to the other companies. In this paper, all the considered jobs are determined to be in-house processed or outsourced. When a job is outsourced, then the firm should pay an outsourcing cost additionally. We want to minimize the sum of the outsourcing costs and the total completion times of finished jobs. In this paper, some solution properties are characterized, and then some heuristic algorithms and a branchand-bound solution algorithm are derived. This paper evaluates finally the performance of the proposed algorithms during the numerical tests.

Minimizing Total Completion Times in a Two-machine Flowshop Scheduling with Outsourcing Strategy allowed