OUTSOURCING DECISIONS IN m-MACHINE PERMUTATION FLOW SHOP SCHEDULING PROBLEMS WITH MACHINE-DEPENDENT PROCESSING TIMES

We consider m-machine permutation flow shop problems with an outsourcing option for a special case where each job's processing time equals the job's processing requirement plus a characteristic value of the machine. The objective is to minimize the sum of the performance measure for in-house jobs (the total completion time or the makespan) and the total outsourcing cost. We prove that two problems are polynomially solvable when the number of machines is fixed.