In order to investigate more realistic group scheduling problems with position-dependent effects,the model of general position-dependent group scheduling is proposed,where the actual group setup times and actual processing times are described by general functions of the normal group setup time and position in the sequence.These general functions are not assumed to have specific function structures,and are not restricted to be monotone.By mathematical analysis and proof,each considered problem is decomposed into a group scheduling process and a job scheduling process,and each scheduling process is transferred into the classic assignment problem or the classic single-machine sequence problem,and then the computational complexity to solve the considered problem is analyzed.Analysis results show that,even with general position-dependent job processing times,both the single machine makespan minimization group scheduling problems and the parallel-machine total load minimization group scheduling problems remain polynomially solvable.
