Some Scheduling Problems on a Single Machine with General Job Effects of Position-Dependent Learning and Start-Time-Dependent Deterioration

Job learning and deterioration coexist in many realistic machine-job scheduling situations. However, in literature, the constructed forms of the machine scheduling models with job learning and/or deteriorating effects were specific types of functions, which constrained their applicability in practice. This paper introduces a new single-machine scheduling model, where the actual processing time of a job is a general function of its starting time as well as scheduled position, which shows a broad generalization in contrast to that of certain existing models. For three objectives corresponding to the single-machine scheduling problem–total weighted completion time, discounted total weighted completion time, and maximum lateness — this paper presents their respective approximation result on the basis of the worst-case bound analysis from the optimal algorithm. The results demonstrate that under our proposed model, minimization of scheduling operations such as the makespan, sum of the kth power of completion times, and total lateness are polynomially solvable. Moreover, under some feasible conditions for the scheduling parameters, the minimum optimization problems of the total weighted completion time, discounted total weighted completion time, maximum lateness, and total tardiness are all recognized as polynomial forms and their solutions are provided.