Single machine past-sequence-dependent delivery times scheduling with general position-dependent and time-dependent learning effects

Abstract

This paper studies the single machine past-sequence-dependent (p-s-d) delivery times scheduling with general position-dependent and time-dependent learning effects. By the general position-dependent and time-dependent learning effects we mean that the actual processing time of a job is not only a function of the total normal processing times of the jobs already processed, but also a function of the job’s scheduled position. We consider the following objective functions: the makespan, the total completion time, the sum of the θth (θ⩾0) power of job completion times, the total lateness, the total weighted completion time, the maximum lateness, the maximum tardiness and the number of tardy jobs. We show that the problems of minimization of the makespan, the total completion time, the sum of the θth (θ⩾0) power of job completion times and the total lateness can be solved by the smallest (normal) processing time first (SPT) rule, respectively. We also show that the total weighted completion time minimization problem, the discounted total weighted completion time minimization problem, the maximum lateness minimization problem, the maximum tardiness minimization problem and the total tardiness minimization problem can be solved in polynomial time under certain conditions.