Single machine scheduling with past-sequence-dependent delivery times and learning effect

This paper studies single-machine scheduling problem with time-dependent delivery times and learning effect. The delivery time of a job is proportional to its waiting time in the system, i.e., the length of the already scheduling jobs. That is, the delivery times are past-sequence-dependent (psd). Delivery time denotes the time a job required to be delivered to the customer. It is assumed that the learning process reflects a decrease in the process time as a function of the number of repetitions, i.e., as a function of the job position in the sequence. We respectively consider the following objectives: the minimization of the makespan, the total completion time, the total absolute differences in completion times and the sum of earliness, tardiness and common due date penalty. We develop polynomial time algorithms to optimally solve these problems.