Single machine scheduling problems with general position-dependent processing times and past-sequence-dependent delivery times

This paper considers single machine scheduling with past-sequence-dependent (psd) delivery times, in which the processing time of a job depends on its position in a sequence. We provide a unified model for solving single machine scheduling problems with psd delivery times. We first show how this unified model can be useful in solving scheduling problems with due date assignment considerations. We analyze the problem with four different due date assignment methods, the objective function includes costs for earliness, tardiness and due date assignment. We then consider scheduling problems which do not involve due date assignment decisions. The objective function is to minimize makespan, total completion time and total absolute variation in completion times. We show that each of the problems can be reduced to a special case of our unified model and solved in O(n ³) time. In addition, we also show that each of the problems can be solved in O(nlogn) time for the spacial case with job-independent positional function.