Four single-machine scheduling problems involving due date determination decisions

The Due Date Assignment Scheduling Problem with Delivery Times and Truncated Sum-of-Processing-Times-Based Learning Effect

This paper considers a single-machine scheduling problem with past-sequence-dependent delivery times and the truncated sum-of-processing-times-based learning effect. The goal is to minimize the total costs that comprise the number of early jobs, the number of tardy jobs and due date. The due date is a decision variable. There will be corresponding penalties for jobs that are not completed on time. Under the common due date, slack due date and different due date, we prove that these problems are polynomial time solvable. Three polynomial time algorithms are proposed to obtain the optimal sequence.

Single machine scheduling and due date assignment with past-sequence-dependent setup time and position-dependent processing time

This paper considers single machine scheduling and due date assignment with setup time. The setup time is proportional to the length of the already processed jobs; that is, the setup time is past-sequence-dependent (p-s-d). It is assumed that a job's processing time depends on its position in a sequence. The objective functions include total earliness, the weighted number of tardy jobs, and the cost of due date assignment. We analyze these problems with two different due date assignment methods. We first consider the model with job-dependent position effects. For each case, by converting the problem to a series of assignment problems, we proved that the problems can be solved in O(n⁴) time. For the model with job-independent position effects, we proved that the problems can be solved in O(n³) time by providing a dynamic programming algorithm.