Abstract
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(n 4) time. For the model with job-independent position effects, we proved that the problems can be solved in O(n 3) time by providing a dynamic programming algorithm.
Highlights
In many realistic scheduling environments, a job’s processing time may be depending on its position in the sequence [1]
The Scientific World Journal with p-s-d setup time and a general learning effect. They showed that the single machine scheduling problems to minimize the makespan and the sum of the kth power of completion time are polynomially solvable under the proposed model
There exists an optimal schedule in which the following properties hold: (1) all the jobs are processed consecutively without idle time and the first job starts at time 0 for both the variants of the problem; (2) all the nontardy jobs are processed before all the tardy jobs for both the variants of the problem
Summary
In many realistic scheduling environments, a job’s processing time may be depending on its position in the sequence [1]. Wang [21] studied the single machine scheduling problems with time-dependent learning effect and p-s-d setup time considerations He showed that the makespan minimization problem, the total completion time minimization problem, and the sum of the quadratic job completion time minimization problem can be solved in polynomial time, respectively. The Scientific World Journal with p-s-d setup time and a general learning effect They showed that the single machine scheduling problems to minimize the makespan and the sum of the kth power of completion time are polynomially solvable under the proposed model. Huang et al [25] considered some single machine scheduling problems with general time-dependent deterioration, position-dependent learning, and p-s-d setup time They proved that the makespan minimization problem, the total completion time minimization problem, and the sum of the μth power of job completion time minimization problem can be solved by the SPT rule. Hsu et al [32] extended part of the objective functions proposed by Gordon and Strusevich [31] to the positional weighted earliness penalty and showed that the problems remain solvable in polynomial time
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