Maximizing the weighted number of just-in-time jobs on a single machine with position-dependent processing times

2013 ◽  
Vol 16 (5) ◽  
pp. 519-527 ◽  
Author(s):  
Gur Mosheiov ◽  
Dvir Shabtay
Keyword(s):  
Single Machine ◽  
Just In Time ◽  
Processing Times ◽  
Weighted Number

Single Machine Scheduling and due Date Assignment with Past-Sequence-Dependent Delivery Times and General Position-Dependent Processing Times

2014 ◽  
Vol 624 ◽  
pp. 675-680
Author(s):  
Yu Fang Zhao
Keyword(s):  
Single Machine ◽  
Machine Scheduling ◽  
Single Machine Scheduling ◽  
Scheduling Problems ◽  
Due Date ◽  
Due Date Assignment ◽  
Processing Times ◽  
Delivery Times ◽  
Weighted Number ◽  
Tardy Jobs

We studied single machine scheduling problems in which the jobs need to be delivered to customers after processing. It is assumed that the delivery times are proportional to the length of the already processed jobs, and a job's processing time depended 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 analyzed these problems with two different due date assignment methods and conclude that the problems are polynomial time solvable.

Common Due-Window Assignment and Group Scheduling with Position-Dependent Processing Times

2015 ◽  
Vol 32 (06) ◽  
pp. 1550045 ◽  
Author(s):  
Shang-Chia Liu
Keyword(s):  
Single Machine ◽  
Group Technology ◽  
Window Size ◽  
Setup Time ◽  
Single Machine Scheduling ◽  
Processing Times ◽  
Weighted Number ◽  
Due Window ◽  
Tardy Jobs ◽  
Due Window Assignment

This paper investigates a single-machine scheduling problem involving both the due-window assignment and position-dependent processing times under a group technology environment. By position-dependent processing times, we mean that the processing time of a job is dependent of its processing position in the job sequence within the group it belongs to. A setup time is incurred whenever the single machine transfers job processing from a group to another group. Each group is assigned an assignable common due-window. A job completed earlier (respectively, later) than the common due-window of the group it belongs to will incur an earliness (respectively, tardiness) penalty. The objective is to determine the optimal group sequence, the optimal job sequence, and the optimal due-window assignment so as to minimize the total cost including the earliness and tardiness (or weighted number of tardy jobs) penalties, black and the due-window starting time and due-window size costs. We show that both the problems can be solved in polynomial times.

scholarly journals Scheduling with Learning Effects and/or Time-Dependent Processing Times to Minimize the Weighted Number of Tardy Jobs on a Single Machine

2013 ◽  
Vol 2013 ◽  
pp. 1-9 ◽  
Author(s):  
Jianbo Qian ◽  
George Steiner
Keyword(s):  
Single Machine ◽  
Single Machine Scheduling ◽  
Time Dependent ◽  
Scheduling Problems ◽  
Processing Times ◽  
Number Of Tardy Jobs ◽  
Special Cases ◽  
Programming Techniques ◽  
Weighted Number ◽  
Tardy Jobs

We consider single machine scheduling problems with learning/deterioration effects and time-dependent processing times, with due date assignment consideration, and our objective is to minimize the weighted number of tardy jobs. By reducing all versions of the problem to an assignment problem, we solve them inO(n4) time. For some important special cases, the time complexity can be improved to beO(n2) using dynamic programming techniques.

Scheduling Jobs with Truncated Exponential Sum-of-Logarithm-Processing-Times Based and Position-based Learning Effects

2015 ◽  
Vol 32 (04) ◽  
pp. 1550026 ◽  
Author(s):  
Yuan-Yuan Lu ◽  
Fei Teng ◽  
Zhi-Xin Feng
Keyword(s):  
Single Machine ◽  
Minimization Problem ◽  
Completion Time ◽  
Heuristic Algorithms ◽  
Exponential Sum ◽  
Total Weighted Completion Time ◽  
Learning Effects ◽  
Processing Times ◽  
Time Minimization ◽  
Weighted Completion Time

In this study, we consider a scheduling problem with truncated exponential sum-of-logarithm-processing-times based and position-based learning effects on a single machine. We prove that the shortest processing time (SPT) rule is optimal for the makespan minimization problem, the sum of the θth power of job completion times minimization problem, and the total lateness minimization problem, respectively. For the total weighted completion time minimization problem, the discounted total weighted completion time minimization problem, the maximum lateness minimization problem, we present heuristic algorithms (the worst-case bound of these heuristic algorithms are also given) according to the corresponding single machine scheduling problems without learning considerations. It also shows that the problems of minimizing the total tardiness, the total weighted completion time and the discounted total weighted completion time are polynomially solvable under some agreeable conditions on the problem parameters.

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