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

Mathematics ◽  
2021 ◽  
Vol 9 (23) ◽  
pp. 3085
Author(s):  
Jin Qian ◽  
Yu Zhan
Keyword(s):  
Polynomial Time ◽  
Learning Effect ◽  
Single Machine Scheduling ◽  
Decision Variable ◽  
Scheduling Problem ◽  
Due Date ◽  
Optimal Sequence ◽  
Processing Times ◽  
Delivery Times ◽  
Tardy Jobs

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 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.

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

2014 ◽  
Vol 1006-1007 ◽  
pp. 498-503 ◽  
Author(s):  
Yu Fang Zhao
Keyword(s):  
Single Machine ◽  
Dynamic Programming Algorithm ◽  
Machine Scheduling ◽  
Single Machine Scheduling ◽  
Programming Algorithm ◽  
Due Date ◽  
Due Date Assignment ◽  
Processing Times ◽  
Delivery Times ◽  
Tardy Jobs

This paper considers single machine scheduling and due date assignment 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 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 the problems with two different due date assignment methods and conclude that the problems are polynomial time solvable. We provide a dynamic programming algorithm with O(n3) times for the problems.

A Branch-and-Bound Algorithm for Two-Agent Scheduling with Learning Effect and Late Work Criterion

2018 ◽  
Vol 35 (05) ◽  
pp. 1850037 ◽  
Author(s):  
Shang-Chia Liu ◽  
Jiahui Duan ◽  
Win-Chin Lin ◽  
Wen-Hsiang Wu ◽  
Jan-Yee Kung ◽  
...  
Keyword(s):  
Branch And Bound ◽  
Learning Effect ◽  
Optimal Schedule ◽  
Optimal Solution ◽  
Single Machine Scheduling ◽  
Branch And Bound Algorithm ◽  
Scheduling Problem ◽  
Late Work ◽  
Processing Times ◽  
Agent Scheduling

This paper studies a two-agent single-machine scheduling problem with sum-of-processing-times-based learning consideration. The goal is to find an optimal schedule to minimize the total late work of the first agent subject to the restriction that the maximum lateness of the second agent has an upper bound. For this problem, a branch-and-bound algorithm along with several dominances and a lower bound is developed to find the optimal solution, and a tabu algorithm with several improvements is proposed to find the near-optimal solution. Computational experiments are provided to further measure the performance of the proposed algorithms.

An Optimal Algorithm for Scheduling with Variable Job Processing Times and Rejection

2015 ◽  
Vol 775 ◽  
pp. 449-452
Author(s):  
Ji Bo Wang ◽  
Chou Jung Hsu
Keyword(s):  
Objective Function ◽  
Polynomial Time ◽  
Single Machine ◽  
Processing Time ◽  
Optimal Algorithm ◽  
Machine Scheduling ◽  
Single Machine Scheduling ◽  
Scheduling Problem ◽  
Processing Times ◽  
Rejection Penalty

This paper studies a single machine scheduling problem with rejection. Each job has a variable processing time and a rejection penalty. The objective function is to minimize the sum of the makespan of the accepted jobs and the total rejection penalty of the rejected jobs. We show that the problem can be solved in polynomial time.

Single-Machine Scheduling with Learning Effect, Deteriorating Jobs and Convex Resource Dependent Processing Times

2015 ◽  
Vol 32 (05) ◽  
pp. 1550033 ◽  
Author(s):  
Xin-Jun Li ◽  
Jian-Jun Wang ◽  
Xue-Ru Wang
Keyword(s):  
Resource Allocation ◽  
Single Machine ◽  
Learning Effect ◽  
Waiting Times ◽  
Deteriorating Jobs ◽  
Machine Scheduling ◽  
Single Machine Scheduling ◽  
Optimal Sequence ◽  
Processing Times ◽  
Convex Resource Allocation

This paper considers single-machine scheduling with learning effect, deteriorating jobs and convex resource dependent processing times, i.e., the processing time of a job is a function of its starting time, its position in a sequence and its convex resource allocation. The objective is to find the optimal sequence of jobs and the optimal convex resource allocation separately to minimize a cost function containing makespan, total completion (waiting) time, total absolute differences in completion (waiting) times and total resource cost. It is proved that the problem can be solved in polynomial time.

scholarly journals Dynamic Restructuring Framework for Scheduling with Release Times and Due-Dates

Mathematics ◽  
2019 ◽  
Vol 7 (11) ◽  
pp. 1104 ◽  
Author(s):  
Nodari Vakhania
Keyword(s):  
Polynomial Time ◽  
Single Machine ◽  
Machine Scheduling ◽  
Single Machine Scheduling ◽  
Scheduling Problem ◽  
Scheduling Problems ◽  
Due Dates ◽  
Processing Times ◽  
Release Times ◽  
Special Case

Scheduling jobs with release and due dates on a single machine is a classical strongly NP-hard combination optimization problem. It has not only immediate real-life applications but also it is effectively used for the solution of more complex multiprocessor and shop scheduling problems. Here, we propose a general method that can be applied to the scheduling problems with job release times and due-dates. Based on this method, we carry out a detailed study of the single-machine scheduling problem, disclosing its useful structural properties. These properties give us more insight into the complex nature of the problem and its bottleneck feature that makes it intractable. This method also helps us to expose explicit conditions when the problem can be solved in polynomial time. In particular, we establish the complexity status of the special case of the problem in which job processing times are mutually divisible by constructing a polynomial-time algorithm that solves this setting. Apparently, this setting is a maximal polynomially solvable special case of the single-machine scheduling problem with non-arbitrary job processing times.

BICRITERIA SCHEDULING ON SINGLE-MACHINE WITH INVENTORY OPERATIONS

2009 ◽  
Vol 01 (02) ◽  
pp. 227-234
Author(s):  
BAOQIANG FAN ◽  
RONGJUN CHEN ◽  
GUOCHUN TANG
Keyword(s):  
Single Machine ◽  
Approximation Scheme ◽  
Optimal Algorithm ◽  
Single Machine Scheduling ◽  
Scheduling Problem ◽  
Bicriteria Scheduling ◽  
Processing Times ◽  
Polynomial Formula ◽  
Tardy Jobs ◽  
Special Case

In this paper, we consider the single machine scheduling problem with inventory operations. The objective is to minimize makespan subject to the constraint that the total number of tardy jobs is minimum. We show the problem is strongly NP-hard. A polynomial [Formula: see text]-approximation scheme for the problem is presented, where m is defined as the total job's processing times ∑ pj divided by the capacity c of the storage, and an optimal algorithm for a special case of the problem, in which each job is one unit in size.

Just-In-Time Scheduling with Generalized Due Dates and Identical Due Date Intervals

2018 ◽  
Vol 35 (06) ◽  
pp. 1850046 ◽  
Author(s):  
Byung-Cheon Choi ◽  
Myoung-Ju Park
Keyword(s):  
Single Machine Scheduling ◽  
Just In Time ◽  
Scheduling Problem ◽  
Np Hard ◽  
Due Dates ◽  
Due Date ◽  
Time Scheduling ◽  
Weighted Number ◽  
Polynomially Solvable ◽  
Tardy Jobs

We consider a single-machine scheduling problem such that the due dates are assigned not to the jobs but to the position at which the job is processed. We focus on the case with identical due date intervals. The objective is to minimize the weighted number of early and tardy jobs. First, we show that the problem is strongly NP-hard and has no [Formula: see text]-approximation algorithm for any fixed value [Formula: see text]. Then, we investigate polynomially solvable cases. Finally, we show that the preemption version is weakly NP-hard through its equivalence to the problem of minimizing the weighted number of tardy jobs.

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