scholarly journals Rescheduling Problems with Agreeable Job Parameters to Minimize the Tardiness Costs under Deterioration and Disruption

2013 ◽  
Vol 2013 ◽  
pp. 1-7
Author(s):  
Zhang Xingong ◽  
Wang Yong
Keyword(s):  
Dynamic Programming ◽  
Polynomial Time ◽  
Single Machine ◽  
Processing Time ◽  
Deteriorating Jobs ◽  
Total Tardiness ◽  
Starting Time ◽  
Polynomial Time Algorithms ◽  
Programming Algorithms ◽  
Increasing Function

This paper considers single-machine rescheduling problems with agreeable job parameters under deterioration and disruption. Deteriorating jobs mean that the processing time of a job is defined by an increasing function of its starting time. Rescheduling means that, after a set of original jobs has already been scheduled, a new set of jobs arrives and creates a disruption. We consider four cases of minimization of the total tardiness costs with agreeable job parameters under a limit of the disruptions from the original job sequence. We propose polynomial-time algorithms or some dynamic programming algorithms under sequence disruption and time disruption.

Rescheduling Problems with Deteriorating Jobs to Minimize the Tardiness Costs under Time Disruptions

2013 ◽  
Vol 787 ◽  
pp. 973-977
Author(s):  
Xin Gong Zhang
Keyword(s):  
Dynamic Programming ◽  
Polynomial Time ◽  
Single Machine ◽  
Optimal Schedule ◽  
Deteriorating Jobs ◽  
Total Tardiness ◽  
Polynomial Time Algorithms ◽  
Programming Algorithms ◽  
New Jobs

This paper studies the issue of rescheduling to allow for the unexpected arrival of new jobs, taking into account the effect of the disruptions on a previously planned optimal schedule. We consider the single-machine rescheduling problems with deteriorating jobs. Rescheduling means that a set of original jobs has already been scheduled to minimize some classical objective, then a new set of jobs arrives and creates a disruption. The objective is to minimize the total tardiness costs under a limit of the disruptions from the original scheduling. We propose polynomial time algorithms or some dynamic programming algorithms for each problem.

SCHEDULING DETERIORATING JOBS ON A SINGLE MACHINE WITH RELEASE TIMES AND REJECTION

2012 ◽  
Vol 04 (02) ◽  
pp. 1250032 ◽  
Author(s):  
MING LIU ◽  
FEIFENG ZHENG ◽  
CHENGBIN CHU ◽  
YINFENG XU
Keyword(s):  
Single Machine ◽  
Processing Time ◽  
Deteriorating Jobs ◽  
Release Time ◽  
Starting Time ◽  
Release Times ◽  
Deteriorating Job ◽  
Total Penalty ◽  
Programming Algorithms ◽  
Increasing Function

This paper considers scheduling deteriorating jobs on a single machine with release times and rejection. Deteriorating job means that its actual processing time is a increasing function on its execution starting time. In this situation, jobs can be rejected by paying penalties. Each job is associated with a release time. The objective is to minimize the makespan plus the total penalty incurred by rejecting jobs. We present two dynamic programming algorithms and then design an FPTAS for the considered problem.

scholarly journals Decomposition approaches for parallel machine scheduling of step-deteriorating jobs to minimize total tardiness and energy consumption

2021 ◽  
Author(s):  
Xiao Wu ◽  
Peng Guo ◽  
Yi Wang ◽  
Yakun Wang
Keyword(s):  
Energy Consumption ◽  
Tabu Search ◽  
Processing Time ◽  
Deteriorating Jobs ◽  
Parallel Machine Scheduling ◽  
Parallel Machine ◽  
Total Tardiness ◽  
Master Problem ◽  
Starting Time ◽  
Extra Energy

AbstractIn this paper, an identical parallel machine scheduling problem with step-deteriorating jobs is considered to minimize the weighted sum of tardiness cost and extra energy consumption cost. In particular, the actual processing time of a job is assumed to be a step function of its starting time and its deteriorating threshold. When the starting time of a job is later than its deteriorating threshold, the job faces two choices: (1) maintaining its status in holding equipment and being processed with a base processing time and (2) consuming an extra penalty time to finish its processing. The two work patterns need different amounts of energy consumption. To implement energy-efficient scheduling, the selection of the pre-processing patterns must be carefully considered. In this paper, a mixed integer linear programming (MILP) model is proposed to minimize the total tardiness cost and the extra energy cost. Decomposition approaches based on logic-based Benders decomposition (LBBD) are developed by reformulating the studied problem into a master problem and some independent sub-problems. The master problem is relaxed by only making assignment decisions. The sub-problems are to find optimal schedules in the job-to-machine assignments given by the master problem. Moreover, MILP and heuristic based on Tabu search are used to solve the sub-problems. To evaluate the performance of our methods, three groups of test instances were generated inspired by both real-world applications and benchmarks from the literature. The computational results demonstrate that the proposed decomposition approaches can compute competitive schedules for medium- and large-size problems in terms of solution quality. In particular, the LBBD with Tabu search performs the best among the suggested four methods.

Scheduling Deteriorating Jobs with Availability Constraints to Minimize the Makespan

2016 ◽  
Vol 33 (06) ◽  
pp. 1650048
Author(s):  
Chuanli Zhao ◽  
Hengyong Tang
Keyword(s):  
Polynomial Time ◽  
Approximation Scheme ◽  
Deteriorating Jobs ◽  
Worst Case ◽  
Time Approximation ◽  
Starting Time ◽  
Polynomial Time Approximation Algorithm ◽  
Availability Constraints ◽  
Increasing Function ◽  
Polynomial Time Approximation

In this paper, we consider the scheduling problem in which the processing time of a job is a linear increasing function of its starting time and machine with availability constraints. The objective is to minimize the makespan. We first present a fully polynomial-time approximation scheme (FPTAS) for the case with a single machine. We then show that there exists no polynomial time approximation algorithm with a constant worst-case bound for the case with two identical machines unless [Formula: see text].

scholarly journals A Two-Agent Single-Machine Scheduling Problem with Learning and Deteriorating Considerations

2013 ◽  
Vol 2013 ◽  
pp. 1-18 ◽  
Author(s):  
Wen-Hsiang Wu
Keyword(s):  
Single Machine ◽  
Processing Time ◽  
Deteriorating Jobs ◽  
Single Machine Scheduling ◽  
Total Weighted Completion Time ◽  
Learning Effects ◽  
Proposed Model ◽  
Agent Scheduling ◽  
Increasing Function ◽  
Annealing Algorithms

Recently, interest in scheduling with deteriorating jobs and learning effects has kept growing. However, research in this area has seldom considered the multiagent setting. Motivated by these observations, we consider two-agent scheduling on a single machine involving the learning effects and deteriorating jobs simultaneously. In the proposed model, we assume that the actual processing time of a job of the first (second) agent is a decreasing (increasing) function of the total processing time of the jobs already processed in a schedule. The objective is to minimize the total weighted completion time of the jobs of the first agent with the restriction that no tardy job is allowed for the second agent. We develop a branch-and-bound and a simulated annealing algorithms for the problem. We perform extensive computational experiments to test the performance of the algorithms.

scholarly journals Two-Agent Single-Machine Scheduling with Resource-Dependent Starting Times

2013 ◽  
Vol 2013 ◽  
pp. 1-5 ◽  
Author(s):  
Peng Liu ◽  
Xiaoyu Tian
Keyword(s):  
Polynomial Time ◽  
Single Machine ◽  
Completion Time ◽  
Single Machine Scheduling ◽  
Resource Consumption ◽  
Scheduling Problems ◽  
Starting Time ◽  
Polynomial Time Algorithms ◽  
Agent Scheduling ◽  
Optimal Polynomial

We consider several two-agent scheduling problems with resource consumption on a single machine, where each of the agents wants to minimize a measure dependent on its own jobs. The starting time of each job of the first agent is related to the amount of resource consumed. The objective is to minimize the total amount of resource consumption of the first agent with the restriction that the makespan or the total completion time of the second agent cannot exceed a given boundU. The optimal properties and the optimal polynomial time algorithms are proposed to solve the scheduling problems.

Uniform Parallel-Machine Scheduling with Deteriorating Jobs and Rejection

2014 ◽  
Vol 644-650 ◽  
pp. 2030-2033 ◽  
Author(s):  
Qi Zhang ◽  
Cheng Xin Luo
Keyword(s):  
Processing Time ◽  
Approximation Scheme ◽  
Deteriorating Jobs ◽  
Machine Scheduling ◽  
Parallel Machine Scheduling ◽  
Parallel Machine ◽  
Polynomial Time Approximation Scheme ◽  
Starting Time ◽  
Uniform Parallel Machine Scheduling ◽  
Increasing Function

This paper considers uniform parallel-machine scheduling with linear deterioration and rejection. The processing time of a job is a linear increasing function of its starting time and jobs can be rejected by paying penalties. The objective is to find a schedule which minimizes the time by which all jobs are delivered. We propose a fully polynomial-time approximation scheme to solve this problem.

scholarly journals Parallel Batch Scheduling of Deteriorating Jobs with Release Dates and Rejection

2014 ◽  
Vol 2014 ◽  
pp. 1-7
Author(s):  
Juan Zou ◽  
Cuixia Miao
Keyword(s):  
Approximation Scheme ◽  
Deteriorating Jobs ◽  
Time Algorithm ◽  
Batch Scheduling ◽  
Release Dates ◽  
Ordinary Sense ◽  
Starting Time ◽  
Total Penalty ◽  
Batching Machine ◽  
Increasing Function

We consider the unbounded parallel batch scheduling with deterioration, release dates, and rejection. Each job is either accepted and processed on a single batching machine, or rejected by paying penalties. The processing time of a job is a simple linear increasing function of its starting time. The objective is to minimize the sum of the makespan of the accepted jobs and the total penalty of the rejected jobs. First, we show that the problem is NP-hard in the ordinary sense. Then, we present two pseudopolynomial time algorithms and a fully polynomial-time approximation scheme to solve this problem. Furthermore, we provide an optimalO(nlog⁡n)time algorithm for the case where jobs have identical release dates.

scholarly journals Parallel-Batch Scheduling with Two Models of Deterioration to Minimize the Makespan

2014 ◽  
Vol 2014 ◽  
pp. 1-10 ◽  
Author(s):  
Cuixia Miao
Keyword(s):  
Polynomial Time ◽  
Single Machine ◽  
Processing Time ◽  
Parallel Machine ◽  
Batch Scheduling ◽  
Approximation Schemes ◽  
Time Approximation ◽  
Identical Parallel Machine ◽  
Parallel Machine Problem ◽  
Machine Problem

We consider the bounded parallel-batch scheduling with two models of deterioration, in which the processing time of the first model ispj=aj+αtand of the second model ispj=a+αjt. The objective is to minimize the makespan. We presentO(n log n)time algorithms for the single-machine problems, respectively. And we propose fully polynomial time approximation schemes to solve the identical-parallel-machine problem and uniform-parallel-machine problem, respectively.

Sign in / Sign up

Export Citation Format

Share Document