Scheduling with Rejection and a Deteriorating Maintenance Activity on a Single Machine

2017 ◽  
Vol 34 (02) ◽  
pp. 1750010 ◽  
Author(s):  
Shi-Sheng Li ◽  
Ren-Xia Chen
Keyword(s):  
Polynomial Time ◽  
Single Machine ◽  
Completion Time ◽  
Single Machine Scheduling ◽  
Total Weighted Completion Time ◽  
Scheduling Problems ◽  
Maintenance Activity ◽  
Polynomial Time Algorithms ◽  
Deteriorating Maintenance ◽  
The Impact

We study single-machine scheduling problems with job rejection and a deteriorating maintenance activity, where the impact of performing this activity is reflected in a reduction of the job processing times. The duration of the maintenance activity is a linear increasing function of its starting time. The aim is to determine the location of the maintenance activity and the job sequence of the accepted jobs so as to minimize scheduling cost of the accepted jobs plus total penalty of the rejected jobs. When the scheduling measures are the makespan, total completion time and combination of earliness, tardiness and due date cost, we provide polynomial time algorithms to solve these problems, respectively. When the scheduling measures are the maximum tardiness and total weighted completion time under the agreeable ratio assumption, we introduce pseudo-polynomial time algorithms to solve these [Formula: see text]-hard problems, respectively.

scholarly journals Optimal algorithms for scheduling under time-of-use tariffs

2021 ◽  
Author(s):  
Lin Chen ◽  
Nicole Megow ◽  
Roman Rischke ◽  
Leen Stougie ◽  
José Verschae
Keyword(s):  
Polynomial Time ◽  
Single Machine ◽  
Completion Time ◽  
Optimal Algorithm ◽  
Optimal Schedule ◽  
Polynomial Time Algorithm ◽  
Time Algorithm ◽  
Single Machine Scheduling ◽  
Total Weighted Completion Time ◽  
Scheduling Problems

AbstractWe consider a natural generalization of classical scheduling problems to a setting in which using a time unit for processing a job causes some time-dependent cost, the time-of-use tariff, which must be paid in addition to the standard scheduling cost. We focus on preemptive single-machine scheduling and two classical scheduling cost functions, the sum of (weighted) completion times and the maximum completion time, that is, the makespan. While these problems are easy to solve in the classical scheduling setting, they are considerably more complex when time-of-use tariffs must be considered. We contribute optimal polynomial-time algorithms and best possible approximation algorithms. For the problem of minimizing the total (weighted) completion time on a single machine, we present a polynomial-time algorithm that computes for any given sequence of jobs an optimal schedule, i.e., the optimal set of time slots to be used for preemptively scheduling jobs according to the given sequence. This result is based on dynamic programming using a subtle analysis of the structure of optimal solutions and a potential function argument. With this algorithm, we solve the unweighted problem optimally in polynomial time. For the more general problem, in which jobs may have individual weights, we develop a polynomial-time approximation scheme (PTAS) based on a dual scheduling approach introduced for scheduling on a machine of varying speed. As the weighted problem is strongly NP-hard, our PTAS is the best possible approximation we can hope for. For preemptive scheduling to minimize the makespan, we show that there is a comparably simple optimal algorithm with polynomial running time. This is true even in a certain generalized model with unrelated machines.

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.

scholarly journals Single-Machine Scheduling with Rejection and an Operator Non-Availability Interval

Mathematics ◽  
2019 ◽  
Vol 7 (8) ◽  
pp. 668 ◽  
Author(s):  
Lili Zuo ◽  
Zhenxia Sun ◽  
Lingfa Lu ◽  
Liqi Zhang
Keyword(s):  
Polynomial Time ◽  
Single Machine ◽  
Polynomial Time Algorithm ◽  
Time Algorithm ◽  
Single Machine Scheduling ◽  
Total Weighted Completion Time ◽  
Scheduling Problems ◽  
Objective Functions ◽  
Rejection Cost ◽  
Scheduling With Rejection

In this paper, we study two scheduling problems on a single machine with rejection and an operator non-availability interval. In the operator non-availability interval, no job can be started or be completed. However, a crossover job is allowed such that it can be started before this interval and completed after this interval. Furthermore, we also assume that job rejection is allowed. That is, each job is either accepted and processed in-house, or is rejected by paying a rejection cost. Our task is to minimize the sum of the makespan (or the total weighted completion time) of accepted jobs and the total rejection cost of rejected jobs. For two scheduling problems with different objective functions, by borrowing the previous algorithms in the literature, we propose a pseudo-polynomial-time algorithm and a fully polynomial-time approximation scheme (FPTAS), respectively.

scholarly journals Some Single-Machine Scheduling Problems with Learning Effects and Two Competing Agents

2014 ◽  
Vol 2014 ◽  
pp. 1-7
Author(s):  
Hongjie Li ◽  
Zeyuan Li ◽  
Yunqiang Yin
Keyword(s):  
Single Machine ◽  
Completion Time ◽  
Single Machine Scheduling ◽  
Total Weighted Completion Time ◽  
Scheduling Problems ◽  
Maximum Cost ◽  
Two Agents ◽  
Solution Algorithms ◽  
Weighted Completion Time ◽  
Machine Scheduling Problems

This study considers a scheduling environment in which there are two agents and a set of jobs, each of which belongs to one of the two agents and its actual processing time is defined as a decreasing linear function of its starting time. Each of the two agents competes to process its respective jobs on a single machine and has its own scheduling objective to optimize. The objective is to assign the jobs so that the resulting schedule performs well with respect to the objectives of both agents. The objective functions addressed in this study include the maximum cost, the total weighted completion time, and the discounted total weighted completion time. We investigate three problems arising from different combinations of the objectives of the two agents. The computational complexity of the problems is discussed and solution algorithms where possible are presented.

scholarly journals Single-Machine Scheduling with Learning Effects and Maintenance: A Methodological Note on Some Polynomial-Time Solvable Cases

2017 ◽  
Vol 2017 ◽  
pp. 1-6
Author(s):  
Kuo-Ching Ying ◽  
Chung-Cheng Lu ◽  
Shih-Wei Lin ◽  
Jie-Ning Chen
Keyword(s):  
Polynomial Time ◽  
Single Machine ◽  
Machine Scheduling ◽  
Polynomial Time Algorithm ◽  
Time Algorithm ◽  
Single Machine Scheduling ◽  
Learning Effects ◽  
Scheduling Problems ◽  
Maintenance Activity ◽  
Processing Times

This work addresses four single-machine scheduling problems (SMSPs) with learning effects and variable maintenance activity. The processing times of the jobs are simultaneously determined by a decreasing function of their corresponding scheduled positions and the sum of the processing times of the already processed jobs. Maintenance activity must start before a deadline and its duration increases with the starting time of the maintenance activity. This work proposes a polynomial-time algorithm for optimally solving two SMSPs to minimize the total completion time and the total tardiness with a common due date.

Single-Machine Scheduling with Due-Window Assignment and Rate-Modifying-Activities under a Deteriorating Maintenance

2013 ◽  
Vol 278-280 ◽  
pp. 2248-2251
Author(s):  
Cheng Xin Luo
Keyword(s):  
Single Machine ◽  
Window Size ◽  
Machine Scheduling ◽  
Single Machine Scheduling ◽  
Optimal Size ◽  
Scheduling Problems ◽  
Maintenance Activity ◽  
Deteriorating Maintenance ◽  
Due Window ◽  
Due Window Assignment

This paper studies single-machine scheduling problems with a due-window assignment and a rate-modifying activity under a deteriorating maintenance consideration simultaneously. Jobs completed within the due-window incur no penalties, other jobs incur either earliness or tardiness penalties. The maintenance activity can be scheduled immediately after any one of the completed jobs. We assume that once the maintenance activity has been completed, the machine efficiency will be improved and the machine maintenance duration depends on its starting time. The objective is to find the optimal maintenance position as well as the optimal size and location of the due-window, and the sequence of jobs to minimize a cost function based on the window size and window location and the earliness and tardiness of the jobs. We propose a polynomial time algorithm to solve the problem optimally.

A Bicriteria Approach for Single Machine Scheduling with Resource Allocation, Learning Effect and a Deteriorating Maintenance Activity

2017 ◽  
Vol 34 (04) ◽  
pp. 1750011 ◽  
Author(s):  
Zhusong Liu ◽  
Zhenyou Wang ◽  
Yuan-Yuan Lu
Keyword(s):  
Resource Allocation ◽  
Single Machine ◽  
Learning Effect ◽  
Machine Scheduling ◽  
Single Machine Scheduling ◽  
Maintenance Activity ◽  
Optimal Resource ◽  
Deteriorating Maintenance ◽  
Polynomially Solvable ◽  
Completion Times

This paper considers the single machine scheduling with learning effect, resource allocation and deteriorating maintenance activity simultaneously. For the convex resource allocation consumption function, we provide a bicriteria analysis where the first (schedule) criterion is to minimize the total weighted sum of makespan, total completion time and total absolute differences in completion times, and the second (resource) criterion is to minimize the total weighted resource consumption. Our aim is to find the optimal resource allocations and job sequence that minimize the three different models of considering the two criterion. We show that these three models are polynomially solvable respectively.

scholarly journals Group Scheduling Problems with Time-Dependent and Position-Dependent DeJong’s Learning Effect

2020 ◽  
Vol 2020 ◽  
pp. 1-8
Author(s):  
Li Sun ◽  
Lei Ning ◽  
Jia-zhen Huo
Keyword(s):  
Polynomial Time ◽  
Completion Time ◽  
Learning Effect ◽  
Time Dependent ◽  
Total Weighted Completion Time ◽  
Group Scheduling ◽  
Scheduling Problems ◽  
Scheduling Model ◽  
Proposed Model ◽  
Weighted Completion Time

In this paper, we introduce a group scheduling model with time-dependent and position-dependent DeJong’s learning effect. The objectives of scheduling problems are to minimize makespan, the total completion time, and the total weighted completion time, respectively. We show that the problems remain solvable in polynomial time under the proposed model.

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