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 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.

SINGLE-MACHINE SCHEDULING WITH PROPORTIONALLY DETERIORATING JOBS SUBJECT TO AVAILABILITY CONSTRAINTS

2012 ◽  
Vol 29 (04) ◽  
pp. 1250019 ◽  
Author(s):  
SHISHENG LI ◽  
BAOQIANG FAN
Keyword(s):  
Polynomial Time ◽  
Single Machine ◽  
Deteriorating Jobs ◽  
Polynomial Time Algorithm ◽  
Time Algorithm ◽  
Single Machine Scheduling ◽  
Total Weighted Completion Time ◽  
Worst Case ◽  
Availability Constraints ◽  
Worst Case Ratio

We address the nonresumable version of the scheduling problem with proportionally deteriorating jobs on a single machine subject to availability constraints. The objective is to minimize the total weighted completion time. We show that there exists no polynomial-time algorithm with a constant worst-case ratio for the problem with two nonavailability intervals unless [Formula: see text]. Furthermore, we propose a pseudo-polynomial-time algorithm and a fully polynomial-time approximation scheme for the problem with a single nonavailability interval.

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.

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 Two-Agent Preemptive Pareto-Scheduling to Minimize Late Work and Other Criteria

Mathematics ◽  
2020 ◽  
Vol 8 (9) ◽  
pp. 1517
Author(s):  
Ruyan He ◽  
Jinjiang Yuan
Keyword(s):  
Objective Function ◽  
Polynomial Time ◽  
Single Machine ◽  
Completion Time ◽  
Polynomial Time Algorithm ◽  
Time Algorithm ◽  
Pareto Optimal ◽  
Scheduling Problems ◽  
Trade Off ◽  
Late Work

In this paper, we consider three preemptive Pareto-scheduling problems with two competing agents on a single machine. In each problem, the objective function of agent A is the total completion time, the maximum lateness, or the total late work while the objective function of agent B is the total late work. For each problem, we provide a polynomial-time algorithm to characterize the trade-off curve of all Pareto-optimal points.

Proportionate Flow Shop Scheduling with Rejection

2017 ◽  
Vol 34 (04) ◽  
pp. 1750015 ◽  
Author(s):  
Shi-Sheng Li ◽  
De-Liang Qian ◽  
Ren-Xia Chen
Keyword(s):  
Processing Time ◽  
Flow Shop ◽  
Polynomial Time Algorithm ◽  
Time Algorithm ◽  
Flow Shop Scheduling ◽  
Total Weighted Completion Time ◽  
Processing Times ◽  
Proportionate Flow Shop ◽  
Total Penalty ◽  
Scheduling With Rejection

We consider the problem of scheduling [Formula: see text] jobs with rejection on a set of [Formula: see text] machines in a proportionate flow shop system where the job processing times are machine-independent. The goal is to find a schedule to minimize the scheduling cost of all accepted jobs plus the total penalty of all rejected jobs. Two variations of the scheduling cost are considered. The first is the maximum tardiness and the second is the total weighted completion time. For the first problem, we first show that it is [Formula: see text]-hard, then we construct a pseudo-polynomial time algorithm to solve it and an [Formula: see text] time for the case where the jobs have the same processing time. For the second problem, we first show that it is [Formula: see text]-hard, then we design [Formula: see text] time algorithms for the case where the jobs have the same weight and for the case where the jobs have the same processing time.

Single-Machine Scheduling with Resource-Dependent Learning Effect and Deteriorating Jobs

2013 ◽  
Vol 423-426 ◽  
pp. 2224-2227
Author(s):  
Yan Peng Fan ◽  
Chuan Li Zhao
Keyword(s):  
Resource Allocation ◽  
Single Machine ◽  
Learning Effect ◽  
Operation Time ◽  
Deteriorating Jobs ◽  
Polynomial Time Algorithm ◽  
Time Algorithm ◽  
Single Machine Scheduling ◽  
Optimal Sequence ◽  
Dependent Learning

This paper considers single-machine due-window assignment and scheduling with learning effect and resource-dependent processing times. The processing time of a job is a function of its position in a sequence, its starting time, and its resource allocation. The objective is to determine the optimal sequence of jobs and optimal resource allocation so as to minimize the sum of earliness, tardiness, due-windows and resource and operation time cost, the considered problem is molded as an assignment problem and can be solved with a polynomial time algorithm.

Single Machine Scheduling with Discretely Compressible Processing Times

2013 ◽  
Vol 787 ◽  
pp. 1020-1024
Author(s):  
Shu Xia Zhang ◽  
Yu Zhong Zhang
Keyword(s):  
Dynamic Programming ◽  
Single Machine ◽  
Processing Time ◽  
Machine Scheduling ◽  
Polynomial Time Algorithm ◽  
Time Algorithm ◽  
Single Machine Scheduling ◽  
Scheduling Problem ◽  
Processing Times ◽  
Release Times

In this paper, we address the single machine scheduling problem with discretely compressible processing times, where processing any job with a compressed processing time incurs a corresponding compression cost. We consider the following problem: scheduling with discretely compressible processing times to minimize makespan with the constraint of total compression cost. Jobs may have different release times. We design a pseudo-polynomial time algorithm by approach of dynamic programming and an FPTAS.

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.

Sign in / Sign up

Export Citation Format

Share Document