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.

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.

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 Scheduling Simple Linear Deteriorating Jobs with Rejection

2014 ◽  
Vol 2014 ◽  
pp. 1-7 ◽  
Author(s):  
Juan Zou ◽  
Yuzhong Zhang
Keyword(s):  
Polynomial Time ◽  
Single Machine ◽  
Approximation Scheme ◽  
Deteriorating Jobs ◽  
Release Dates ◽  
Polynomial Time Approximation Scheme ◽  
Machine Model ◽  
Time Approximation ◽  
Total Penalty ◽  
Polynomial Time Approximation

We consider the problems of scheduling deteriorating jobs with release dates on a single machine (parallel machines) and jobs can be rejected by paying penalties. The processing time of a job is a simple linear increasing function of its starting time. For a single machine model, the objective is to minimize the maximum lateness of the accepted jobs plus the total penalty of the rejected jobs. We show that the problem is NP-hard in the strong sense and presents a fully polynomial time approximation scheme to solve it when all jobs have agreeable release dates and due dates. For parallel-machine model, the objective is to minimize the maximum delivery completion time of the accepted jobs plus the total penalty of the rejected jobs. When the jobs have identical release dates, we first propose a fully polynomial time approximation scheme to solve it. Then, we present a heuristic algorithm for the case where all jobs have to be accepted and evaluate its efficiency by computational experiments.

SCHEDULING WITH POSITION-BASED DETERIORATING JOBS AND MULTIPLE DETERIORATING RATE-MODIFYING ACTIVITIES

2014 ◽  
Vol 31 (01) ◽  
pp. 1450009 ◽  
Author(s):  
GUIYI WEI ◽  
YONG QIU ◽  
MIN JI
Keyword(s):  
Polynomial Time ◽  
Single Machine ◽  
Completion Time ◽  
Heuristic Algorithms ◽  
Deteriorating Jobs ◽  
Single Machine Scheduling ◽  
Integer Program ◽  
Total Completion Time ◽  
Unique Integer ◽  
Optimal Polynomial

In a recent paper, Ozturkoglu and Bulfin (Ozturkoglu, Y. and RL Bulfin (2011). A unique integer mathematical model for scheduling deteriorating jobs with rate-modifying activities on a single machine. The International Journal of Advanced Manufacturing Technology, 57, 753–762.) formulate a unique integer program to solve the single-machine scheduling for the objectives of minimizing makespan and total completion time. They also propose efficient heuristic algorithms for solving large size problems. However their heuristics are not optimal and so the NP-hardness of the considered problem is still open. In this note, we show that a more general problem can be optimally solved in polynomial time. We also provide optimal polynomial-time solution algorithm for the parallel-machine case to minimize total completion time.

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.

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 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.

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