scholarly journals A Note on Two-Agent Scheduling with Resource Dependent Release Times on a Single Machine

2015 ◽  
Vol 2015 ◽  
pp. 1-4 ◽  
Author(s):  
Peng Liu ◽  
Lini Duan
Keyword(s):  
Cost Function ◽  
Single Machine ◽  
Polynomial Time Algorithm ◽  
Time Algorithm ◽  
Release Time ◽  
Scheduling Problem ◽  
Two Agents ◽  
Release Times ◽  
Agent Scheduling ◽  
Optimal Polynomial

We consider a scheduling problem in which both resource dependent release times and two agents exist simultaneously. Two agents share a common single machine, and each agent wants to minimize a cost function dependent on its own jobs. The release time of eachA-agent’s job is related to the amount of resource consumed. The objective is to find a schedule for the problem of minimizingA-agent’s total amount of resource consumption with a constraint onB-agent’s makespan. The optimal properties and the optimal polynomial time algorithm are proposed to solve the scheduling problem.

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 A Combinatorial 2-Approximation Algorithm for the Parallel-Machine Scheduling with Release Times and Submodular Penalties

Mathematics ◽  
2021 ◽  
Vol 10 (1) ◽  
pp. 61
Author(s):  
Wencheng Wang ◽  
Xiaofei Liu
Keyword(s):  
Approximation Algorithm ◽  
Single Machine ◽  
Machine Scheduling ◽  
Parallel Machine Scheduling ◽  
Parallel Machine ◽  
Single Machine Scheduling ◽  
Release Time ◽  
Release Dates ◽  
Scheduling Problem ◽  
Release Times

In this paper, we consider parallel-machine scheduling with release times and submodular penalties (P|rj,reject|Cmax+π(R)), in which each job can be accepted and processed on one of m identical parallel machines or rejected, but a penalty must paid if a job is rejected. Each job has a release time and a processing time, and the job can not be processed before its release time. The objective of P|rj,reject|Cmax+π(R) is to minimize the makespan of the accepted jobs plus the penalty of the rejected jobs, where the penalty is determined by a submodular function. This problem generalizes a multiprocessor scheduling problem with rejection, the parallel-machine scheduling with submodular penalties, and the single machine scheduling problem with release dates and submodular rejection penalties. In this paper, inspired by the primal-dual method, we present a combinatorial 2-approximation algorithm to P|rj,reject|Cmax+π(R). This ratio coincides with the best known ratio for the parallel-machine scheduling with submodular penalties and the single machine scheduling problem with release dates and submodular rejection penalties.

scholarly journals Nature-Inspired Metaheuristics for Two-Agent Scheduling with Due Date and Release Time

Complexity ◽  
2020 ◽  
Vol 2020 ◽  
pp. 1-13
Author(s):  
Hongwei Li ◽  
Yuvraj Gajpal ◽  
Chirag Surti ◽  
Dongliang Cai ◽  
Amit Kumar Bhardwaj
Keyword(s):  
Heuristic Algorithms ◽  
Computational Time ◽  
Release Time ◽  
Medium Size ◽  
Scheduling Problem ◽  
Due Dates ◽  
Two Agents ◽  
Cloud Computing Service ◽  
Agent Scheduling ◽  
Tardy Jobs

This paper delves into a two-agent scheduling problem in which two agents are competing for a single resource. Each agent has a set of jobs to be processed by a single machine. The processing time, release time, weight, and the due dates of each job are known in advance. Both agents have their objectives, which are conflicting in nature. The first agent tries to minimize the total completion time, while the second agent tries to minimize the number of tardy jobs. The two agents’ scheduling problem, an NP-hard problem, has a wide variety of applications ranging from the manufacturing industry to the cloud computing service provider. Due to the wide applicability, each variation of the problem requires a different algorithm, adapted according to the user’s requirements. This paper provides mathematical models, heuristic algorithms, and two nature-based metaheuristic algorithms to solve the problem. The algorithm’s performance was gauged against the optimal solution obtained from the AMPL-CPLEX solver for both solution quality and computational time. The outlined metaheuristics produce a solution that is comparable with a short computational time. The proposed metaheuristics even have a better solution than the CPLEX solver for medium-size problems, whereas the computation times are much less than the CPLEX solvers.

scholarly journals Optimization for Due-Window Assignment Scheduling with Position-Dependent Weights

2020 ◽  
Vol 2020 ◽  
pp. 1-7 ◽  
Author(s):  
Li-Yan Wang ◽  
Dan-Yang Lv ◽  
Bo Zhang ◽  
Wei-Wei Liu ◽  
Ji-Bo Wang
Keyword(s):  
Single Machine ◽  
General Position ◽  
Processing Time ◽  
Window Size ◽  
Polynomial Time Algorithm ◽  
Time Algorithm ◽  
Scheduling Problem ◽  
Starting Time ◽  
Due Window ◽  
Due Window Assignment

This paper considers a single-machine due-window assignment scheduling problem with position-dependent weights, where the weights only depend on their position in a sequence. The objective is to minimise the total weighted penalty of earliness, tardiness, due-window starting time, and due-window size of all jobs. Optimal properties of the problem are given, and then, a polynomial-time algorithm is provided to solve the problem. An extension to the problem is offered by assuming general position-dependent processing time.

scholarly journals Scheduling Jobs and a Variable Maintenance on a Single Machine with Common Due-Date Assignment

2014 ◽  
Vol 2014 ◽  
pp. 1-5 ◽  
Author(s):  
Long Wan
Keyword(s):  
Single Machine ◽  
Optimal Solution ◽  
Polynomial Time Algorithm ◽  
Time Algorithm ◽  
Due Date ◽  
Due Date Assignment ◽  
Common Due Date ◽  
Optimal Polynomial ◽  
Special Case ◽  
Identical Jobs

We investigate a common due-date assignment scheduling problem with a variable maintenance on a single machine. The goal is to minimize the total earliness, tardiness, and due-date cost. We derive some properties on an optimal solution for our problem. For a special case with identical jobs we propose an optimal polynomial time algorithm followed by a numerical example.

A study of the single-machine two-agent scheduling problem with release times

2013 ◽  
Vol 13 (2) ◽  
pp. 998-1006 ◽  
Author(s):  
Chin-Chia Wu ◽  
Wen-Hung Wu ◽  
Juei-Chao Chen ◽  
Yunqiang Yin ◽  
Wen-Hsiang Wu
Keyword(s):  
Single Machine ◽  
Scheduling Problem ◽  
Release Times ◽  
Agent Scheduling

Supply Chain Scheduling on a Single Machine with Availability Constraint

2013 ◽  
Vol 380-384 ◽  
pp. 4736-4739 ◽  
Author(s):  
Jing Fan
Keyword(s):  
Supply Chain ◽  
Polynomial Time ◽  
Single Machine ◽  
Arrival Time ◽  
Polynomial Time Algorithm ◽  
Time Algorithm ◽  
Supply Chain Scheduling ◽  
Delivery Cost ◽  
Availability Constraint ◽  
Optimal Polynomial

In the actual industrial engineering, the machine may be checked to ensure that they can work efficiently. Thus, the machine has an unavailable interval so that the job could be interrupted. When the machine becomes available again, the job can be resumed processing. When the job is completed, it can be delivered in batches to one customer by vehicles with capacity constraint. Our goal is to minimize the sum of arrival time of batches and the total delivery cost. We develop an optimal polynomial time algorithm and give an instance to verify the algorithm.

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