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

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.

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.

Single Machine Two-Agent Scheduling with Deteriorating Jobs

2016 ◽  
Vol 33 (05) ◽  
pp. 1650034 ◽  
Author(s):  
Zhenyou Wang ◽  
Cai-Min Wei ◽  
Yu-Bin Wu
Keyword(s):  
Single Machine ◽  
Completion Time ◽  
Processing Time ◽  
Deteriorating Jobs ◽  
Single Machine Scheduling ◽  
Total Weighted Completion Time ◽  
Scheduling Problem ◽  
Agent Scheduling ◽  
Polynomially Solvable ◽  
Weighted Completion Time

This paper deals with the single machine scheduling problem with deteriorating jobs in which there are two distinct families of jobs (i.e., two-agent) pursuing different objectives. In this model the processing time of a job is defined as a function that is proportional to a linear function of its stating time. For the following three scheduling criteria: minimizing the makespan, minimizing the total weighted completion time, and minimizing the maximum lateness, we show that some basic versions of the problem are polynomially solvable. We also establish the conditions under which the problem is computationally hard.

scholarly journals Competitive Two-Agent Scheduling with Learning Effect and Release Times on a Single Machine

2013 ◽  
Vol 2013 ◽  
pp. 1-9 ◽  
Author(s):  
Der-Chiang Li ◽  
Peng-Hsiang Hsu
Keyword(s):  
Single Machine ◽  
Learning Effect ◽  
Optimal Solution ◽  
Total Weighted Completion Time ◽  
Optimal Solutions ◽  
Release Times ◽  
Agent Scheduling ◽  
Weighted Completion Time ◽  
Dominance Properties ◽  
Annealing Algorithms

The learning effect has gained much attention in the scheduling research recently, where many researchers have focused their problems on only one optimization. This study further addresses the scheduling problem in which two agents compete to perform their own jobs with release times on a common single machine with learning effect. The aim is to minimize the total weighted completion time of the first agent, subject to an upper bound on the maximum lateness of the second agent. We propose a branch-and-bound approach with several useful dominance properties and an effective lower bound for searching the optimal solution and three simulated-annealing algorithms for the near-optimal solutions. The computational results show that the proposed algorithms perform effectively and efficiently.

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