An Ordered Flow Shop with Two Agents

2016 ◽  
Vol 33 (05) ◽  
pp. 1650037 ◽  
Author(s):  
Byung-Cheon Choi ◽  
Myoung-Ju Park
Keyword(s):  
Polynomial Time ◽  
Processing Time ◽  
Flow Shop ◽  
Fixed Number ◽  
Scheduling Problem ◽  
Np Hard ◽  
Two Agents ◽  
Agent Scheduling ◽  
Polynomially Solvable ◽  
Machine Problem

In this paper, we consider a two-agent scheduling problem in an [Formula: see text]-machine ordered flow shop where each agent is responsible for his own set of jobs and wishes to minimize the makespan. Since the problem is NP-hard, we develop a pseudo-polynomial time approach for the case with a fixed number of machines and investigate the conditions that make the problem polynomially solvable. Finally, we consider a three-machine problem with a special processing time structure, and demonstrate its polynomiality.

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.

Group Scheduling with Two Competing Agents on a Single Machine

2014 ◽  
Vol 31 (06) ◽  
pp. 1450043 ◽  
Author(s):  
Shi-Sheng Li ◽  
Ren-Xia Chen
Keyword(s):  
Polynomial Time ◽  
Single Machine ◽  
Upper Bound ◽  
Completion Time ◽  
Group Technology ◽  
Setup Time ◽  
Group Scheduling ◽  
Scheduling Problem ◽  
Two Agents ◽  
Polynomially Solvable

We consider the scheduling problem in which two agents, each with a set of jobs, compete to perform their respective jobs on a single machine under a group technology (GT) environment. The jobs of agents are classified into groups according to their production similarities in advance, all jobs of the same group are required to be processed contiguously on the machine. A sequence-independent setup time precedes the processing of each group. We propose a polynomial time solution for the problem of minimizing the maximum regular cost of one agent, subject to an upper bound on the maximum regular cost of the second agent. We also show that the problem of minimizing the total completion time of the first agent, subject to an upper bound on the maximum lateness of the second agent is strongly [Formula: see text]-hard. The case where all groups of the first agent have the same number of jobs is shown to be polynomially solvable.

scholarly journals Two-Agent Scheduling to Minimize the Maximum Cost with Position-Dependent Jobs

2015 ◽  
Vol 2015 ◽  
pp. 1-4 ◽  
Author(s):  
Long Wan
Keyword(s):  
Polynomial Time ◽  
Single Machine ◽  
Processing Time ◽  
Pareto Optimal ◽  
Scheduling Problem ◽  
Maximum Cost ◽  
Feasible Method ◽  
Actual Position ◽  
Variable Function ◽  
Agent Scheduling

This paper investigates a single-machine two-agent scheduling problem to minimize the maximum costs with position-dependent jobs. There are two agents, each with a set of independent jobs, competing to perform their jobs on a common machine. In our scheduling setting, the actual position-dependent processing time of one job is characterized by variable function dependent on the position of the job in the sequence. Each agent wants to fulfil the objective of minimizing the maximum cost of its own jobs. We develop a feasible method to achieve all the Pareto optimal points in polynomial time.

Two-Machine and Two-Agent Flow Shop with Special Processing Times Structures

2017 ◽  
Vol 34 (04) ◽  
pp. 1750017 ◽  
Author(s):  
Byung-Gyoo Kim ◽  
Byung-Cheon Choi ◽  
Myoung-Ju Park
Keyword(s):  
Computational Complexity ◽  
Flow Shop ◽  
Special Structure ◽  
Scheduling Problem ◽  
Np Hard ◽  
Processing Times ◽  
Special Cases ◽  
Agent Scheduling ◽  
Agent Flow

We consider a two-agent scheduling problem in a two-machine flow shop environment where each agent is responsible for his own set of jobs and wishes to minimize the makespan. The objective is to minimize one agent’s makespan, subject to the other’s objective of not exceeding a given threshold. It is known that the problem is NP-hard. Thus, we consider special cases such that the processing times of each agent have a special structure, and analyze their computational complexity.

The Research of Heuristic Algorithm for Flow Shop Scheduling Problem

2012 ◽  
Vol 605-607 ◽  
pp. 528-531
Author(s):  
Dan Tang ◽  
Hong Ping Shu
Keyword(s):  
Heuristic Algorithm ◽  
Processing Time ◽  
Flow Shop ◽  
Heuristic Method ◽  
Flow Shop Scheduling ◽  
Scheduling Problem ◽  
Average Quality ◽  
Simulation Experiments ◽  
Shop Scheduling ◽  
Better Than

For the flow shop scheduling problem which aims to minimize makespan, this paper gives a new derivation about its mathematical definition, and mining characteristics of the problem itself further. By which analysis, the new heuristic method proposed in the paper shorten the waiting time of each job as much as possible on the basis of reduce the processing time of the first machine and last job. The result of simulation experiments shows that, our new heuristic algorithm has good performance, and the average quality and stability of scheduling sequences generated by new method is significantly better than other heuristic algorithm which has the same complexity.

scholarly journals Parallel-Batch Scheduling with Two Models of Deterioration to Minimize the Makespan

2014 ◽  
Vol 2014 ◽  
pp. 1-10 ◽  
Author(s):  
Cuixia Miao
Keyword(s):  
Polynomial Time ◽  
Single Machine ◽  
Processing Time ◽  
Parallel Machine ◽  
Batch Scheduling ◽  
Approximation Schemes ◽  
Time Approximation ◽  
Identical Parallel Machine ◽  
Parallel Machine Problem ◽  
Machine Problem

We consider the bounded parallel-batch scheduling with two models of deterioration, in which the processing time of the first model ispj=aj+αtand of the second model ispj=a+αjt. The objective is to minimize the makespan. We presentO(n log n)time algorithms for the single-machine problems, respectively. And we propose fully polynomial time approximation schemes to solve the identical-parallel-machine problem and uniform-parallel-machine problem, respectively.

Genetic Algorithm for a Two-Agent Scheduling Problem with Truncated Learning Consideration

2014 ◽  
Vol 31 (06) ◽  
pp. 1450046 ◽  
Author(s):  
Wen-Hsiang Wu ◽  
Yunqiang Yin ◽  
Shuenn-Ren Cheng ◽  
Peng-Hsiang Hsu ◽  
Chin-Chia Wu
Keyword(s):  
Processing Time ◽  
Optimal Solution ◽  
Total Weighted Completion Time ◽  
Scheduling Problem ◽  
Learning Effects ◽  
Research Attention ◽  
Multiple Agent ◽  
Agent Scheduling ◽  
Dominance Properties ◽  
Actual Processing Time

Scheduling with learning effects has received lots of research attention lately. However, the multiple-agent setting with learning consideration is relatively limited. On the other hand, the actual processing time of a job under an uncontrolled learning effect will drop to zero precipitously as the number of the jobs already processed increases. This is rather absurd in reality. Based on these observations, this paper considers a single-machine two-agent scheduling problem in which the actual processing time of a job depends not only on the job's scheduled position, but also on a control parameter. The objective is to minimize the total weighted completion time of jobs from the first agent with the restriction that no tardy job is allowed for the second agent. A branch-and-bound algorithm incorporated with several dominance properties and lower bounds is proposed to derive the optimal solution for the problem. In addition, genetic algorithms (GAs) are also provided to obtain the near-optimal solution. Finally, a computational experiment is conducted to evaluate the performance of the proposed algorithms.

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.

A Bee Colony Algorithm based Solver for Flow Shop Scheduling Problem

2021 ◽  
Vol 5 (2) ◽  
Author(s):  
Yosua Halim ◽  
Cecilia Esti Nugraheni
Keyword(s):  
Processing Time ◽  
Flow Shop ◽  
Flow Shop Scheduling ◽  
Food Sources ◽  
Scheduling Problem ◽  
Total Processing Time ◽  
Shop Scheduling ◽  
Bee Colony ◽  
Problem Instances ◽  
Parameter Values

Flow Shop Scheduling (FSS) is scheduled to involve n jobs and m machines in the same process sequence, where each machine processes precisely one job in a certain period. In FSS, when a machine is doing work, other machines cannot do the same job simultaneously. The solution to this problem is the job sequence with minimal total processing time.  Many algorithms can be used to determine the order in which the job is performed. In this paper, the algorithm used to solve the flow shop scheduling problem is the bee colony algorithm. The bee colony algorithm is an algorithm that applies the metaheuristic method and performs optimization according to the workings of the bee colony. To measure the performance of this algorithm, we conducted some experiments by using Taillard's Benchmark as problem instances. Based on experiments that have been carried out by changing the existing parameter values, the size of the bee population, the number of iterations, and the limit number of bees can affect the candidate solutions obtained. The limit is a control parameter for a bee when looking for new food sources. The more the number of bees, the more iterations, and the limit used, the better the final time of the sequence of work. The bee colony algorithm can reach the upper limit of the Taillard case in some cases in the number of machines 5 and 20 jobs. The more the number of machines and jobs to optimize, the worse the total processing time.

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