scholarly journals Sum-of-Processing-Times-Based Two-Agent Single-Machine Scheduling with Aging Effects and Tardiness

2015 ◽  
Vol 2015 ◽  
pp. 1-12 ◽  
Author(s):  
Do Gyun Kim ◽  
Jin Young Choi
Keyword(s):  
Genetic Algorithm ◽  
Single Machine ◽  
Optimal Solution ◽  
Machine Scheduling ◽  
Single Machine Scheduling ◽  
Total Weighted Tardiness ◽  
Aging Effects ◽  
Weighted Tardiness ◽  
Processing Times ◽  
Tardy Jobs

We consider a two-agent single-machine scheduling problem that minimizes the total weighted tardiness of one agent under the restriction that the second agent is prohibited from having tardy jobs. The actual processing times of all jobs are affected by a sum-of-processing-times-based aging effect. After showing the NP-hardness of the problem, we design a branch-and-bound (B&B) algorithm to find an optimal solution by developing dominance properties and a lower bound for the total weighted tardiness to increase search efficiency. Because B&B takes a long time to find an optimal solution, we propose a genetic algorithm as an efficient, near optimal solution approach. Four methods for generating initial populations are considered, and edge recombination crossover is adopted as a genetic operator. Through numerical experiments, we verify the outstanding performance of the proposed genetic algorithm.

Single Machine Scheduling and due Date Assignment with Past-Sequence-Dependent Delivery Times and General Position-Dependent Processing Times

2014 ◽  
Vol 624 ◽  
pp. 675-680
Author(s):  
Yu Fang Zhao
Keyword(s):  
Single Machine ◽  
Machine Scheduling ◽  
Single Machine Scheduling ◽  
Scheduling Problems ◽  
Due Date ◽  
Due Date Assignment ◽  
Processing Times ◽  
Delivery Times ◽  
Weighted Number ◽  
Tardy Jobs

We studied single machine scheduling problems in which the jobs need to be delivered to customers after processing. It is assumed that the delivery times are proportional to the length of the already processed jobs, and a job's processing time depended on its position in a sequence. The objective functions include total earliness, the weighted number of tardy jobs and the cost of due date assignment. We analyzed these problems with two different due date assignment methods and conclude that the problems are polynomial time solvable.

Single Machine Scheduling and Due Date Assignment with Past-Sequence-Dependent Delivery Times and Position-Dependent Processing Times

2014 ◽  
Vol 1006-1007 ◽  
pp. 498-503 ◽  
Author(s):  
Yu Fang Zhao
Keyword(s):  
Single Machine ◽  
Dynamic Programming Algorithm ◽  
Machine Scheduling ◽  
Single Machine Scheduling ◽  
Programming Algorithm ◽  
Due Date ◽  
Due Date Assignment ◽  
Processing Times ◽  
Delivery Times ◽  
Tardy Jobs

This paper considers single machine scheduling and due date assignment problems in which the jobs need to be delivered to customers after processing. It is assumed that the delivery times are proportional to the length of the already processed jobs, and a job's processing time depends on its position in a sequence. The objective functions include total earliness, the weighted number of tardy jobs and the cost of due date assignment. We analyze the problems with two different due date assignment methods and conclude that the problems are polynomial time solvable. We provide a dynamic programming algorithm with O(n3) times for the problems.

New Properties for Solving the Single-Machine Scheduling Problem with Early/Tardy Jobs

2017 ◽  
Vol 26 (3) ◽  
pp. 531-543
Author(s):  
Hemmak Allaoua ◽  
Bouderah Brahim
Keyword(s):  
Genetic Algorithm ◽  
Single Machine ◽  
Machine Scheduling ◽  
Single Machine Scheduling ◽  
Computational Effort ◽  
Due Date ◽  
Common Due Date ◽  
Mathematical Properties ◽  
Penalty Costs ◽  
Tardy Jobs

AbstractThis paper presents a mathematically enhanced genetic algorithm (MEGA) using the mathematical properties of the single-machine scheduling of multiple jobs with a common due date. The objective of the problem is to minimize the sum of earliness and tardiness penalty costs in order to encourage the completion time of each job as close as possible to the common due date. The importance of the problem is derived from its NP-hardness and its ideal modeling of just-in-time concept. This philosophy becomes very significant in modern manufacturing and service systems, where policy makers emphasize that a job should be completed as close as possible to its due date. That is to avoid inventory costs and loss of customer’s goodwill. Five mathematical properties are identified and integrated into a genetic algorithm search process to avoid premature convergence, reduce computational effort, and produce high-quality solutions. The computational results demonstrate the significant impact of the introduced properties on the efficiency and effectiveness of MEGA and its competitiveness to state-of-the-art approaches.

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