A Pareto-optimal solution procedure for the single-machine scheduling problem with release time and multiple performance measures

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.

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A Pareto-Optimal Solution for a Multi-Objective Scheduling Problem with Periodic Maintenance Requirement

International Journal of Operations Research and Information Systems ◽

10.4018/joris.2012040102 ◽

2012 ◽

Vol 3 (2) ◽

pp. 24-45 ◽

Cited By ~ 2

Author(s):

Deniz Mungan ◽

Junfang Yu ◽

Bhaba R. Sarker ◽

Mohammad Anwar Rahman

Keyword(s):

Objective Function ◽

Single Machine ◽

Pareto Optimality ◽

Optimal Solution ◽

Pareto Optimal Solution ◽

Neighborhood Search ◽

Pareto Optimal ◽

Scheduling Problem ◽

Objective Functions ◽

Periodic Maintenance

A Pareto-optimal solution is developed in this paper for a scheduling problem on a single machine with periodic maintenance and non-preemptive jobs. Most of the scheduling problems address only one objective function, while in the real world, such problems are always associated with more than one objective. In this paper, both multi-objective functions and multi-maintenance periods are considered for a machine scheduling problem. To avoid complexities, multiple objective functions are consolidated and transformed into a single objective function after they are weighted and assigned proper weighting factors. In addition, periodic maintenance schedules are also considered in the model. The objective of the model addressed is to minimize the weighted function of the total job flow time, the maximum tardiness, and the machine idle time in a single machine problem with periodic maintenance and non-preemptive jobs. An algorithm is developed to solve this multiple criterion problem and to construct the Pareto-set. The parametric analysis of the trade-offs of all solutions with all possible weighted combination of the criteria is performed. A neighborhood search heuristic is also developed. Results are provided to explore the best schedule among all the Pareto-optimality sets and to compare the result of the modified Pareto-optimality algorithm with the result of the neighborhood search heuristic.

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Hybridization Simulated Annealing Algorithm in a Single Machine Scheduling Problem

WSEAS TRANSACTIONS ON MATHEMATICS ◽

10.37394/23206.2021.20.63 ◽

2021 ◽

Vol 20 ◽

pp. 597-605

Author(s):

Hafed M. Motair

Keyword(s):

Simulated Annealing ◽

Single Machine ◽

Simulated Annealing Algorithm ◽

Optimal Solution ◽

Machine Scheduling ◽

Single Machine Scheduling ◽

Scheduling Problem ◽

Metaheuristic Algorithm ◽

Annealing Algorithm ◽

Completion Times

In this paper, we investigate a single machine scheduling problem (SMSP). We try to reach the optimal or near optimal solution which minimize the sum of three objective functions: total completion times, total tardiness and total earliness. Firstly, we solve this problem by Branch and bound algorithm (BAB alg) to find optimal solutions, dominance rules (DR)s are used to improve the performance of BAB alg, the resulting is BABDR, secondly, we solve this problem by simulated annealing algorithm (SA alg) as metaheuristic algorithm (MET alg). It is known that combining MET alg with other algorithms can improve the resulting solutions. In this paper we developed the concept of insertion preselected jobs one by one through all positions of remaining jobs of considered sequence, the proposed MET alg called Insertion Metaheuristic Algorithm (IMA). This procedure improves the performance of SA alg in two directions: in the first one, we use the IMA to generate initial solution for SA alg, in the second one, we use the IMA to improve the solution obtained through the iterations of SA alg. The experiments showed that IMA can improve the performance of SA alg in these two directions.

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A Single Machine Scheduling Problem with Earliness and Tardiness Penalties Using Memetic Algorithm

Advanced Materials Research ◽

10.4028/www.scientific.net/amr.314-316.2353 ◽

2011 ◽

Vol 314-316 ◽

pp. 2353-2357

Author(s):

Parinya Kaweegitbundit

Keyword(s):

Single Machine ◽

Memetic Algorithm ◽

Optimal Solution ◽

Machine Scheduling ◽

Single Machine Scheduling ◽

Computational Time ◽

Scheduling Problem ◽

Average Percentage ◽

Earliness And Tardiness ◽

Time Required

This paper considers single machine scheduling problem. The objective is to determine sum of earliness and tardiness cost has been minimized. The memetic algorithm is developed to solve this problem. To evaluate performance of memetic algorithm, the solution of propose method is compare with the optimal solution. The results show that the average percentage deviation is less than 10. Here, the computational time required by the MA is significantly less than the time required by the optimal solution method. This result is more emphasized as the problem size is getting larger.

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