Pareto and scalar bicriterion optimization in scheduling deteriorating jobs

2006 ◽  
Vol 33 (3) ◽  
pp. 746-767 ◽  
Author(s):  
S. Gawiejnowicz ◽  
W. Kurc ◽  
L. Pankowska
Keyword(s):  
Deteriorating Jobs ◽  
Bicriterion Optimization

scholarly journals Parallel Batch Scheduling of Deteriorating Jobs with Release Dates and Rejection

2014 ◽  
Vol 2014 ◽  
pp. 1-7
Author(s):  
Juan Zou ◽  
Cuixia Miao
Keyword(s):  
Approximation Scheme ◽  
Deteriorating Jobs ◽  
Time Algorithm ◽  
Batch Scheduling ◽  
Release Dates ◽  
Ordinary Sense ◽  
Starting Time ◽  
Total Penalty ◽  
Batching Machine ◽  
Increasing Function

We consider the unbounded parallel batch scheduling with deterioration, release dates, and rejection. Each job is either accepted and processed on a single batching machine, or rejected by paying penalties. The processing time of a job is a simple linear increasing function of its starting time. The objective is to minimize the sum of the makespan of the accepted jobs and the total penalty of the rejected jobs. First, we show that the problem is NP-hard in the ordinary sense. Then, we present two pseudopolynomial time algorithms and a fully polynomial-time approximation scheme to solve this problem. Furthermore, we provide an optimalO(nlog⁡n)time algorithm for the case where jobs have identical release dates.

Scheduling step-deteriorating jobs on bounded parallel-batching machines to maximise the total net revenue

2018 ◽  
Vol 70 (10) ◽  
pp. 1830-1847 ◽  
Author(s):  
Jun Pei ◽  
Xingming Wang ◽  
Wenjuan Fan ◽  
Panos M. Pardalos ◽  
Xinbao Liu
Keyword(s):  
Deteriorating Jobs ◽  
Parallel Batching ◽  
Net Revenue

scholarly journals Decomposition approaches for parallel machine scheduling of step-deteriorating jobs to minimize total tardiness and energy consumption

2021 ◽  
Author(s):  
Xiao Wu ◽  
Peng Guo ◽  
Yi Wang ◽  
Yakun Wang
Keyword(s):  
Energy Consumption ◽  
Tabu Search ◽  
Processing Time ◽  
Deteriorating Jobs ◽  
Parallel Machine Scheduling ◽  
Parallel Machine ◽  
Total Tardiness ◽  
Master Problem ◽  
Starting Time ◽  
Extra Energy

AbstractIn this paper, an identical parallel machine scheduling problem with step-deteriorating jobs is considered to minimize the weighted sum of tardiness cost and extra energy consumption cost. In particular, the actual processing time of a job is assumed to be a step function of its starting time and its deteriorating threshold. When the starting time of a job is later than its deteriorating threshold, the job faces two choices: (1) maintaining its status in holding equipment and being processed with a base processing time and (2) consuming an extra penalty time to finish its processing. The two work patterns need different amounts of energy consumption. To implement energy-efficient scheduling, the selection of the pre-processing patterns must be carefully considered. In this paper, a mixed integer linear programming (MILP) model is proposed to minimize the total tardiness cost and the extra energy cost. Decomposition approaches based on logic-based Benders decomposition (LBBD) are developed by reformulating the studied problem into a master problem and some independent sub-problems. The master problem is relaxed by only making assignment decisions. The sub-problems are to find optimal schedules in the job-to-machine assignments given by the master problem. Moreover, MILP and heuristic based on Tabu search are used to solve the sub-problems. To evaluate the performance of our methods, three groups of test instances were generated inspired by both real-world applications and benchmarks from the literature. The computational results demonstrate that the proposed decomposition approaches can compute competitive schedules for medium- and large-size problems in terms of solution quality. In particular, the LBBD with Tabu search performs the best among the suggested four methods.

Scheduling Piecewise Linear Deteriorating Jobs to Minimize Makespan in a Two-Machine Flowshop

2021 ◽  
Vol 2 (4) ◽  
Author(s):  
Abbasali Jafari-Nodoushan ◽  
Hassan Khademi Zare ◽  
M. M. Lotfi ◽  
R. Tavakkoli-Moghaddam
Keyword(s):  
Piecewise Linear ◽  
Deteriorating Jobs
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