scholarly journals Scheduling Jobs with Maintenance Subject to Load-Dependent Duration on a Single Machine

2015 ◽  
Vol 2015 ◽  
pp. 1-6 ◽  
Author(s):  
Yawei Qi ◽  
Long Wan ◽  
Zhigang Yan
Keyword(s):  
Integer Programming ◽  
Single Machine ◽  
Numerical Experiments ◽  
Heuristic Algorithms ◽  
Programming Model ◽  
Scheduling Problem ◽  
Np Hard ◽  
Ordinary Sense ◽  
Starting Time ◽  
Special Case

This paper investigates a scheduling problem on a single machine with maintenance, in which the starting time of the maintenance is given in advance but its duration depends on the load of the machine before the maintenance. The goal is to minimize the makespan. We formulate it as an integer programming model and show that it is NP-hard in the ordinary sense. Then, we propose an FPTAS and point out that a special case is polynomial solvable. Finally, we design fast heuristic algorithms to solve the scheduling problem. Numerical experiments are implemented to evaluate the performance of the proposed heuristic algorithms. The results show the proposed heuristic algorithms are effective.

scholarly journals Single-Machine Parallel-Batch Scheduling with Nonidentical Job Sizes and Rejection

Mathematics ◽  
2020 ◽  
Vol 8 (2) ◽  
pp. 258
Author(s):  
Miaomiao Jin ◽  
Xiaoxia Liu ◽  
Wenchang Luo
Keyword(s):  
Integer Programming ◽  
Single Machine ◽  
Heuristic Algorithms ◽  
Batch Processing ◽  
Batch Scheduling ◽  
Scheduling Problem ◽  
Programming Formulation ◽  
Processing Times ◽  
Batch Processing Machine ◽  
Rejection Penalty

We investigate the single-machine parallel-batch scheduling problem with nonidentical job sizes and rejection. In this problem, a set of jobs with different processing times and nonidentical sizes is given to be possibly processed on a parallel-batch processing machine. Each job is either accepted and then processed on the machine or rejected by paying its rejection penalty. Preemption is not allowed. Our task is to choose the accepted jobs and schedule them as batches on the machine to minimize the makespan of the accepted jobs plus the total rejection penalty of the rejected jobs. We provide an integer programming formulation to exactly solve our problem. Then, we propose three fast heuristic algorithms to solve the problem and evaluate their performances by using a small numerical example.

Applying Constraint Programming and Integer Programming to Solve the Crew Scheduling Problem for Railroad Systems: Model Formulation and a Case Study

2021 ◽  
pp. 036119812110363
Author(s):  
Guei-Hao Chen ◽  
Jyh-Cherng Jong ◽  
Anthony Fu-Wha Han
Keyword(s):  
Integer Programming ◽  
Constraint Programming ◽  
Heuristic Algorithms ◽  
Programming Model ◽  
Hybrid Approach ◽  
Crew Scheduling ◽  
Scheduling Problem ◽  
Scheduling Problems ◽  
Systems Model ◽  
Crew Scheduling Problem

Crew scheduling is one of the crucial processes in railroad operation planning. Based on current regulations and working and break time requirements, as well as the operational rules, this process aims to find a duty arrangement with minimal cost that covers all trips. Most past studies considered this subject for railroad systems as an optimization problem and solved it with mathematical programming-based methods or heuristic algorithms, despite numerous logical constraints embedded in this problem. Few studies have applied constraint programming (CP) approaches to tackle the railroad crew scheduling problem. This paper proposes a hybrid approach to solve the problem with a CP model for duty generation, and an integer programming model for duty optimization. These models have been applied to the Kaohsiung depot of Taiwan Railways Administration, the largest railroad operator in Taiwan. The encouraging results show that the proposed approach is more efficient than the manual process and can achieve 30% savings of driver cost. Moreover, the approach is robust and provides flexibility to easily accommodate related operational concerns such as minimizing the number of overnight duties. Thus, this hybrid two-phase approach seems to have the potential for applications to the railroad crew scheduling problems outside Taiwan.

scholarly journals Heuristic Algorithms for MapReduce Scheduling Problem with Open-Map Task and Series-Reduce Tasks

2020 ◽  
Vol 2020 ◽  
pp. 1-10
Author(s):  
Feifeng Zheng ◽  
Zhaojie Wang ◽  
Yinfeng Xu ◽  
Ming Liu
Keyword(s):  
Numerical Experiments ◽  
Simulated Annealing Algorithm ◽  
Heuristic Algorithms ◽  
Programming Model ◽  
Mixed Integer ◽  
Scheduling Problem ◽  
Scheduling Model ◽  
Open Map ◽  
Annealing Algorithm ◽  
Mapreduce Scheduling

Based on the classical MapReduce concept, we propose an extended MapReduce scheduling model. In the extended MapReduce scheduling problem, we assumed that each job contains an open-map task (the map task can be divided into multiple unparallel operations) and series-reduce tasks (each reduce task consists of only one operation). Different from the classical MapReduce scheduling problem, we also assume that all the operations cannot be processed in parallel, and the machine settings are unrelated machines. For solving the extended MapReduce scheduling problem, we establish a mixed-integer programming model with the minimum makespan as the objective function. We then propose a genetic algorithm, a simulated annealing algorithm, and an L-F algorithm to solve this problem. Numerical experiments show that L-F algorithm has better performance in solving this problem.

scholarly journals A Dynamic Scheduling Method of Earth-Observing Satellites by Employing Rolling Horizon Strategy

2013 ◽  
Vol 2013 ◽  
pp. 1-11 ◽  
Author(s):  
Qiu Dishan ◽  
He Chuan ◽  
Liu Jin ◽  
Ma Manhao
Keyword(s):  
Integer Programming ◽  
Dynamic Scheduling ◽  
Heuristic Algorithms ◽  
Programming Model ◽  
Scheduling Algorithms ◽  
Scheduling Problem ◽  
Rolling Horizon ◽  
Static Scheduling ◽  
Event Triggering ◽  
Scheduling Method

Focused on the dynamic scheduling problem for earth-observing satellites (EOS), an integer programming model is constructed after analyzing the main constraints. The rolling horizon (RH) strategy is proposed according to the independent arriving time and deadline of the imaging tasks. This strategy is designed with a mixed triggering mode composed of periodical triggering and event triggering, and the scheduling horizon is decomposed into a series of static scheduling intervals. By optimizing the scheduling schemes in each interval, the dynamic scheduling of EOS is realized. We also propose three dynamic scheduling algorithms by the combination of the RH strategy and various heuristic algorithms. Finally, the scheduling results of different algorithms are compared and the presented methods in this paper are demonstrated to be efficient by extensive experiments.

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