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Scheduling problems with a common due window assignment: A survey

100%
Janiak A., Kwiatkowski T., Lichtenstein M.
International Journal of Applied Mathematics and Computer Science
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2013
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tom 23
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nr 1
231-241
EN
In this article a survey of studies on scheduling problems with a common due window assignment and earliness/tardiness penalty functions is presented. A due window is a generalization of the classical due date and describes a time interval in which a job should be finished. If a job is completed before or after the due window, it incurs an earliness or a tardiness penalty, respectively. In this survey we separately analyse the classical models with job-independent and job-dependent earliness/tardiness penalty functions and some other more complicated models. We describe the computational complexity of the problems and the main features of the approaches developed to solve them. Particular attention is paid to practical applications of the analysed models. As turns out, some complicated models combining classical scheduling problems with, e.g., learning and aging effects have no reasonable practical justification in the literature.
2
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Modern approaches to modeling user requirements on resource and task allocation in hierarchical computational grids

75%
Kołodziej J., Xhafa F.
International Journal of Applied Mathematics and Computer Science
|
2011
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tom 21
|
nr 2
243-257
EN
Tasks scheduling and resource allocation are among crucial issues in any large scale distributed system, including Computational Grids (CGs). These issues are commonly investigated using traditional computational models and resolution methods that yield near-optimal scheduling strategies. One drawback of such approaches is that they cannot effectively tackle the complex nature of CGs. On the one hand, such systems account for many administrative domains with their own access policies, user privileges, etc. On the other, CGs have hierarchical nature and therefore any computational model should be able to effectively express the hierarchical architecture in the optimization model. Recently, researchers have been investigating the use of game theory for modeling user requirements regarding task and resource allocation in grid scheduling problems. In this paper we present two general non-cooperative game approaches, namely, the symmetric non-zero sum game and the asymmetric Stackelberg game for modeling grid user behavior defined as user requirements. In our game-theoretic approaches we are able to cast new requirements arising in allocation problems, such as asymmetric users relations, security and reliability restrictions in CGs. For solving the games, we designed and implemented GA-based hybrid schedulers for approximating the equilibrium points for both games. The proposed hybrid resolution methods are experimentally evaluated through the grid simulator under heterogeneity, and large-scale and dynamics conditions. The relative performance of the schedulers is measured in terms of the makespan and flowtime metrics. The experimental analysis showed high efficiency of meta-heuristics in solving the game-based models, especially in the case of an additional cost of secure task scheduling to be paid by the users.
3
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Timed Petri-net based formulation and an algorithm for the optimal scheduling of batch plants

75%
Gu T., Bahri P. A., Cai G.
International Journal of Applied Mathematics and Computer Science
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2003
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tom 13
|
nr 4
527-536
EN
The effective scheduling of operations in batch plants has a great potential for high economic returns, in which the formulation and an optimal solution algorithm are the main issues of study. Petri nets have proven to be a promising technique for solving many difficult problems associated with the modelling, formal analysis, design and coordination control of discrete-event systems. One of the major advantages of using a Petri-net model is that the same model can be used for the analysis of behavioural properties and performance evaluation, as well as for the systematic construction of discrete-event simulators and controllers. This paper aims at presenting a Petri-net based approach to the scheduling of operations in batch plants. Firstly, the short term of the 'scheduling of batch plants' is formulated by means of a timed Petri net which can accommodate various intermediate storage policies, such as unlimited intermediate storage (UIS), no intermediate storage (NIS), finite intermediate storage (FIS), and mixed intermediate storage (MIS). Secondly, a heuristic search algorithm for the optimal scheduling of batch plants is given, which is based on generating and checking the markings in the reachability tree of the Petri-net model. Finally, the novel formulation and algorithm are tested with several simulation case studies.
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