A Flexible Integrated Scheduling Algorithm for Dynamic Determination Processing Equipment Considering the Root-Subtree Vertical and Horizontal Pre-Scheduling

Teng, Haikun; Xie, Zhiqiang; Yue, Xiao‐Guang; Cao, Wangcheng

doi:10.1109/access.2022.3230757

IEEE Access

2022

DOI: 10.1109/access.2022.3230757

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A Flexible Integrated Scheduling Algorithm for Dynamic Determination Processing Equipment Considering the Root-Subtree Vertical and Horizontal Pre-Scheduling

Haikun Teng

Zhiqiang Xie

Xiao‐Guang Yue

et al.

Abstract: Aiming at the existing flexible integrated scheduling algorithms that use unified rules to solve the conflicts between processes and equipment, and ignore the vertical and horizontal characteristics of the process relative positions in the process tree, a flexible integrated scheduling algorithm for dynamic determination processing equipment considering the Root-Subtree vertical and horizontal pre-scheduling (FISA-DEVH) is proposed. The process sorting strategy of the Root-Subtree vertical and horizontal presc… Show more

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Cited by 3 publications

References 19 publications

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Flexible Integrated Scheduling Considering Periodic Maintenance

Ding,

Xie,

Zhou

et al. 2024

Electronics

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Aiming at the problem of current flexible integrated scheduling, most of the current research shortens the total processing time of products and ignores the loss of the equipment in the processing, which affects the scheduling ability of the equipment; in this context, a flexible integrated scheduling algorithm considering periodic maintenance (FIS-PM) is proposed. The algorithm flexibly mobilizes the processing sequence of the selected processing equipment, and uniformly maintains all equipment at a certain time. First, the ISA-PM algorithm adopts the strategy combination of the layer priority, the short-time, and the equipment priority strategy to schedule the operations. Then, based on the forest firefighting model, the maintenance start point and duration of the equipment are determined by the relationship between the number of the processed operations and the number of the unprocessed operations and the loss of equipment during the maintenance. Finally, the dynamic adjustment strategy is adopted, which not only realizes the maintenance of the equipment, but also reduces the makespan of the products. The experimental results show that the proposed ISA-PM algorithm realizes the optimization effect of reducing the makespan of complex products, completing the maintenance, and improving the overall utilization rate of equipment systems.

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Flexible Integrated Scheduling Considering Periodic Maintenance

Ding,

Xie,

Zhou

et al. 2024

Electronics

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The New Way to Solve Physical Problems Described by ODE of the Second Order with the Special Structure

Ibrahimov

Imanova²

2023

Wseas Transactions on Systems

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In the last decade, many researchers have studied extensively theoretical and practical problems of natural sciences using ODEs as a means to analyze and understand them. Specifically, second-order ODEs with special complex structures provide the necessary tools to construct mathematical models for several physical - and other- processes such as the Schturm-Liouville, Schrölinger, Population, etc. As a result, it is of great importance to construct special stable methods of a higher order as a means to solve differential equations. One of the most important efficiency methods for solving these problems is the Stёrmer-Verlet method which consists of hybrid methods with constant coefficients. In this paper, we expand on recent studies that prove that the hybrid methods are more precise than the Stёrmer-Verlet method while investigating the convergence variable. This paper aims to prove the existence of a new, stable hybrid method using a special structure of degree(p)=3k+2, where k is the order of the multistep methods. Lastly, we also provide a detailed mathematical explanation of how to construct stable methods on the intersection of multistep and hybrid methods having a degree(p)≤3k+3.

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Application of the Bilateral Hybrid Methods to Solving Initial -Value Problems for the Volterra Integro-Differential Equations

Ibrahimov,

Mehdiyeva,

Imanova

et al. 2023

Wseas Transactions on Mathematics

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The many problems of natural sciences are reduced to solving integro-differential equations with variable boundaries. It is known that Vito Volterra, for the study of the memory of Earth, has constructed the integro-differential equations. As is known, there is a class of analytical and numerical methods for solving the Volterra integro-differential equation. Among them, the numerical methods are the most popular. For solving this equation Volterra himself used the quadrature methods. How known in solving the initial-value problem for the Volterra integro-differential equations, increases the volume of calculations, when moving from one point to another, which is the main disadvantage of the quadrature methods. Here the method is exempt from the specified shortcomings and has found the maximum value for the order of accuracy and also the necessary conditions imposed on the coefficients of the constructed methods. The results received here are the development of Dahlquist’s results. Using Dahlquist’s theory in solving initial-value problem for the Volterra integro-differential equation engaged the known scientists as P.Linz, J.R.Sobka, A.Feldstein, A.A.Makroglou, V.R.Ibrahimov, M.N.Imanova, O.S.Budnikova, M.V.Bulatova, I.G.Buova and ets. The scientists taking into account the direct connection between the initial value problem for both ODEs and the Volterra integrodifferential equations, the scientists tried to modify methods, that are used in solving ODEs and applied them to solve Integro-differential equations. Here, proved that some modifications of the methods, which are usually applied to solve initial-value problems for ODEs, can be adapted for solving the Volterra integro-differential equations. Here, for this aim, it is suggested to use a multistep method with the new properties. In this case, a question arises, how one can determine the validity of calculated values. For this purpose, it is proposed here to use bilateral methods. As is known for the calculation of the validity values of the solution of investigated problems, usually have used the predictor-corrector method or to use some bounders for the step-size. And to define the value of the boundaries, one can use the stability region using numerical methods. As was noted above, for this aim proposed to use bilateral methods. For the illustration advantage of bilateral methods is the use of very simple methods, which are called Euler’s explicit and implicit methods. In the construction of the bilateral methods it often becomes necessary to define the sign for some coefficients. By taking this into account, here have defined the sign for some coefficients.

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A Flexible Integrated Scheduling Algorithm for Dynamic Determination Processing Equipment Considering the Root-Subtree Vertical and Horizontal Pre-Scheduling

Cited by 3 publications

References 19 publications

Flexible Integrated Scheduling Considering Periodic Maintenance

Flexible Integrated Scheduling Considering Periodic Maintenance

The New Way to Solve Physical Problems Described by ODE of the Second Order with the Special Structure

Application of the Bilateral Hybrid Methods to Solving Initial -Value Problems for the Volterra Integro-Differential Equations

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