A Two-Workshop Collaborative, Integrated Scheduling Algorithm considering the Prescheduling of the Root-Subtree Processes

Xie, Zhiqiang; Teng, Haikun; Ming, Jingwei; Yue, Xiao‐Guang

doi:10.1155/2022/9065638

Cited by 4 publications

(6 citation statements)

References 16 publications

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“…To solve these problems, have used the hybrid method (22), which has degree p = 4. Obviously, utilizing these techniques requires using some methods as a predictor.…”

Section: Numerical Resultsmentioning

confidence: 99%

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On Some Advantages of the Predictor-Corrector Methods

Ibrahimov,

Yue,

Juraev

2023

IETI Trans. Data Anal. Forecast.

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Usually, all numerical methods are divided into two sets known as explicit and implicit methods. Explicit methods (EM) are used to find a solution to a problem directly, without requiring initial preparation. But when using the implicit method (IM), other methods can sometimes be employed. Implicit methods are known to be more accurate than explicit ones. Therefore, the question arises about finding the golden mean. To accomplish this, we utilize certain properties of the predictor and corrector methods. We take into account that in forecasting methods, we use EM. However, I will show here that in some cases, IMs can be used as correction methods. It is clear that the results obtained here are fully consistent with the theoretical ones. To address the aforementioned issues, we employ the initial value problem (IVP) for a first-order ordinary differential equation (ODE). Conventional methods compare various nanomaterials (NMs) using multi-step, extended, and hybrid approaches.

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“…To solve these problems, have used the hybrid method (22), which has degree p = 4. Obviously, utilizing these techniques requires using some methods as a predictor.…”

Section: Numerical Resultsmentioning

confidence: 99%

“…When comparing identities (11)(12)(13)(14), the HMs type is considered the best among MSMs. Some of the weaknesses of these methods can be found in [18][19][20][21][22][23][24][25][26][27][28][29][30][31]. Note that point [ J l 2 for the method ( 14) is a hybrid point.…”

Section: Construction Pcms By Using the Known Simple Methodsmentioning

confidence: 99%

On Some Advantages of the Predictor-Corrector Methods

Ibrahimov,

Yue,

Juraev

2023

IETI Trans. Data Anal. Forecast.

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“…In integrated scheduling, Ref. [28] first defined the machine with the longest scheduling time to process the operations as the key machine. However, in this paper, such machine is defined as the more-time machine.…”

Section: Definition 1 ([33]mentioning

confidence: 99%

“…Nowadays, integrated scheduling is widely used in many fields (see Refs. [19][20][21][22][23][24][25][26][27][28][29][30][31][32][33][34]). For example, for the flexible integrated scheduling problem, Yang D. et al [19] proposed an improved artificial bee colony algorithm considering MSE with two new strategies.…”

Section: Introductionmentioning

confidence: 99%

“…Based on the time-selected scheduling idea, Zhang X. et al [27] proposed an algorithm to consider the precision of serial operations. Zhou W. et al [28] proposed an algorithm that considers the hierarchical scheduling order for the integrated scheduling problem with a large number of operations in the same layer. For the scheduling solution approaches, Papatya S. et al [29] proposed a new formulation for this problem and compared it with a recent formulation.…”

Section: Introductionmentioning

confidence: 99%

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A Heuristic Integrated Scheduling Algorithm via Processing Characteristics of Various Machines

Zhou

Zheng

et al. 2022

Symmetry

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Complex products with a tree-like structure usually have an asymmetric structure. Therefore, in order to avoid the separation of equipment and operation correlation during the scheduling, the structural attributes of products and the use of equipment resources should be fully considered. However, this feature is ignored in the current research works on the scheduling of multi-variety and small batch products. This leads to increased idle time for equipment and an extended makespan for products. To avoid this situation, a heuristic integrated scheduling algorithm via processing characteristics of various machines (HIS-PCVM) is proposed. In the integrated scheduling, the algorithm first divides the equipment into two categories: the special equipment and the general equipment according to the resources of the production scheduling system. Then, different scheduling methods are designed according to the equipment categories. The makespan of the product is further optimized through various combination methods. Moreover, the constraint audit strategy to guarantee the constraint relationship between the operations is optimized. The earliest scheduling time strategy is proposed to improve the parallelism and serial tightness of the operations. These strategies reduce the idle time of equipment effectively. Experimental results show that the proposed algorithm has a better application effect in reducing the makespan of complex products, both with asymmetric structures and symmetric structures. This also shows that the algorithm is effective in improving the utilization rate of equipment.

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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 Two-Workshop Collaborative, Integrated Scheduling Algorithm considering the Prescheduling of the Root-Subtree Processes

Cited by 4 publications

References 16 publications

On Some Advantages of the Predictor-Corrector Methods

On Some Advantages of the Predictor-Corrector Methods

A Heuristic Integrated Scheduling Algorithm via Processing Characteristics of Various Machines

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

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