Applied Mathematics

Lapidus, Leon

doi:10.1021/ie50720a007

Cited by 5 publications

(4 citation statements)

References 58 publications

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“…Thus, a "vicious cycle" occurs that can destabilize the project and lead it to collapse [3]. Of course, such a development can be prevented by increasing workforce, but such an increase faces a number of constraints, such as lack of space [18,19]. Other negative consequences of changes are related to violation of stakeholders' own plans, which leads to inefficient resource allocation, conflicts [12], and other problems.…”

Section: Methodsmentioning

confidence: 99%

Dynamic scheduling in construction projects

Undozerov

2023

E3S Web Conf.

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The aim of the study is to investigate the theoretical foundations of dynamic scheduling in construction projects and provide some recommendations for further research. While the theory of "static" scheduling is the most developed, much less attention is paid to "dynamic" scheduling. At the same time, research shows that "dynamic" scheduling is most suitable for construction industry, especially for complex and large projects. To achieve the aim of the study, such tasks as (1) the formulation of the problem associated with insufficient elaboration scheduling dynamism and complexity issues in construction; (2) a review of the scientific literature on this problem; (3) the formation of some possible directions for the development of the theory of dynamic scheduling, were solved. Research methods are: analysis, synthesis, review of scientific literature. The result of the study is recommendations on one of the directions of dynamic scheduling theoretical foundations’ development in construction projects, namely scheduling visualization techniques on the example of the "spring chart" developed by the author. The relevance of the results is due to the fact that the developed recommendations can be useful to researchers in the field of project scheduling for a systematic study of the problem.

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Section: Methodsmentioning

confidence: 99%

Dynamic scheduling in construction projects

Undozerov

2023

E3S Web Conf.

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“…The optimal solution to the problem posed above may be solved in many ways; by dynamic programming (5,14), by the maximum principle {14), by assuming the a priori solution (77), and even by an elaborate use of ordinary calculus (75). However, we shall use the Hamilton-Jacobi theory here since it is basically new to the chemical engineering literature.…”

Section: Control Problem Solutionmentioning

confidence: 99%

“…where 77z is the gradient vector of 77 with respect to z> are satisfied and that the minimum condition 77(x*, z*, t; u*) < 77(x, z, t; u) (14) hold for any u J). In addition, z must satisfy certain boundary conditions at tf.…”

Section: Control Problem Solutionmentioning

confidence: 99%

Control, Stability, and Filtering

Lapidus¹

1967

Ind. Eng. Chem.

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The functionality of I shows that the initial state, xo, the initial time, to, the final time, t,, and the control, u, all determine its numerical value. In these equations is the dot or inner product of x(t,) with itself but weighted by the matrix S at time f,; S, Q, and R are suitably selected weighting matrices with the constraints that: S and Q are symmetric positive-semidefinite (S, Q 2 0) R is symmetric positivedefinite (R > 0) (6) There are some simple physical interpretations to Equations 3-5, namely: X [x(f,)] = a weighted measure of the final state which J: (x, Qx)df = a weighted integrated measure of the overall path of the system from time t o tot, J: (u, Ru)dt = a weighted integrated measure of the overall amount of control used from time to tot, the system achieves at time t,Since we shall try to minimize I (see below) and S, Q, and R are open for selection, subject only to the constraints of Equation 6, we, in general, will try to make

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“…He treats the concept of "quantitation" quite broadly, ranging from statistical analysis to information theory. Applied mathematics, particularly as related to chemical engineering was reviewed by Lapidus (326). Coverage included a number of mathematical topics such as optimization, simulation, dynamic programming, linear algebra, statistical analysis, and the solution of differential equations.…”

mentioning

confidence: 99%