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Introduction Operations research, i.e. the application of scientific methodology to operational problems in the search for improved understanding and control, can be said to have started with the application of mathematical tools to military problems of supply bombing and strategy, during the Second World War. Post‐war these tools were applied to business problems, particularly production scheduling, inventory control and physical distribution because of the acute shortages of goods and the numerical aspects of these problems.

The purpose of this paper is to survey and express the advantages and disadvantages of the existing approaches for solving grey linear programming in decision-making problems.

After presenting the concepts of grey systems and grey numbers, this paper surveys existing approaches for solving grey linear programming problems and applications. Also, methods and approaches for solving grey linear programming are classified, and its advantages and disadvantages are expressed.

The progress of grey programming has been expressed from past to present. The main methods for solving the grey linear programming problem can be categorized as Best-Worst model, Confidence degree, Whitening parameters, Prediction model, Positioned solution, Genetic algorithm, Covered solution, Multi-objective, Simplex and dual theory methods. This survey investigates the developments of various solving grey programming methods and its applications.

Different methods for solving grey linear programming problems are presented, where each of them has disadvantages and advantages in providing results of grey linear programming problems. This study attempted to review papers published during 35 years (1985–2020) about grey linear programming solving and applications. The review also helps clarify the important advantages, disadvantages and distinctions between different approaches and algorithms such as weakness of solving linear programming with grey numbers in constraints, inappropriate results with the lower bound is greater than upper bound, out of feasible region solutions and so on.

Gives introductory remarks about chapter 1 of this group of 31 papers, from ISEF 1999 Proceedings, in the methodologies for field analysis, in the electromagnetic community. Observes that computer package implementation theory contributes to clarification. Discusses the areas covered by some of the papers ‐ such as artificial intelligence using fuzzy logic. Includes applications such as permanent magnets and looks at eddy current problems. States the finite element method is currently the most popular method used for field computation. Closes by pointing out the amalgam of topics.

This study aims to provide a solution of the power flow calculation for the low-voltage ditrect current power grid. The direct current (DC) power grid is becoming a reliable and economic alternative to millions of residential loads. The power flow (PF) in the DC network has some similarities with the alternative current case, but there are important differences that deserve to be further concerned. Moreover, the dispatchable distributed generators (DGs) in DC network can realize the flexible voltage control based on droop-control or virtual impedance-based methods. Thus, DC PF problems are still required to further study, such as hosting all load types and different DGs.

The DC power analysis was explored in this paper, and an improved Newton–Raphson based linear PF method has been proposed. Considering that constant impedance (CR), constant current (CI) and constant power (CP) (ZIP) loads can get close to the practical load level, ZIP load has been merged into the linear PF method. Moreover, DGs are much common and can be easily connected to the DC grid, so V nodes and the dispatchable DG units with droop control have been further taken into account in the proposed method.

The performance and advantages of the proposed method are investigated based on the results of the various test systems. The two existing linear models were used to compare with the proposed linear method. The numerical results demonstrate enough accuracy, strong robustness and high computational efficiency of the proposed linear method even in the heavily-loaded conditions and with 10 times the line resistances.

The conductance corresponding to each constant resistance load and the equivalent conductance for the dispatchable unit can be directly merged into the self-conductance (diagonal component) of the conductance matrix. The constant current loads and the injection powers from dispatchable DG units can be treated as the current sources in the proposed method. All of those make the PF model much clear and simple. It is capable of offering enough accuracy level, and it is suitable for applications in DC networks that require a large number of repeated PF calculations to optimize the energy flows under different scenarios.

The use of linear regression analysis is common in the social sciences. The purpose of this paper is to show the advantage of a qualitative research method, namely, structured qualitative analysis (SQA), over the linear regression method by using different characteristics of data.

Data were gathered from a study of online consumer behavior in Taiwan. The authors changed the content of the data to have different sets of data. These data sets were used to demonstrate how SQA and linear regression works individually, and to contrast the empirical analyses and empirical results from linear regression and SQA.

The linear regression method uses one equation to model different characteristics of data. When facing a data set containing a big and a small size of different characteristics, linear regression tends to provide an equation by modeling the characteristics of the big size data and subsuming those of the small size. When facing a data set containing similar sizes of data with different characteristics, linear regression tends to provide an equation by averaging these data. The major concern is that the one equation may not be able to reflect the data of various characteristics (different values of independent variables) that result in the same outcome (the same value of dependent variable). In contrast, SQA can identify various variable combinations (multiple relationships) leading to the same outcome. SQA provided multiple relationships to represent different sizes of data with different characteristics so it created consistent empirical results.

Two research methods work differently. The popular linear regression tends to use one equation to model different sizes and characteristics of data. The single equation may not be able to cover different behaviors but may lead to the same outcome. Instead, SQA provides multiple relationships for different sizes of data with different characteristics. The analyses are more consistent and the results are more appropriate. The academics may re-think the existing literature using linear regression. It would be interesting to see if there are new findings for similar problems by using SQA. The practitioners have a new method to model real world problems and to understand different possible combinations of variables leading to the same outcome. Even the relationship obtained from a small data set may be very valuable to practitioners.

This paper compared online consumer behavior by using two research methods to analyze different data sets. The paper offered the manipulation of real data sets to create different data sizes of different characteristics. The variations in empirical results from both methods due to the various data sets facilitate the comparison of both methods. Hence, this paper can serve as a complement to the existing literature, focusing on the justification of research methods and on limitations of linear regression.

To propose novel predictor‐corrector time‐integration algorithms for pseudo‐dynamic testing.

The novel predictor‐corrector time‐integration algorithms are based on both the implicit and the explicit version of the generalized‐α method. In the non‐linear unforced case second‐order accuracy, stability in energy, energy decay in the high‐frequency range as well as asymptotic annihilation are distinctive properties of the generalized‐α scheme; while in the non‐linear forced case they are the limited error near the resonance in terms of frequency location and intensity of the resonant peak. The implicit generalized‐α algorithm has been implemented in a predictor‐one corrector form giving rise to the implicit IPC‐ρ_∞ method, able to avoid iterative corrections which are expensive from an experimental standpoint and load oscillations of numerical origin. Moreover, the scheme embodies a secant stiffness formula able to approximate closely the actual stiffness of a structure. Also an explicit algorithm has been implemented, the EPC‐ρ_b method, endowed with user‐controlled dissipation properties. The resulting schemes have been tested experimentally both on a two‐ and on a six‐degrees‐of‐freedom system, exploiting substructuring techniques.

The analytical findings and the tests have indicated that the proposed numerical strategies enhance the performance of the pseudo‐dynamic test (PDT) method even in an environment characterized by considerable experimental errors. Moreover, the schemes have been tested numerically on strongly non‐linear multiple‐degrees‐of‐freedom systems reproduced with the Bouc‐Wen hysteretic model, showing that the proposed algorithms reap the benefits of the parent generalized‐α methods.

Further developments envisaged for this study are the application of the IPC‐ρ_∞ method and of EPC‐ρ_b scheme to partitioned procedures for high‐speed pseudo‐dynamic testing with substructuring.

The implicit IPC‐ρ_∞ and the explicit EPC‐ρ_b methods allow a user to have defined dissipation which reduces the effects of experimental error in the PDT without needing onerous iterations.

The paper proposes novel time‐integration algorithms for pseudo‐dynamic testing. Thanks to a predictor‐corrector form of the generalized‐α method, the proposed schemes maintain a high computational efficiency and accuracy.

To realize the operation optimizing of today’s distribution power system (DPS), like economic dispatch, contingency analysis, and reliability and security assessment etc., it is beneficial and indispensable that a faster linear load flow method is adopted with a reasonable accuracy. Considering the high R/X branch ratios and unbalanced features of DPS, the purpose of this paper is to propose a faster and non-iterative linear load flow solution for DPS.

Based on complex function theory, the derivations of the injection current linear approximation have been proposed for the balanced and the single-, double- and three-phase unbalanced loads of DPS on complex plane. Then, a simple and direct linear load flow has been developed with loop-analysis theory and node-branch incidence matrix.

The methodology is appropriate for balanced and single-, double- and three-phase hybrid distribution system with different load models. It provides a fast and robust load flow method with a satisfactory accuracy to handle the problems of DPS whenever the load flow solutions are required.

The distributed generators (DGs) with unity or fixed power factors can be easily included. But the power and voltage nodes cannot be dealt with directly and need to be further studied.

By combining the current linear approximation with the loop theory-based method, a new linear load flow method for DPS has been proposed. The method is valid and acute enough for balanced and unbalanced systems and has no convergent problems.

The use of three non‐linear mathematical programming techniques for the optimization of structural design problems is discussed. The methods — sequential linear programming, the feasible direction method and the sequential unconstrained minimization technique — are applied to a portal frame problem to enable a study of their convergence efficiency to be studied. These methods are used for both the sizing of the structural members and determining the optimum roof pitch. The sequential linear programming method is shown to be particularly efficient for application to structural design problems. Some comments on the development of computer software for structural optimization are also given.

The different types of estimators of rational expectations models are surveyed. A key feature is that the model′s solution has to be taken into account when it is estimated. The two ways of doing this, the substitution and errors‐in‐variables methods, give rise to different estimators. In the former case, a generalised least‐squares or maximum‐likelihood type estimator generally gives consistent and efficient estimates. In the latter case, a generalised instrumental variable (GIV) type estimator is needed. Because the substitution method involves more complicated restrictions and because it resolves the solution indeterminacy in a more arbitary fashion, when there are forward‐looking expectations, the errors‐in‐variables solution with the GIV estimator is the recommended combination.