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The interruption event will seriously affect the normal operation of urban rail transit lines,causing a large number of passengers to be stranded in the station and even making the train stranded in the interval between stations. This study aims to reduce the impact of interrupt events and improve service levels.

To address this issue, this paper considers the constraints of train operation safety, capacity and dynamic passenger flow demand. It proposes a method for adjusting small loops during interruption events and constructs a train operation adjustment model with the objective of minimizing the total passenger waiting time. This model enables the rapid development of train operation plans in interruption scenarios, coordinating train scheduling and line resources to minimize passenger travel time and mitigate the impact of interruptions. Regarding the proposed train operation adjustment model, an improved genetic algorithm (GA) is designed to solve it.

The model and algorithm are applied to a case study of interruption events on Beijing Subway Line 5. The results indicate that after solving the constructed model, the train departure intervals can be maintained between 1.5 min and 3 min. This ensures both the safety of train operations on the line and a good match with passengers’ travel demands, effectively reducing the total passenger waiting time and improving the service level of the urban rail transit system during interruptions. Compared to the GA algorithm, the algorithm proposed in this paper demonstrates faster convergence speed and better computational results.

This study explicitly outlines the adjustment method of using short-turn operation during operational interruptions, with train departure times and station stop times as decision variables. It takes into full consideration safety constraints on train operations, train capacity constraints and dynamic passenger demand. It has constructed a train schedule optimization model with the goal of minimizing the total waiting time for all passengers in the system.

With the use of the grey incidence analysis (GIA), indicators such as the absolute degree of grey incidence (ε_ij), relative degree of grey incidence (r_ij) or synthetic degree of grey incidence (ρ_ij) are calculated. However, it seems that some assumptions made to calculate them are arguable, which may also have a material impact on the reliability of test results. In this paper, the authors analyse one of the indicators of the GIA, namely the relative degree of grey incidence. The aim of the article was to verify the hypothesis: in determining the relative degree of grey incidence, the method of standardisation of elements in a series significantly affects the test results.

To achieve the purpose of the article, the authors used the numerical simulation method and the logical analysis method (in order to draw conclusions from our tests).

It turned out that the applied method of standardising elements in series when calculating the relative degree of grey incidence significantly affects the test results. Moreover, the manner of standardisation used in the original method (which involves dividing all elements by the first element) is not the best. Much more reliable results are obtained by a standardisation that involves dividing all elements by their arithmetic mean.

Limitations of the conducted evaluation involve in particular the limited scope of inference. This is since the obtained results referred to only one of the indicators classified into the GIA.

In this article, the authors have evaluated the model of GIA in which the relative degree of grey incidence is determined. As a result of the research, the authors have proposed a recommendation regarding a change in the method of standardising variables, which will contribute to obtaining more reliable results in relational tests using the grey system theory.

In this paper, the author introduces a degenerate exponential integral function and further studies some of its analytical properties. The new function is a generalization of the classical exponential integral function and the properties established are analogous to those satisfied by the classical function.

The methods adopted in establishing the results are theoretical in nature.

A degenerate exponential integral function which is a generalization of the classical exponential integral function has been introduced and its properties investigated. Upon taking some limits, the established results reduce to results involving the classical exponential integral function.

The results obtained in this paper are new and have the potential of inspiring further research on the subject.

The authors explore the hypothesis that some movements in commodity prices are anticipated (news shocks) and can trigger aggregate fluctuations in small open emerging economies. This paper aims to discuss the aforementioned objective.

The authors build a multi-sector dynamic stochastic general equilibrium model with endogenous commodity production. There are five exogenous processes: a country-specific interest rate shock that responds to commodity price fluctuations, a productivity (TFP) shock for each sector and a commodity price shock. Both TFP and commodity price shocks are composed of unanticipated and anticipated components.

The authors show that news shocks to commodity prices lead to higher output, investment and consumption, and a countercyclical movement in the trade-balance-to-output ratio. The authors also show that commodity price news shocks explain about 24% of output aggregate fluctuations in the small open economy.

Given the importance of both anticipated and unanticipated commodity price shocks, policymakers should pay attention to developments in commodity markets when designing policies to attenuate the business cycles. Future research should investigate the design of optimal fiscal and monetary policies in SOE subject to news shocks in commodity prices.

This paper contributes to the knowledge of the sources of fluctuations in emerging economies highlighting the importance of a new source: news shocks in commodity prices.

This study aims to focus on the optimal green R&D of a capital-constrained supply chain under different channel power structures as well as the impact of capital constraint, financing cost, channel power structure and cost-reducing efficiency on green R&D and supply chain profitability.

A two-echelon supply chain is considered. The upstream firm engages in green R&D but has capital constraints that can be overcome by external financing. Green R&D is beneficial to reduce production costs and increase consumer demand. Based on whether or not the upstream firm is capital constrained and dominates the supply chain, four models are developed.

Capital constraints significantly lower green R&D and supply chain profitability. Transferring leadership from the upstream to the downstream firms leads to higher green R&D levels and downstream firm profitability, whereas the upstream firm's profitability is increased (decreased) if green R&D investment efficiency is high (low) enough. Greater financing costs reduce green R&D and downstream firm profitability; however, the upstream firm's profitability under the model in which it functions as the follower increases if the initial capital is sufficient. More importantly, empirical analysis based on practice data is used to verify the theoretical results reported above.

This study reveals how upstream firms in supply chains decide green R&D decisions in situations with capital constraints, providing managers and governments with an understanding of the impact of capital constraint, channel power structure, financing cost and cost-reducing efficiency on supply chain green R&D and profitability.

The major contributions are the exploration of supply chain green R&D by taking into consideration channel power structures and cost-reducing efficiency and the validation of theoretical results using practice data.

The principal aim of this paper is to review three basic theoretical growth models, namely the Harrod-Domar model, the Solow model and the Ramsey model, and examine their implications for economic policies.

The paper utilizes a positivist research framework that emphasizes the causal relationships between the variables in each of the three models. Mathematical methods are employed to formulate and examine the three models under study. Since the paper is theoretical, it does not use any empirical data although numerical illustrations are provided whenever they are appropriate.

The Harrod-Domar model explains why countries with high rates of saving may also enjoy high rate of economic growth. Both the Solow and Ramsey models can be used to explain the medium-income trap. The paper examines the impact of Covid shocks on the macroeconomy. While the growth rate can be recovered, it may not always possible to recover the output level.

For the Harrod-Domar model, the public spending decreases the private consumption at the period 1, but there is no change in the capital stock and hence the production in subsequent periods. For the Ramsey model with AK production function, both the private consumption and the outputs will be lowered. In both the Harrod-Domar and Ramsey models with Cobb-Douglas production function, if the debt is not high and the interest rate is sufficiently low, it is better to use public debt for production rather than for consumption. If the country borrows to recover the Total Factor Productivity after the Covid pandemic, both the Harrod-Domar and Ramsey models with Cobb-Douglas production function show that the rate of growth is higher for the year just after the pandemic but is the same as before the pandemic.

The economy can recover the growth rate after a Covid shock, but the recovery process will generally take many periods.

This paper focuses on economic implications and does not aim to examine social implications of policy changes or Covid-type shock.

The paper provides a comparison of three basic growth models with respect to public spending, public debts and repayments and Covid-type shocks.

This paper attempts to develop a simple, static model of tax administration that is capable of explaining the widespread collusive petty tax administration corruption observed in developing countries.

This paper utilizes a positivist research framework and adopts a theoretical method of analysis, although secondary data will also be mentioned to support theoretical arguments whenever it is appropriate to do so.

A high rate of collusive tax corruption is inevitable in developing countries.

The model is static and needs to be extended into a dynamic model.

Traditional enforcement tools such as higher audits or a higher penalty regime against tax evasion do not work. Tax simplification can lessen the incidence of tax corruption.

Fighting tax corruption requires significant changes in the attitudes of taxpayers and tax auditors.

This paper combines the literature on Kantian economics and tax compliance in an innovative fashion.

This paper is a dedication to Professor Ngo Van Long who introduced the idea of Kant–Nash equilibrium. The author extends this analysis to the study of adult and child labor markets.

This is a game theoretic analysis of the market for adult and child workers when some firms behave in the neoclassical Nashian way and some firms follow a Kantian social norm.

The presence of Kantian firms in the output market in addition to Nashian lowers industry output and labor demand. This raises the possibility that Kantian behavior in the output market could lower wages sufficiently and increase the incidence of child labor. If firms engage in Kantian behavior in the labor market by not hiring child workers, adult wage rises but could lower child wage as children if they work can only work for Nashian firms. When labor demand is sufficiently high, more Kantians could raise adult wage above subsistence and eliminate child labor supply.

This is the first paper to apply Kant–Nash equilibrium to the labor market. The result that Kantian behavior could have an unintended negative spillover effect in other markets is new. The paper keeps alive the ideas of Professor Long, which hopefully will stimulate further work and build on his ideas.

This study aims to improve the passenger accessibility of passenger demands in the end-of-operation period.

A mixed integer nonlinear programming model for last train timetable optimization of the metro was proposed considering the constraints such as the maximum headway, the minimum headway and the latest end-of-operation time. The objective of the model is to maximize the number of reachable passengers in the end-of-operation period. A solution method based on a preset train service is proposed, which significantly reduces the variables of deciding train services in the original model and reformulates it into a mixed integer linear programming model.

The results of the case study of Wuhan Metro show that the solution method can obtain high-quality solutions in a shorter time; and the shorter the time interval of passenger flow data, the more obvious the advantage of solution speed; after optimization, the number of passengers reaching the destination among the passengers who need to take the last train during the end-of-operation period can be increased by 10%.

Existing research results only consider the passengers who take the last train. Compared with previous research, considering the overall passenger demand during the end-of-operation period can make more passengers arrive at their destination. Appropriately delaying the end-of-operation time can increase the proportion of passengers who can reach the destination in the metro network, but due to the decrease in passenger demand, postponing the end-of-operation time has a bottleneck in increasing the proportion of passengers who can reach the destination.

The objective of this work is to demonstrate the relationships between the two main processes of research and development (R&D) activities: the knowledge generation phase (KPP) and the knowledge commercialization, or transfer, phase (KCP), in a sector that is intensive in this type of activity, such as the pharmaceutical sector. In addition, within the framework of the general objective of this work, the authors propose two other objectives: (1) make advances in network efficiency measurement models, and (2) determine the factors associated with efficiency in the KPP and in the KCP in companies of the pharmaceutical sector in Spain.

A Network Data Envelopment Analysis (NDEA) model (Färe and Grosskopf, 2000) with categorical variables (Lee et al., 2020; Yeh and Chang, 2020) has been applied, and a sensitivity analysis of the obtained results has been performed through a DEA model of categorical variables, in accordance with the work of Banker and Morey (1986), to corroborate the results of the proposed model. The sample is made up of 77 companies in the pharmaceutical sector in Spain.

The results obtained point to a greater efficiency of pharmaceutical companies in the KPP, rather than in the KCP. Furthermore, the study finds that 1) alliances between companies have been the accelerating factors of efficiency in the KCP (but patents have slowed this down the most); 2) the quality of R&D and the number of R&D personnel are the factors that most affect efficiency in the KPP; and 3) the quality of R&D again, the benefits obtained and the position in the market are the factors that most affect efficiency in the KCP.

The authors have not found studies that show whether the efficiency obtained by R&D-intensive companies in the KPP phase is related to better results in terms of efficiency in the KCP phase. No papers have been found that analyse the role of alliances between R&D-intensive companies and patents, as agents that facilitate efficiency in the KCP phase, covering the gap in the research on both problems. Notwithstanding, this work opens up a research path which is related to the improvement of network efficiency models (since it includes categorical variables) and the assessment of the opinions of those who are responsible for R&D departments; it can be applied to decision-making on the aspects to improve efficiency in R&D-intensive companies.