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Hamming distance of a two bit strings u and v of length n is defined to be the number of positions of u and v with different digit. If G is a simple graph on n vertices and m edges and B is an edge–vertex incidence matrix of G, then every edge e of G can be labeled using a binary digit string of length n from the row of B which corresponds to the edge e. We discuss Hamming distance of two different edges of the graph G. Then, we present formulae for the sum of all Hamming distances between two different edges of G, particularly when G is a path, a cycle, and a wheel, and some composite graphs.

This paper presents an alternative approach to evaluating the overall efficiency and performance of Taiwanese container ports. Specifically, a parallel activity with series structure concept in the form of data envelopment analysis (MNDEA) is used to construct a model that applies to three different activities: harbor management, stevedoring and warehousing operations. We will further divide each activity into two process types, production processes and services processes. We will also adopt a Delphi survey approach and use the Analytic Network Process (ANP) to identify these processes’influence dependence and their degree of importance for the MNDEA model setting. An empirical application demonstrates the performance of Taiwanese container ports by using MNDEA with window analysis techniques via the directional distance functionThe results demonstrate that the application is effective in indicating and/or suggesting resource-adjustments, while considering which undesirable output levels and shared inputs were involved. The results also present directions for possible improvements in workplace efficiency.

Disaster management and humanitarian logistics (HT) play crucial roles in large-scale events such as earthquakes, floods, hurricanes and tsunamis. Well-organized disaster response is crucial for effectively managing medical centres, staff allocation and casualty distribution during emergencies. To address this issue, this study aims to introduce a multi-objective stochastic programming model to enhance disaster preparedness and response, focusing on the critical first 72 h after earthquakes. The purpose is to optimize the allocation of resources, temporary medical centres and medical staff to save lives effectively.

This study uses stochastic programming-based dynamic modelling and a discrete-time Markov Chain to address uncertainty. The model considers potential road and hospital damage and distance limits and introduces an a-reliability level for untreated casualties. It divides the initial 72 h into four periods to capture earthquake dynamics.

Using a real case study in Istanbul’s Kartal district, the model’s effectiveness is demonstrated for earthquake scenarios. Key insights include optimal medical centre locations, required capacities, necessary medical staff and casualty allocation strategies, all vital for efficient disaster response within the critical first 72 h.

This study innovates by integrating stochastic programming and dynamic modelling to tackle post-disaster medical response. The use of a Markov Chain for uncertain health conditions and focus on the immediate aftermath of earthquakes offer practical value. By optimizing resource allocation amid uncertainties, the study contributes significantly to disaster management and HT research.

The purpose of this study is to develop an optimization method for charging plans with the implementation of time-of-day (TOD) electricity tariff, to reduce electricity bill.

Two optimization models for charging plans respectively with fixed and stochastic trip travel times are developed, to minimize the electricity costs of daily operation of an electric bus. The charging time is taken as the optimization variable. The TOD electricity tariff is considered, and the energy consumption model is developed based on real operation data. An optimal charging plan provides charging times at bus idle times in operation hours during the whole day (charging time is 0 if the bus is not get charged at idle time) which ensure the regular operation of every trip served by this bus.

The electricity costs of the bus route can be reduced by applying the optimal charging plans.

This paper produces a viable option for transit agencies to reduce their operation costs.

Our result of this paper aims to indicate that the beta pricing formula could be applied in a long-term model setting as well.

In this paper, we show that the capital asset pricing model can be derived from a three-period general equilibrium model.

We show that our extended model yields a Pareto efficient outcome.

The capital asset pricing model (CAPM) model can be used for pricing long-lived assets.

Long-term modelling and sustainability can be modelled in our setting.

Our results were only known for two periods. The extension to 3 periods opens up a large scope of applicational possibilities in asset pricing, behavioural analysis and long-term efficiency.

This paper analyses how firm births and deaths are influenced by previous firm births and deaths in related and unrelated sectors. Competition and multiplier effects are used as the theoretical lens for this analysis.

This paper uses 2008–2016 Irish business demography data pertaining to 568 NACE 4-digit sectors within 20 NACE 1-digit industries across 34 Irish county and sub-county regions within 8 NUTS3 regions. A three-stage least squares (3SLS) estimation is used to analyse the impact of past firm deaths (births) on future firm births (deaths). The effect of relatedness on firm interrelationships is explicitly modelled and captured.

Findings indicate that the multiplier effect operates mostly through related sectors, while the competition effect operates mostly through unrelated sectors.

This paper's findings show that firm interrelationships are significantly influenced by the degree of relatedness between firms. The raw data used to calculate firm birth and death rates in this analysis are count data. Each new firm is measured the same as another regardless of differing features like size. Some research has shown that smaller firms have a greater propensity to create entrepreneurs (Parker, 2009). Thus, it is possible that the death of differently sized firms may contribute differently to multiplier effects where births induce further births. Future research could seek to examine this.

These findings have implications for policy initiatives concerned with increasing entrepreneurship. Some express concerns that public investment into entrepreneurship can lead to “crowding out” effects (Cumming and Johan, 2019), meaning that public investment into entrepreneurship could displace or reduce private investment into entrepreneurship (Audretsch and Fiedler, 2023; Zikou et al., 2017). This study’s findings indicate that using public investment to increase firm births could increase future firm births in related and unrelated sectors. However, more negative “crowding out” effects may also occur in unrelated sectors, meaning that public investment which stimulates firm births in a certain sector could induce firm deaths and crowd out entrepreneurship in unrelated sectors.

This paper is the first in the literature to explicitly account for the role of relatedness in firm interrelationships.

This research explores the spillovers and portfolio implications for green bonds and environmental, social and governance (ESG) assets in the context of the rapidly expanding trend in green finance investments and the need for a green recovery in the post-COVID-19 era.

This study utilizes Diebold and Yilmaz’s (2014) spillover method and portfolio strategies (hedge ratio, optimal weights and hedging effectiveness) for the data starting from February 29, 2012, to March 14, 2022.

The study’s findings reveal that the lower volatility spillover is evidenced between the green bonds and ESG stocks during tranquil and turbulent periods (e.g. COVID-19 and Russia-Ukraine War). Furthermore, hedging costs are lower both in normal times and during economic slumps. Investing the bulk of the funds in green bonds makes it possible to achieve maximum hedging effectiveness between the S&P green bond (GB) and the S&P 500 ESG.

Both investors and policymakers may use these findings to make wise investment and policy choices to achieve post-COVID environmental sustainability.

Unlike previous research, this is the first to explore the interconnectedness among the major global and country-specific green bonds and ESG assets. The major findings of this study about the lower volatility spillovers and hedging costs between green bonds and ESG assets during the tranquil and turbulent periods may contribute to the post-COVID investment portfolio for environmental sustainability.

The purpose of this article is to propose a detailed methodology to estimate, model and incorporate the non-constant volatility onto a numerical tree scheme, to evaluate a real option, using a quadrinomial multiplicative recombination.

This article uses the multiplicative quadrinomial tree numerical method with non-constant volatility, based on stochastic differential equations of the GARCH-diffusion type to value real options when the volatility is stochastic.

Findings showed that in the proposed method with volatility tends to zero, the multiplicative binomial traditional method is a particular case, and results are comparable between these methodologies, as well as to the exact solution offered by the Black–Scholes model.

The originality of this paper lies in try to model the implicit (conditional) market volatility to assess, based on that, a real option using a quadrinomial tree, including into this valuation the stochastic volatility of the underlying asset. The main contribution is the formal derivation of a risk-neutral valuation as well as the market risk premium associated with volatility, verifying this condition via numerical test on simulated and real data, showing that our proposal is consistent with Black and Scholes formula and multiplicative binomial trees method.