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In this paper, the authors prove that the Douglas space of second kind with a generalised form of special (α, β)-metric F, is conformally invariant.

For, the authors have used the notion of conformal transformation and Douglas space.

The authors found some results to show that the Douglas space of second kind with certain (α, β)-metrics such as Randers metric, first approximate Matsumoto metric along with some special (α, β)-metrics, is invariant under a conformal change.

The authors introduced Douglas space of second kind and established conditions under which it can be transformed to a Douglas space of second kind.

When in‐plant and college‐based courses are run for supervisors and managers, it is conventional to use a U‐shaped seating arrangement in the training room to promote participation and discussion. However, at each class session, people will tend to sit with the same companions habitually, which may be more comfortable, but less productive than if they sat with different people each time.

Inspired by a food bank distribution operation, this paper aims to study synchronized vehicle routing for equitable and effective food allocation. The primary goal is to improve operational efficiency while ensuring equitable and effective food distribution among the partner agencies.

This study introduces a multiobjective Mixed Integer Programming (MIP) model aimed at addressing the complex challenge of effectively distributing food, particularly for food banks serving vulnerable populations in low-income urban and rural areas. The optimization approach described in this paper places a significant emphasis on social and economic considerations by fairly allocating food to food bank partner agencies while minimizing routing distance and waste. To assess the performance of the approach, this paper evaluates three distinct models, focusing on key performance measures such as effectiveness, equity and efficiency. The paper conducts a comprehensive numerical analysis using randomly generated data to gain insights into the trade-offs that arise and provide valuable managerial insights for food bank managers.

The results of the analysis highlight the models that perform better in terms of equity and effectiveness. Additionally, the results show that restocking the vehicles through the concept of synchronization improves the overall quantity of food allocation to partner agencies, thereby increasing accessibility.

This paper contributes significantly to the literature on optimization approaches in the field of humanitarian logistics.

This study provides food bank managers with three different models, each with a multifaceted nature of trade-offs, to better address the complex challenges of food insecurity.

This paper contributes significantly to social responsibility by enhancing the operational efficiency of food banks, ultimately improving their ability to serve communities in need.

To the best of the authors’ knowledge, this paper is the first to propose and analyze this new variant of vehicle routing problems in nonprofit settings.

This study aims to treat a novel system of Volterra integro-differential equations with multiple delays and variable bounds, constituting a generic numerical method based on the matrix equation and a combinatoric-parametric Charlier polynomials. The proposed method utilizes these polynomials for the matrix relations at the collocation points.

Thanks to the combinatorial eligibility of the method, the functional terms can be transformed into the generic matrix relations with low dimensions, and their resulting matrix equation. The obtained solutions are tested with regard to the parametric behaviour of the polynomials with $\alpha$, taking into account the condition number of an outcome matrix of the method. Residual error estimation improves those solutions without using any external method. A calculation of the residual error bound is also fulfilled.

All computations are carried out by a special programming module. The accuracy and productivity of the method are scrutinized via numerical and graphical results. Based on the discussions, one can point out that the method is very proper to solve a system in question.

This paper introduces a generic computational numerical method containing the matrix expansions of the combinatoric Charlier polynomials, in order to treat the system of Volterra integro-differential equations with multiple delays and variable bounds. Thus, the method enables to evaluate stiff differential and integral parts of the system in question. That is, these parts generates two novel components in terms of unknown terms with both differentiated and delay arguments. A rigorous error analysis is deployed via the residual function. Four benchmark problems are solved and interpreted. Their graphical and numerical results validate accuracy and efficiency of the proposed method. In fact, a generic method is, thereby, provided into the literature.

Considering the bounded confidence of decision-makers (DMs), a new grey multi-criteria group consensus decision-making (GMCGCDM) model is established by using interval grey number (IGN), cobweb model, social network analysis (SNA) and consensus reaching process (CPR).

Firstly, the model analyzes the social relationship of DM under social networks and proposes a calculation method for DMs’ weights based on SNA. Secondly, the model defines a cobweb model to consider the preferences of decision-making alternatives in the decision-making process. The consensus degree is calculated by the area surrounded by the connections between each index value of DMs and the group. Then, the model coordinates the different opinions of various DMs to reduce the degree of bias of each DM and designs a consensus feedback mechanism based on bounded confidence to guide DMs to reach consensus.

The advantage of the proposed method is to highlight the practical application, taking the selection of low-carbon suppliers in the context of dual carbon as an example. Comparison analysis is performed to reveal the interpretability and applicability of the method.

The main contribution of this paper is to propose a new GMCGCDM model, which can not only expand the calculation method of DM’s weight and consensus degree but also reduce the time and cost of decision-making.

The discrete Fourier transform (dft) of a fractional process is studied. An exact representation of the dft is given in terms of the component data, leading to the frequency domain form of the model for a fractional process. This representation is particularly useful in analyzing the asymptotic behavior of the dft and periodogram in the nonstationary case when the memory parameter d≥12. Various asymptotic approximations are established including some new hypergeometric function representations that are of independent interest. It is shown that smoothed periodogram spectral estimates remain consistent for frequencies away from the origin in the nonstationary case provided the memory parameter d < 1. When d = 1, the spectral estimates are inconsistent and converge weakly to random variates. Applications of the theory to log periodogram regression and local Whittle estimation of the memory parameter are discussed and some modified versions of these procedures are suggested for nonstationary cases.

With numerous and ambiguous sets of information and often conflicting requirements, construction management is a complex process involving much uncertainty. Decision makers may be challenged with satisfying multiple criteria using vague information. Fuzzy multi-criteria decision-making (FMCDM) provides an innovative approach for addressing complex problems featuring diverse decision makers’ interests, conflicting objectives and numerous but uncertain bits of information. FMCDM has therefore been widely applied in construction management. With the increase in information complexity, extensions of fuzzy set (FS) theory have been generated and adopted to improve its capacity to address this complexity. Examples include hesitant FSs (HFSs), intuitionistic FSs (IFSs) and type-2 FSs (T2FSs). This chapter introduces commonly used FMCDM methods, examines their applications in construction management and discusses trends in future research and application. The chapter first introduces the MCDM process as well as FS theory and its three main extensions, namely, HFSs, IFSs and T2FSs. The chapter then explores the linkage between FS theory and its extensions and MCDM approaches. In total, 17 FMCDM methods are reviewed and two FMCDM methods (i.e. T2FS-TOPSIS and T2FS-PROMETHEE) are further improved based on the literature. These 19 FMCDM methods with their corresponding applications in construction management are discussed in a systematic manner. This review and development of FS theory and its extensions should help both researchers and practitioners better understand and handle information uncertainty in complex decision problems.