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This research was prompted by work undertaken by the author on the efficiency of shipping operations in the Suez Canal. The physical limitations of the Canal allow only one-way movement of ships for the greater part of its length, and thus ships are organised in convoys. These convoys have fixed starting times, with normally just one convoy per day operating in each direction. When traffic is heavy in the southbound direction, a second (smaller) relief convoy is organised to reduce waiting times which can otherwise exceed 24 hours. The process can be analysed by means of a bulk-service queueing model, where convoys of ships correspond to service batches of customers.

The model has application in the many other fields of transport where relief services are supplied. For example, a coach or train operator will often provide a relief service when customer demand is high. The process may be extended to cover cases where relief is provided for the relief service, resulting in a “cascade” of relief service queues.

The paper considers a discrete-time, Markov, stochastic process model of drivers' day-to-day evolving route choice, the evolving ‘state’ of such a system being governed by the traffic interactions between vehicles, and the adaptive behaviour of drivers in response to previous travel experiences. An approximating deterministic process is proposed, by approximating both the probability distribution of previous experiences—the “memory filter”—and the conditional distribution of future choices. This approximating process includes both flow means and variances as state variables. Existence and uniqueness of fixed points of this process are examined, and an example used to contrast these with conventional stochastic equilibrium models. The elaboration of this approach to networks of an arbitrary size is discussed.

Spurred by the high turnover in the pharmaceutical industry, locating pharmacies inside urban areas along with the high product perishability in this industry, the pharmaceutical supply chain management has recently gained increasing attention. Accordingly, this paper unveils an inventory-routing problem for designing a pharmaceutical supply chain with perishable products and time-dependent travel time in an uncertain environment.

In this study, mathematical programming is employed to formulate a multi-graph network affected by the traffic volume in order to adapt to real-world situations. Likewise, by transforming the travel speed function to the travel time function using a step-by-step algorithm, the first-in-first-out property is warranted. Moreover, the Box–Jenkins forecasting method is employed to diminish the demand uncertainty.

An appealing result is that the delivery horizon constraint in the under-study multi-graph network may eventuate in selecting a longer path. Our analysis also indicates that the customers located in the busy places in the city are not predominantly visited in the initial and last delivery horizon, which are the rush times. Moreover, it is concluded that integrating disruption management, routing planning and inventory management in the studied network leads to a reduction of costs in the long term.

Applying the time-dependent travel time with a heterogeneous fleet of vehicles on the multi-graph network, considering perishability in the products for reducing inventory costs, considering multiple trips of transfer fleet, considering disruption impacts on supply chain components and utilizing the Box–Jenkins method to reduce uncertainty are the contributions of the present study.

Three-way decision (3WD) and probabilistic rough sets (PRSs) are theoretical tools capable of simulating humans' multi-level and multi-perspective thinking modes in the field of decision-making. They are proposed to assist decision-makers in better managing incomplete or imprecise information under conditions of uncertainty or fuzziness. However, it is easy to cause decision losses and the personal thresholds of decision-makers cannot be taken into account. To solve this problem, this paper combines picture fuzzy (PF) multi-granularity (MG) with 3WD and establishes the notion of PF MG 3WD.

An effective incomplete model based on PF MG 3WD is designed in this paper. First, the form of PF MG incomplete information systems (IISs) is established to reasonably record the uncertain information. On this basis, the PF conditional probability is established by using PF similarity relations, and the concept of adjustable PF MG PRSs is proposed by using the PF conditional probability to fuse data. Then, a comprehensive PF multi-attribute group decision-making (MAGDM) scheme is formed by the adjustable PF MG PRSs and the VlseKriterijumska Optimizacija I Kompromisno Resenje (VIKOR) method. Finally, an actual breast cancer data set is used to reveal the validity of the constructed method.

The experimental results confirm the effectiveness of PF MG 3WD in predicting breast cancer. Compared with existing models, PF MG 3WD has better robustness and generalization performance. This is mainly due to the incomplete PF MG 3WD proposed in this paper, which effectively reduces the influence of unreasonable outliers and threshold settings.

The model employs the VIKOR method for optimal granularity selections, which takes into account both group utility maximization and individual regret minimization, while incorporating decision-makers' subjective preferences as well. This ensures that the experiment maintains higher exclusion stability and reliability, enhancing the robustness of the decision results.

The main aim of the current paper is to find a numerical plan for hydraulic fracturing problem with application in extracting natural gases and oil.

First, time discretization is accomplished via Crank-Nicolson and semi-implicit techniques. At the second step, a high-order finite element method using quadratic triangular elements is proposed to derive the spatial discretization. The efficiency and time consuming of both obtained schemes will be investigated. In addition to the popular uniform mesh refinement strategy, an adaptive mesh refinement strategy will be employed to reduce computational costs.

Numerical results show a good agreement between the two schemes as well as the efficiency of the employed techniques to capture acceptable patterns of the model. In central single-crack mode, the experimental results demonstrate that maximal values of displacements in x- and y- directions are 0.1 and 0.08, respectively. They occur around both ends of the line and sides directly next to the line where pressure takes impact. Moreover, the pressure of injected fluid almost gained its initial value, i.e. 3,000 inside and close to the notch. Further, the results for non-central single-crack mode and bifurcated crack mode are depicted. In central single-crack mode and square computational area with a uniform mesh, computational times corresponding to the numerical schemes based on the high order finite element method for spatial discretization and Crank-Nicolson as well as semi-implicit techniques for temporal discretizations are 207.19s and 97.47s, respectively, with 2,048 elements, final time T = 0.2 and time step size τ = 0.01. Also, the simulations effectively illustrate a further decrease in computational time when the method is equipped with an adaptive mesh refinement strategy. The computational cost is reduced to 4.23s when the governed model is solved with the numerical scheme based on the adaptive high order finite element method and semi-implicit technique for spatial and temporal discretizations, respectively. Similarly, in other samples, the reduction of computational cost has been shown.

This is the first time that the high-order finite element method is employed to solve the model investigated in the current paper.

Contemporary stochastic optimal control by synergy of the probability density evolution method (PDEM) and conventional optimal controller exhibits less capability to guarantee economical energy consumption versus control efficacy when non-stationary stochastic excitations drive hysteretic structures. In this regard, a novel multiscale stochastic optimal controller is invented based on the wavelet transform and the PDEM.

For a representative point, a conventional control law is decomposed into sub-control laws by deploying the multiresolution analysis. Then, the sub-control laws are classified into two generic control laws using resonant and non-resonant bands. Both frequency bands are established by employing actual natural frequency(ies) of structure, making computed efforts depend on actual structural properties and time-frequency effect of non-stationary stochastic excitations. Gain matrices in both bands are then acquired by a probabilistic criterion pertaining to system second-order statistics assessment. A multi-degree-of-freedom hysteretic structure driven by non-stationary and non-Gaussian stochastic ground accelerations is numerically studied, in which three distortion scenarios describing uncertainties in structural properties are considered.

Time-frequency-dependent gain matrices sophisticatedly address non-stationary stochastic excitations, providing efficient ways to independently suppress vibrations between resonant and non-resonant bands. Wavelet level, natural frequency(ies), and ratio of control forces in both bands influence the scheme’s outcomes. Presented approach outperforms existing approach in ensuring trade-off under uncertainty and randomness in system and excitations.

Presented control law generates control efforts relying upon resonant and non-resonant bands, and deploys actual structural properties. Cost-function weights and probabilistic criterion are promisingly developed, achieving cost-effectiveness of energy demand versus controlled structural performance.

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.

As the scale of mega transportation infrastructure projects (MTIs) continues to expand, the complexity of engineering construction sharply increases and decision-making sustainability faces severe challenges. Decision-making for mega transportation infrastructure projects unveils the knowledge-intensive characteristic, requiring collaborative decisions by cross-domain decision-makers. However, the exploration of heterogeneous knowledge fusion-driven decision-making problems is limited. This study aims to improve the deficiencies of existing decision-making by constructing a knowledge fusion-driven multi-attribute group decision model under fuzzy context to improve the sustainability of MTIs decision-making.

This study utilizes intuitionistic fuzzy information to handle uncertain information; calculates decision-makers and indicators weights by hesitation, fuzziness and intuitionistic fuzzy entropy; applies the intuitionistic fuzzy weighted averaging (IFWA) operator to fuse knowledge and uses consensus to measure the level of knowledge fusion. Finally, a calculation example is given to verify the rationality and effectiveness of the model.

This research finally constructs a two-level decision model driven by knowledge fusion, which alleviates the uncertainty and fuzziness of decision knowledge, promotes knowledge fusion among cross-domain decision-makers and can be effectively applied in practical applications.

This study provides an effective decision-making model for mega transportation infrastructure projects and guides policymakers.

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 purpose of this paper is to establish a dynamic model considering the actual operating conditions of the train and to study the dynamic performance and vibration characteristics of axle box bearings under different operating conditions.

In this paper, based on the internal contact characteristics of double-row tapered roller bearings, a dynamic model considering the actual operating conditions of the train is established. The correctness of the model is verified by the vibration test of the bearing. Comparative analysis was conducted on the effects of axial force, radial force and rotational speed on the angular velocity of the cage, slip rate and vibration acceleration level of the inner ring.

As the force increases, the slip rate of the cages on both sides decreases, and the vibration acceleration level of the inner ring increases. With the increase of rotational speed, the cage slip rate of the axle box bearing increases and the vibration acceleration level of the inner ring increases.

A dynamic model is established considering the actual operating conditions, and the dynamic performance and vibration characteristics of the axle box bearing under different operating conditions are analyzed by numerical method. The research content can provide reference for the parameter design of high-speed railway bearings.

The peer review history for this article is available at: https://publons.com/publon/10.1108/ILT-03-2024-0085/