Solution Methodology Research Articles

Vehicle routing problem for cold-chain drug distribution with epidemic spread situation

We investigate a vehicle routing problem considering the influence of epidemic spread (VRP-ES) for the design of a novel cold-chain drug distribution system, in which the disease spread model is used to capture virus transmission characteristics and demand fluctuations. To this end, we aim to minimize the total travel time and transmission risk of the distribution network by incorporating realistic features including priority distribution and temperature control. We propose a hybrid tabu search heuristic (HTS) with a specifically designed initial solution, several neighborhood operators, and diversification strategies to solve this problem. A series of numerical experiments are conducted to test the proposed solution methodology. The virus spread model and vehicle routing results are discussed to analyze the VRP-ES optimization strategies through an empirical case study of Chongqing city in China. Sensitivity analysis is conducted to identify the impact of various parameters on the VRP-ES and provide some management implications as well.

Vibration suppression of a platform by a fractional type electromagnetic damper and inerter-based nonlinear energy sink

The theory of linear and nonlinear dynamic vibration absorbers is a well-established topic for many years. However, many recent contributions paid attention to the nonlinear vibration absorbers and different practical realizations of corresponding devices. Here, we propose a mechanical system constituted of the inerter-based nonlinear energy sink attached to the main body that is resting on an elastic foundation and is grounded through the fractional type electromagnetic damper. The two-degree-of-freedom system is described via two coupled differential equations with one of them having a fractional-order derivative term and the other one containing cubic stiffness nonlinearity. The incremental harmonic balance (IHB) method is employed to solve the equations and studies the strongly nonlinear periodic responses of the system. Applied approximated solution methodology is validated by the numerical Newmark method adapted to deal with the system of nonlinear fractional-order differential equations. The appropriate and necessary number of harmonics used in the IHB solution is commented and validated. This study can be a first step in understanding the dynamics and giving directions for the future design of vibration-isolating platforms based on inerter-based nonlinear vibration absorbers and electromagnetic dampers.

The modified physics-informed neural network (PINN) method for the thermoelastic wave propagation analysis based on the Moore-Gibson-Thompson theory in porous materials

This paper presents novel contributions to both theory and solution methodology in AI-based analysis of solid mechanics. The physics-informed neural network (PINN) method is developed for thermoelastic wave propagation and Moore-Gibson-Thompson (MGT) coupled thermoelasticity analysis of porous media, a first in the field. The coupled thermoelasticity governing equations, based on the MGT heat conduction model, are derived for a porous half-space, with the thermal relaxation coefficient and strain relaxation factor being considered. Mechanical and thermal shock loading boundary conditions are imposed. The behavior of a magnesium-made porous body is analyzed using the PINN method, with highly accurate results being achieved for the system of coupled PDEs. An adaptive hyperparameter tuning approach, integrating a generalized subset design (GSD) and Bayesian optimization algorithm, is used to automatically select the optimal structure based on the L2 relative error. This hybrid methodology eliminates manual adjustment concerns. The proposed method is verified through a thorough comparison with the Lord-Shulman theory of coupled thermoelasticity. The strength of the methodology lies in its ability to operate without domain data, with only boundary and initial points being required. Four example sets are examined to demonstrate the capabilities of the modified PINN, and high-quality predictions of dimensionless fields’ variables over an extended time interval are obtained, confirming its extrapolation abilities.

Applying fuzzy logic to balanced scorecard for the performance evaluation of government e-services

Purpose The purpose of this study is to assess the performance of United Arab Emirates (UAE) Government e-services by using the fuzzy technique for order preference by similarity to ideal solution (TOPSIS) methodology, integrating insights from the balanced scorecard (BSC) framework across financial, customer, internal business and learning and growth perspectives. Design/methodology/approach Using the fuzzy TOPSIS method, this paper evaluate three e-services in the UAE against 12 criteria representing the balanced scorecard perspectives. Expert evaluation and sensitivity analysis are used to identify the most sustainable e-service alternative. Findings The study findings emphasize the importance of prioritizing customer-centric metrics, improving service reliability and efficiency, and investing in employee training to enhance e-government service performance in the UAE. Sensitivity analysis reinforces the robustness of our results and identifies key criteria influencing decision-making. Research limitations/implications The data was collected only from experts in selected UAE Government departments. This may affect the generalization of the findings. Also, only three e-services were evaluated. Future studies could include various e-services not covered in this study and use different multi-criteria decision-making methods. Practical implications Prioritizing customer satisfaction: Priority should be given to customer satisfaction as it is a critical factor in evaluating e-services because of its importance. It also highlights the importance of considering user feedback and ensuring that e-services have a high level of friendliness and responsiveness to their needs. It follows that minimizing errors and ensuring quick and efficient transactions are crucial. Emphasizing reliability and transaction efficiency: Reliable services and transaction efficiency are also essential criteria for evaluating e-government services. This suggests that e-government services should be designed to minimize errors and ensure that transactions are completed quickly and efficiently. Managing IT costs: To deliver e-government services affordably, effective IT cost management is crucial. This emphasizes how crucial it is to effectively manage IT costs to guarantee the efficient delivery of e-government services. Social implications From a customer perspective, adopting BSC can create a favorable customer attitude, encourage long-term customer support, and increase customer satisfaction and loyalty. These factors have significant social implications for UAE and expatriate individuals who are using such e-government services. Originality/value This study contributes to the literature by showcasing the applicability of the fuzzy TOPSIS methodology in evaluating UAE e-government service performance. By examining multiple perspectives of the BSC, this paper provide valuable insights into enhancing the efficiency and effectiveness of e-services in the UAE Government sector.

Optimal drone deployment for cost‐effective and sustainable last‐mile delivery operations

AbstractDelivery by drones holds significant potential to solve issues (such as high costs, access to remote areas, etc.) faced in last‐mile delivery operations, particularly in the e‐commerce industry. Still, it involves complex issues such as multi‐trip operations, energy estimation, and battery recharge planning. A sound drone delivery problem entails an optimal drone deployment plan with routing details at the lowest possible cost. To this end, this study focuses on formulating a delivery problem that involves multi‐trip drone routing, energy optimization, and travel time optimization problems where energy consumption by drones is modeled as a non‐linear function. We develop a mixed integer non‐linear programming model as an integrated optimization model. This model aims to: (a) maximize revenue by meeting demand completely without leaving idle drones, (b) optimize energy use by drones, and (c) minimize the required drone fleet size for an optimal plan. The proposed model is solved using the Gurobi Solver, which employs data supplied by a well‐known e‐commerce firm. We introduce a two‐phase heuristic solution methodology to tackle larger networks’ complexities. This method consists of the clustering phase (K‐means clustering method) and the optimization phase. The robustness of the developed mathematical modeling is demonstrated by testing with varied large problem instances. The evaluation shows that expanding destination options boosts drone demand until saturation, necessitating more drones. Efficient route planning and fleet adjustments are crucial for meeting rising demand and satisfying customers amidst dense clustering. This model helps e‐commerce manage daily last‐mile drone deliveries and anticipate future growth.

Advancing differential equation solutions: A novel Laplace-reproducing kernel Hilbert space method for nonlinear fractional Riccati equations

Fractional ordinary differential equations are crucial for modeling various phenomena in engineering and physics. This study aims to enhance solution methodologies by combining the Laplace transform with the reproducing kernel Hilbert space method (RKHSM). This integration leads to a more effective approach compared to the classical RKHSM. We apply the Laplace-reproducing kernel Hilbert space method (L-RKHSM) to develop novel numerical solutions for nonlinear fractional Riccati differential equations. The L-RKHSM systematically produces both approximate and analytic solutions in series form. We present detailed results for four illustrative examples, showcasing the superior performance of the L-RKHSM over traditional methods. This innovative approach not only advances our understanding of nonlinear fractional ordinary differential equations but also demonstrates its effectiveness through significantly improved outcomes in various applications.

Applications of neural networking in Eyring-Powell nanofluid dynamics on a rotating surface in a porous medium

One of the fundamental aspects of solving difficult and nonlinear mathematical ideas is the use of Artificial Neural Networks due to their exceptional efficiency in handling such problems. In many complex fields such as computational fluid system, biological computation, and biotechnology, a distinct computing structure is provided by Artificial Neural Networks, which is extremely valuable. The main purpose of this article is to dig out the abilities of the Levenberg-Marquardt technique using back-propagation artificial neural networks regarding the fluid mechanics and the heat transport assessment in nanoparticles. This interdisciplinary field explores heat and mass transfer through objects and fluids, and their impacts on temperature as well as concentration distributions. With the help of mathematical modelling and numerical solution methodologies, researchers can simulate and analyze these processes. The present analysis communicates the Eyring-Powell fluid flow caused by a rotating disk placed in the horizontal direction. The fluid flow over a rotating disk through non-linear partial differential equations is modeled. After converting the partial differential equations to ordinary ones, they are tackled numerically through shooting technique. The Levenberg-Marquardt algorithm using back-propagation artificial neural networks technique is used with reference datasets, having 70 % training, 15 % testing, and 15 % to validation. The method is validated with the help of mean squared error, error histogram and comprehensive regression analysis. These figures show the accuracy of the proposed method for solving nonlinear problems. Flow features such as velocity, temperature as well as the concentration profiles are exemplified quantitatively and have been graphically discussed. Velocity of the fluid decreases for porosity and increases for fluid parameter while temperature increases for thermophoresis and Brownian motion parameters. Consistency is shown by getting a minimum absolute error approaching zero, showing the strength of the proposed approach.

Hierarchical Optimization Framework for Layout Design of Star–Tree Gas-Gathering Pipeline Network in Discrete Spaces

The gas-gathering pipeline network is a critical infrastructure for collecting and conveying natural gas from the extraction site to the processing facility. This paper introduces a design optimization model for a star–tree gas-gathering pipeline network within a discrete space, aimed at determining the optimal configuration of this infrastructure. The objective is to reduce the investment required to build the network. Key decision variables include the locations of stations, the plant location, the connections between wells and stations, and the interconnections between stations. Several equality and inequality constraints are formulated, primarily addressing the affiliation between wells and stations, the transmission radius, and the capacity of the stations. The design of a star–tree pipeline network represents a complex, non-deterministic polynomial (NP) hard combinatorial optimization problem. To tackle this challenge, a hierarchical optimization framework coupled with an improved genetic algorithm (IGA) is proposed. The efficacy of the genetic algorithm is validated through testing and comparison with other traditional algorithms. Subsequently, the optimization model and solution methodology are applied to the layout design of a pipeline network. The findings reveal that the optimized network configuration reduces investment costs by 16% compared to the original design. Furthermore, when comparing the optimal layout under a star–star topology, it is observed that the investment needed for the star–star topology is 4% higher than that needed for the star–tree topology.

Assessing vehicle interdiction strategies on a complex transportation network: A simulation-based study

The escape interdiction problem within the context of attacker activities on a transportation network is addressed in this study. In the absence of traffic within the network, the attacker attempts to flee the city by choosing one of the shortest paths from the crime scene to a randomly selected exit point. However, in the presence of traffic, the attacker strategically selects the optimal route that minimizes his time to reach a randomly selected exit point. On the other side, defenders try to interdict the attacker on his escape route. Defenders face the daunting challenge of interdicting the attacker’s escape route while operating under limited resources. Dealing with a real city road network further adds complexity to the scenario. A simulation-based model is proposed for the optimal allocation of resources to tackle this issue. The focus then shifts to the development of an advanced search strategy that involves routing with optimal resource allocation. This paper presents the first comparative study for escape interdiction problems within a simulation environment, explicitly focusing on solution methodologies. An optimal resource allocation approach is proposed in the presence of traffic, constituting a novel contribution that has not been previously implemented in escape interdiction problems. In addition, the paper introduces a Genetic Algorithm (GA)-based meta-heuristic approach within a simulation environment. This approach generates optimal paths for defenders, wherein each node is associated with a fixed time window, representing the defender’s waiting time. In this proposed methodology, defenders undertake a tour of the network rather than remaining stationary at a single location. This approach expands the network search capabilities, thereby requiring optimization to ascertain the optimal routes and schedules for the defender vehicles. A case study is conducted using the map of IIT Kharagpur, India, to evaluate the effectiveness of this approach. By employing this approach and conducting in-depth analyses, the aim is to provide valuable insights into the efficiency and practicality of the developed methods on real-world transportation networks.

Radial Inertia Effect of Ultra-Soft Materials from Hopkinson Bar and Solution Methodologies.

The split-Hopkinson pressure bar technique is widely used to determine the dynamic mechanical behavior of materials. However, spike-like stress features appear in the initial stress behavior of ultra-soft materials tested with a split-Hopkinson bar. These features are not intrinsic characteristics of the materials. Potential causes were investigated through experiments and numerical simulations. It was found that the spike feature represents derived stress resulting from the radial inertia effect during dynamic loading. In this work, we propose and experimentally verify effective methods to reduce this effect. The influences of density, strain acceleration, ratio between inner and outer diameter, and Poisson's ratio on the radial inertia effect were investigated. The spike stress was found to change linearly with density and strain acceleration but decrease significantly when the inner/outer diameter ratio was below 0.3, after which it remained nearly constant. A parabolic stress distribution was observed along the radial direction due to the Poisson effect, especially when the ratio exceeded 0.3, leading to higher spike stress. Finally, suggestions were proposed as experimental guidance when testing ultra-soft materials.

Determining the Location of Solar Power Plant in Indonesia Using Fuzzy-AHP TOPSIS

Solar is a promising renewable energy source for Indonesia's increasing electricity demand, which grows at the rate of 3.3% annually. However, high investment costs and unclear policies hinder Solar Power Plant (SPP) development. Considering the potential for growth in energy demand and the low long-term operational costs, it is imperative to foster SPP expansion in Indonesia. This study aims to identify location criteria and potential SPP development sites in Indonesia. We employ Multi-Criteria Decision-Making (MCDM) combining Fuzzy-AHP and Technique for Order of Preference by Similarity to Ideal Solution (TOPSIS) methodologies to assign criteria weights and prioritize alternative SPP locations. Results show that, from all respondents using the geometric mean in the Fuzzy Analytic Hierarchy Process (AHP), it is found that the Economic criteria give the highest weight at 31%, and subcriteria of Land Availability, Peak Sun Hours, Geographic Location, Distance from Transportation Networks, Construction Costs, and Government Regulations contribute significantly. The ranking of alternative solutions indicates that South Sumatra Province holds the highest priority for SPP development with a 0.572 score, closely followed by North Sumatra at 0.571

Decision-focused neural adaptive search and diving for optimizing mining complexes

Optimizing industrial mining complexes, from extraction to end-product delivery, presents a significant challenge due to non-linear aspects and uncertainties inherent in mining operations. The two-stage stochastic integer program for optimizing mining complexes under joint supply and demand uncertainties leads to a formulation with tens of millions of variables and non-linear constraints, thereby challenging the computational limits of state-of-the-art solvers. To address this complexity, a novel solution methodology is proposed, integrating context-aware machine learning and optimization for decision-making under uncertainty. This methodology comprises three components: (i) a hyper-heuristic that optimizes the dynamics of mining complexes, modeled as a graph structure, (ii) a neural diving policy that efficiently performs dives into the primal heuristic selection tree, and (iii) a neural adaptive search policy that learns a block sampling function to guide low-level heuristics and restrict the search space. The proposed neural adaptive search policy introduces the first soft (heuristic) branching strategy in mining literature, adapting the learning-to-branch framework to an industrial context. Deployed in an online fashion, the proposed hybrid methodology is shown to optimize some of the most complex case studies, accounting for varying degrees of uncertainty modeling complexity. Theoretical analyses and computational experiments validate the components’ efficacy, adaptability, and robustness, showing substantial reductions in primal suboptimality and decreased execution times, with improved and more robust solutions that yield higher net present values of up to 40%. While primarily grounded in mining, the methodology shows potential for enabling smart, robust decision-making under uncertainty.

Induced Generalized Intuitionistic Fuzzy OWA Operator on GRA Method for Evaluation of Self-Propelled Artillery System: Ammunition Based Computer Assisted Military Experiment

The Self-Propelled Artillery System selection problem, which is a sub-problem of the Weapon Systems Selection Problems (WSSP), is an extremely important strategic level decision problem and constitutes the main focus of this study. To solve the problem, 3 different weapon systems were evaluated based on 7 criteria. The solution methodology consists of the integration of induced generalized ordered weighted averaging (IG-IFOWA) operator and Grey Relational Analysis (GRA). Such a solution proposal has not been seen in previous WSSP applications. To test the validity and applicability of the proposed methodology, the results of the study were tested on an ammunition-based computer-aided military experiment. The results reveal the effectiveness of the selected weapon system.

Shelter location–allocation problem for disaster evacuation planning: A simulation optimization approach

Immediately after a major earthquake strikes, a segment of the people in the disaster region must evacuate to relief shelters. If the evacuation proceeds in an efficient and safe manner, many lives can potentially be saved as the effects of secondary factors, e.g., secondary collapses, stampedes, and aftershocks, can largely be mitigated, while at the same time the people taking refuge can quickly gain access to vital relief goods. Formulating the best possible protocols for post-earthquake evacuation is a crucial, yet highly challenging problem considering the profound uncertainty which is present in the post-disaster environment, including the location and degree of infrastructural damage, the number and location of people who need to evacuate, the behavior and psychology of evacuees, etc. In this research, we formulate a two-stage stochastic evacuation simulation model capable of credibly accounting for these uncertainties. We develop a solution methodology to solve the shelter location–allocation problem represented by the two-stage model, finding the optimal location of shelters to be open as the first stage solution and the optimal assignment of evacuees to shelters as the second stage solution to minimize the total expected cost. The cost-based objective function consists of the cost of opening shelters, a deprivation cost component, the cost of trapped evacuees, and the cost of shelters exceeding capacity. In developing this framework, we collaborate with the National Science and Technology Center for Disaster Reduction (NCDR) in utilizing GIS-based probabilistic models of road damage. We apply the proposed framework to run an extensive numerical study and present various valuable observations and insights which can be gained.

Review of Thermal Energy Storage Materials for Application in Large-Scale Integrated Energy Systems—Methodology for Matching Heat Storage Solutions for Given Applications

Review of Thermal Energy Storage Materials for Application in Large-Scale Integrated Energy Systems—Methodology for Matching Heat Storage Solutions for Given Applications

Enhancing Supplier Selection for Sustainable Raw Materials: A Comprehensive Analysis Using Analytical Network Process (ANP) and TOPSIS Methods

Background: This research endeavors to enhance supplier selection processes by combining the Analytic Network Process (ANP) and Technique for Order of Preference by Similarity to Ideal Solution (TOPSIS) methodologies, with a specific focus on sustainability criteria. Method: Initially comprising 21 sub-criteria derived from prior research, the selection criteria are refined to 17, eliminating redundant elements. The core principle guiding this refinement is the comprehensive coverage of economic, social, and environmental dimensions, essential for sustainable supplier evaluation. Results: The study’s outcomes underscore the paramount importance of economic criteria (0.0652) in supplier selection, followed by environmental (0.0343) and social dimensions (0.0503). Key sub-criteria contributing significantly to this evaluation encompassed consistent product quality, competitive raw material pricing, proficient labor capabilities, recycling potential, punctual delivery performance, and effective waste management practices. Conclusions: These sub-criteria are thoughtfully integrated into the sustainable assessment framework, aligning seamlessly with the economic, environmental, and social criteria.

A new Fermatean fuzzy multi‐objective indefinite quadratic transportation problem with an application to sustainable transportation

AbstractIn this work, a Fermatean fuzzy (FF) multi‐objective indefinite quadratic transportation problem (TP) is introduced. Due to some unavoidable reasons, real‐life transportation parameters such as supply, demand and costs are indeterminate in nature and cannot be expressed in crisp terms. We represent these parameters using FF numbers, an extension of fuzzy numbers, which are capable of representing indeterminacy efficiently. A multi‐objective indefinite quadratic TP where each objective is a product of two linear factors (cost functions) is considered. Defuzzification of FF numbers is accomplished by the introduction of ‐cut for the first time. The obtained crisp TP is solved using the intuitionistic fuzzy programming approach and FF programming approach to arrive at a compromise solution. To substantiate the work, solution methodology based on defuzzification using the ranking function is also deliberated. The applicability of the model is demonstrated through a sustainable TP, which simultaneously minimizes transportation cost with depreciation cost and packaging cost with wastage cost. The resulting value of the objective functions and the aspiration levels are compared to depict the efficacy of the proposed method over the ranking function method. The concluding section summarizes the work, and future avenues along with some limitations of the work are also specified.

Synthesis of Metallic and Metal Oxide Nanoparticles Using Homopolymers as Solid Templates: Luminescent Properties of the Eu+3 Nanoparticle Products

Starting from poly(4-vinylpyridine) ((P4VP)n), poly(2-vinylpyridine) ((P2VP)n), and [N=P(O2CH2CF3)]m-b-P2VP20 block copolymers, a series of metal-containing homopolymers, (P4VP)n⊕MXm, (P2VP)n⊕MXm, and [N=P(O2CH2CF3)]m-b-P2VP20]⊕MXm MXm = PtCl2, ZnCl2, and Eu(NO3)3, have been successfully prepared by using a direct and simple solution methodology. Solid-state pyrolysis of the prepared metal-containing polymeric precursors led to the formation of a variety of different metallic and metal oxide nanoparticles (Pt, ZnO, Eu2O3, and EuPO4) depending on the composition and nature of the polymeric template precursor. Thus, whereas Eu2O3 nanostructures were obtained from europium-containing homopolymers ((P4VP)n⊕MXm and (P2VP)n⊕MXm), EuPO4 nanostructures were achieved using phosphorus-containing block copolymer precursors, [N=P(O2CH2CF3)]m-b-P2VP20]⊕MXm with MXm = Eu(NO3)3. Importantly, and although both Eu2O3 and EuPO4 nanostructures exhibited a strong luminescence emission, these were strongly influenced by the nature and composition of the macromolecular metal-containing polymer template. Thus, for P2VP europium-containing homopolymers ((P4VP)n⊕MXm and (P2VP)n⊕MXm), the highest emission intensity corresponded to the lowest-molecular-weight homopolymer template, [P4VP(Eu(NO3)3]6000, whereas the opposite behavior was observed when block copolymer precursors, [N=P(O2CH2CF3)]m-b-P2VP20]⊕MXm MXm= Eu(NO3)3, were used (highest emission intensity corresponded to [N=P(O2CH2CF3)]100-b-[P2VP(Eu(NO3)3)x]20). The intensity ratio of the emission transitions: 5D0 → 7F2/5D0 → 7F1, suggested a different symmetry around the Eu3+ ions depending on the nature of the polymeric precursor, which also influenced the sizes of the prepared Pt°, ZnO, Eu2O3, and EuPO4 nanostructures.

Cold chain distribution network design with heterogeneous fleet under carbon reduction policy application effect

ABSTRACT To integrate cold chain distribution network design problem with heterogeneous fleet, a multi-objective optimisation model is proposed to simultaneously optimise distribution routes, the quantity of internal combustion and electric refrigerated trucks (ERTs), and the number and location of distribution centres and charging stations with time window constraints, where the cold chain distribution operating cost and the customer dissatisfaction cost are minimised. A hybrid solution methodology, combining a multi-objective artificial fish swarm algorithm with a label-based optimisation algorithm, is presented to address this model. Extensive computational experiments verify the effectiveness of the proposed method. Moreover, a sensitivity analysis, focusing on the range of ERTs, the purchase subsidy for ERTs, the carbon tax and the carbon emission quota, informs the development of diverse carbon reduction policies. A comparative analysis of the implementation effect of carbon reduction policies can provide optimisation decision support for promoting sustainability in the electrification of cold chain distribution.

Bending-based solution methodology using eigenvalue-eigenvector approach for analysis of foldable reinforced Golf Clubs cylindrical shell

This paper is organized to present eigenvalue-eigenvector based solution method for elastic bending analysis of foldable Golf Clubs cylindrical shell reinforced with graphene origami. The axisymmetric kinematic and constitutive relations are extended using the models with shear deformability and three-dimensional relations. The effective material properties are inserted into integration constants and constitutive relations in terms of angle and content of folded structure as well as thermal load. The virtual work principle is extended in order to derive governing equations and the eigenvalue-eigenvector method is applied for analytical solution. The results are presented along the longitudinal and radial coordinates with changes of angle and content of folded structure as well as thermal load. The results of this analysis may be used for optimized design and manufacturing of the golf clubs and other sport equipment.