Search results for: logistics equation

Authors: Paschal A. Ochang, Emmanuel C. Oji

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The Duffing’s Equation is a second order system that is very important because they are fundamental to the behaviour of higher order systems and they have applications in almost all fields of science and engineering. In the biological area, it is useful in plant stem dependence and natural frequency and model of the Brain Crash Analysis (BCA). In Engineering, it is useful in the study of Damping indoor construction and Traffic lights and to the meteorologist it is used in the prediction of weather conditions. However, most Problems in real life that occur are non-linear in nature and may not have analytical solutions except approximations or simulations, so trying to find an exact explicit solution may in general be complicated and sometimes impossible. Therefore we aim to find out if it is possible to obtain one analytical fixed point to the non-linear ordinary equation using fixed point analytical method. We started by exposing the scope of the Duffing’s equation and other related works on it. With a major focus on the fixed point and fixed point iterative scheme, we tried different iterative schemes on the Duffing’s Equation. We were able to identify that one can only see the fixed points to a Damped Duffing’s Equation and not to the Undamped Duffing’s Equation. This is because the cubic nonlinearity term is the determining factor to the Duffing’s Equation. We finally came to the results where we identified the stability of an equation that is damped, forced and second order in nature. Generally, in this research, we approximate the solution of Duffing’s Equation by converting it to a system of First and Second Order Ordinary Differential Equation and using Fixed Point Iterative approach. This approach shows that for different versions of Duffing’s Equations (damped), we find fixed points, therefore the order of computations and running time of applied software in all fields using the Duffing’s equation will be reduced.

Keywords: damping, Duffing's equation, fixed point analysis, second order differential, stability analysis

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Authors: Ayda Nikkar, Roghayye Ahmadiasl

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In this letter, a new analytical method called homotopy perturbation method, which does not need small parameter in the equation is implemented for solving the nonlinear Whitham–Broer–Kaup (WBK) partial differential equation. In this method, a homotopy is introduced to be constructed for the equation. The initial approximations can be freely chosen with possible unknown constants which can be determined by imposing the boundary and initial conditions. Comparison of the results with those of exact solution has led us to significant consequences. The results reveal that the HPM is very effective, convenient and quite accurate to systems of nonlinear equations. It is predicted that the HPM can be found widely applicable in engineering.

Keywords: homotopy perturbation method, Whitham–Broer–Kaup (WBK) equation, Modified Boussinesq, Approximate Long Wave

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Authors: Theresa Steiner, Markus Pajones, Christian Haider

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Traffic is being induced by companies due to their economic behavior. Basically, two different types of traffic occur at company sites: freight traffic and commuting traffic. Due to the fact that these traffic types are connected to each other in different kinds, an integrated approach to manage them is useful. Mobility management is a proved method for companies, to handle the traffic processes caused by their business activities. According to recent trend analysis in Austria, the freight traffic as well as the individual traffic, as part of the commuting traffic, will continue to increase. More traffic jams, as well as negative environmental impacts, are expected impacts for the future. Mobility management is a tool to control the traffic behavior with the scope to reduce emissions and other negative effects which are caused by traffic. Until now, mobility management is mainly used for optimizing commuting traffic without taking the freight logistics processes into consideration. However, the method of mobility management can be used to improve the freight traffic area of a company as well. The focus of this paper will be particularly laid on analyzing to what extent companies are already using mobility management to influence not only the commuting traffic they produce but also their processes of freight logistics. A further objective is to acquire knowledge about the motivating factors which persuade companies to introduce and apply mobility management. Additionally, advantages and disadvantages of this tool will be defined as well as limitations and factors of success, with a special focus on freight logistics, will be depicted. The first step of this paper is to conduct a literature review on the issue of mobility management with a special focus on freight logistics processes. To compare the theoretical findings with the practice, interviews, following a structured interview guidline, with mobility managers of different companies in Upper Austria will be undertaken. A qualitative analysis of these surveys will in a first step show the motivation behind using mobility management to improve traffic processes and how far this approach is already being used to especially influence the freight traffic of the companies. An evaluation to what extent the method of mobility management is already being approached at Upper Austrian companies to regulate freight logistics processes will be one outcome of this publication. Furthermore, the results of the theoretical and practical analysis will reveal not only the possibilities but also the limitations of using mobility management to influence the processes of freight logistics.

Keywords: freight logistics processes, freight traffic, mobility management, passenger traffic

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Authors: Sachin Kumar

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Fuzzy fractional diffusion equation is widely useful to depict different physical processes arising in physics, biology, and hydrology. The motive of this article is to deal with the fuzzy fractional diffusion equation. We study a mathematical model of fuzzy space-time fractional diffusion equation in which unknown function, coefficients, and initial-boundary conditions are fuzzy numbers. First, we find out a fuzzy operational matrix of Legendre polynomial of Caputo type fuzzy fractional derivative having a non-singular Mittag-Leffler kernel. The main advantages of this method are that it reduces the fuzzy fractional partial differential equation (FFPDE) to a system of fuzzy algebraic equations from which we can find the solution of the problem. The feasibility of our approach is shown by some numerical examples. Hence, our method is suitable to deal with FFPDE and has good accuracy.

Keywords: fractional PDE, fuzzy valued function, diffusion equation, Legendre polynomial, spectral method

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Authors: Wen-Shan Lin, Shu-Lu Hsu

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Environmental concern and consumer rights have entailed e-tailers to adopt better strategies to facilitate product returns from customers. As the demand for reverse logistics (RL) continues to grow, little is known about what motivates e-tailers to enhance their RL capabilities and about the role RL capabilities plays in enabling e-tailers to achieve better customer satisfaction and economic performance. Based on resource-based theory and institutional theory, this article proposes that the following factors play a critical role in influencing the RL capability of e-tailers: (a) Financial resource commitment to RL, (b) managerial resource commitment to RL, and (c) institutional pressure to implement RL. Based on the role of these factors, the study provides a framework and propositions that serve to guide future research addressing the link among resources, institutional pressure, and RL capability.

Keywords: reverse logistics, e-tailing, resource-based theory, institutional theory

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Authors: Chor Nejmeddine, Ines Ben Omrane, Mohamed Abdelwahed

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In this paper, we present a posteriori analysis of the discretization of the heat equation by spectral element method. We apply Euler's implicit scheme in time and spectral method in space. We propose two families of error indicators, both of which are built from the residual of the equation and we prove that they satisfy some optimal estimates. We present some numerical results which are coherent with the theoretical ones.

Keywords: heat equation, spectral elements discretization, error indicators, Euler

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Authors: Emad K. Jaradat, Ala’a Al-Faqih

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Nonlinear Schrödinger equations are regularly experienced in numerous parts of science and designing. Varieties of analytical methods have been proposed for solving these equations. In this work, we construct an approximate solution for the nonlinear Schrodinger equations, with harmonic oscillator potential, by Elzaki Decomposition Method (EDM). To illustrate the effects of harmonic oscillator on the behavior wave function, nonlinear Schrodinger equation in one and two dimensions is provided. The results show that, it is more perfectly convenient and easy to apply the EDM in one- and two-dimensional Schrodinger equation.

Keywords: non-linear Schrodinger equation, Elzaki decomposition method, harmonic oscillator, one and two-dimensional Schrodinger equation

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Authors: A. Suparmi, C. Cari, M. Yunianto, B. N. Pratiwi

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D-dimensional Dirac equations of q-deformed shape invariant potentials were solved using supersymmetric quantum mechanics (SUSY QM) in the case of exact spin symmetry. The D dimensional radial Dirac equation for shape invariant potential reduces to one-dimensional Schrodinger type equation by an appropriate variable and parameter change. The relativistic energy spectra were analyzed by using SUSY QM and shape invariant properties from radial D dimensional Dirac equation that have reduced to one dimensional Schrodinger type equation. The SUSY operator was used to generate the D dimensional relativistic radial wave functions, the relativistic energy equation reduced to the non-relativistic energy in the non-relativistic limit.

Keywords: D-dimensional dirac equation, non-central potential, SUSY QM, radial wave function

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Authors: Weiping Liu

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This paper presents an equation to calculate stock prices of different growth model. This equation is mathematically derived by using discounted cash flow method. It has the advantages of being very easy to use and very accurate. It can still be used even when the first stage is lengthy. This equation is more generalized because it can be used for all the three popular stock price models. It can be programmed into financial calculator or electronic spreadsheets. In addition, it can be extended to a multistage model. It is more versatile and efficient than the traditional methods.

Keywords: stock price, multistage model, different growth model, discounted cash flow method

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Authors: Marinko Maslaric, Maja Jokic

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When searching for fast and long term responses, sustainable logistics and supply chain applications have developed irrefutable theories and hypotheses towards market requirements. Nevertheless, there are certain misunderstandings on how the implementation of sustainability principles (social, economical, and environmental) and concepts should work in practice, more specifically, within a humanitarian supply chain management context. This paper will focus on the review and analysis of risk management concepts in humanitarian supply chain in order to identify their compliance with sustainable principles. In this direction, the study will look for strategies that suggest: minimization of environmental impacts throughout the reduction of resources consumption, depreciation of logistics costs, including supply chain ones, minimization of transportation and service costs, elaboration of quality performance of supply chain and logistics, and reduction of supply chain delivery time. On the side of meeting all defense, trades and humanitarian logistics needs, the research will be aligned to UN Sustainable Development Goals, standards, and performances. It will start with relevant strategies for identification of risk indicators and it will end with suggestion of valuable strategic approaches for their minimization or total prevention. Finally, a content analysis will propose a suitable methodological structure for the creation of most sustainable strategy in risk management of humanitarian supply chain. Content analysis will accompany thorough, consistent and methodical approach of literature review for potential disaster risk management plan. Thereupon, the propositions of this research will look for contemporary literature gaps, with respect to operate the literature analysis and to suggest the appropriate sustained risk low master plan. The indicated is here to secure the high quality of logistics practices in hazardous events.

Keywords: humanitarian logistics, sustainability, supply chain risk, risk management plan

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Authors: Eugene Benilov, Mikhail Benilov

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The Enskog-Vlasov (EV) equation is a widely used semi-phenomenological model of gas/liquid phase transitions. We show that it does not generally conserve energy, although there exists a restriction on its coefficients for which it does. Furthermore, if an energy-preserving version of the EV equation satisfies an H-theorem as well, it can be used to rigorously derive the so-called Maxwell construction which determines the parameters of liquid-vapor equilibria. Finally, we show that the EV model provides an accurate description of the thermodynamics of noble fluids, and there exists a version simple enough for use in applications.

Keywords: Enskog collision integral, hard spheres, kinetic equation, phase transition

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Authors: Abdulrahman Abdulrahman

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When the Manning equation is used, a unique value of normal depth in the uniform flow exists for a given channel geometry, discharge, roughness, and slope. Depending on the value of normal depth relative to the critical depth, the flow type (supercritical or subcritical) for a given characteristic of channel conditions is determined whether or not flow is uniform. There is no general solution of Manning's equation for determining the flow depth for a given flow rate, because the area of cross section and the hydraulic radius produce a complicated function of depth. The familiar solution of normal depth for a rectangular channel involves 1) a trial-and-error solution; 2) constructing a non-dimensional graph; 3) preparing tables involving non-dimensional parameters. Author in this paper has derived semi-analytical solution to Manning's equation for determining the flow depth given the flow rate in rectangular open channel. The solution was derived by expressing Manning's equation in non-dimensional form, then expanding this form using Maclaurin's series. In order to simplify the solution, terms containing power up to 4 have been considered. The resulted equation is a quartic equation with a standard form, where its solution was obtained by resolving this into two quadratic factors. The proposed solution for Manning's equation is valid over a large range of parameters, and its maximum error is within -1.586%.

Keywords: channel design, civil engineering, hydraulic engineering, open channel flow, Manning's equation, normal depth, uniform flow

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Authors: A. Zerarka, W. Djoudi

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We use some fractional transformations to obtain many types of new exact solutions of nonlinear lattice equation. These solutions include rational solutions, periodic wave solutions, and doubly periodic wave solutions.

Keywords: fractional transformations, nonlinear equation, travelling wave solutions, lattice equation

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Authors: Hebert Montegranario, Mauricio Londoño

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Solutions of Helmholtz equation are essential in seismic imaging methods like full wave inversion, which needs to solve many times the wave equation. Traditional methods like Finite Element Method (FEM) or Finite Differences (FD) have sparse matrices but may suffer the so called pollution effect in the numerical solutions of Helmholtz equation for large values of the wave number. On the other side, global radial basis functions have a better accuracy but produce full matrices that become unstable. In this research we combine the virtues of both approaches to find numerical solutions of Helmholtz equation, by applying a meshless method that produce sparse matrices by local radial basis functions. We solve the equation with absorbing boundary conditions of the kind Clayton-Enquist and PML (Perfect Matched Layers) and compared with results in standard literature, showing a promising performance by tackling both the pollution effect and matrix instability.

Keywords: Helmholtz equation, meshless methods, seismic imaging, wavefield inversion

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Authors: Tsun-Hui Huang, Shyue-Cheng Yang, Chiou-Fen Shieha

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In this paper, a nonlinear constitutive law and a curve fitting, two relationships between the stress-strain and the shear stress-strain for sandstone material were used to obtain a second-order polynomial constitutive equation. Based on the established polynomial constitutive equations and Newton’s second law, a mathematical model of the non-homogeneous nonlinear wave equation under an external pressure was derived. The external pressure can be assumed as an impulse function to simulate a real earthquake source. A displacement response under nonlinear two-dimensional wave equation was determined by a numerical method and computer-aided software. The results show that a suit pressure in the sandstone generates the phenomenon of stress solitary waves.

Keywords: polynomial constitutive equation, solitary, stress solitary waves, nonlinear constitutive law

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Authors: Fadi Awawdeh, O. Alsayyed, S. Al-Shará

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Considering the inhomogeneities of media, the variable-coefficient Sharma-Tasso-Olver (STO) equation is hereby investigated with the aid of symbolic computation. A newly developed simplified bilinear method is described for the solution of considered equation. Without any constraints on the coefficient functions, multiple kink solutions are obtained. Parametric analysis is carried out in order to analyze the effects of the coefficient functions on the stabilities and propagation characteristics of the solitonic waves.

Keywords: Hirota bilinear method, multiple kink solution, Sharma-Tasso-Olver equation, inhomogeneity of media

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Authors: Tarak Barhoumi, Younes Boujelbene

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Nowadays, the problems of freight transport pose logistical constraints on the urban system in the city. The aim of this article is to gain a better understanding of the interactions between local traffic and interurban traffic on the one hand and between the location system and the transport system on the other hand. Thus, in a simulation and analysis approach cannot be restricted to the only transport system. The proposed approach is based on an assessment of the impact of freight transport, which is closely linked to the diagnostic method, based on two surveys carried out on the territory of the urban community of Sfax. These surveys are based on two main components 'establishment component' first and 'driver component' second. The results propose a reorganization of freight transport in the city of Sfax. First, an orientation of the heavy goods vehicles traffic towards the major axes of transport namely the ring roads (ring road N° 2, ring road N° 4 and ring road N° 11) and the penetrating news of the city. Then, the implementation of a retail goods delivery policy and the strengthening of logistics in the city. The creation of a logistics zone at the ring road N° 11 where various modes of freight transport meet, in order to decongest the roads of heavy goods traffic, reduce the cost of transport and thus improve the competitiveness of the economy regional.

Keywords: urban logistics systems, transport freight, diagnostics, evaluation

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Authors: Seyed Sadegh Naseralavi

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This paper presents a Kernel parallelization equation for damage identification in structures under unknown periodic excitations. Herein, the dynamic differential equation of the motion of structure is viewed as a mapping from displacements to external forces. Utilizing this viewpoint, a new method for damage detection in structures under periodic loads is presented. The developed method requires only two periods of load. The method detects the damages without finding the input loads. The method is based on the fact that structural displacements under free and forced vibrations are associated with two parallel subspaces in the displacement space. Considering the concept, kernel parallelization equation (KPE) is derived for damage detection under unknown periodic loads. The method is verified for a case study under periodic loads.

Keywords: Kernel, unknown periodic load, damage detection, Kernel parallelization equation

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Authors: Mehmood Faisal

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In this globalization era, the supply chain management has acquired strategic importance in diverse business environments. In the current highly competitive business environment, the success of any business considerably depends on the efficiency of the supply chain. The importance of petroleum industry cannot be avoided in the global market; however, supply chain management in the petroleum industry is facing various challenges, particularly in the logistics area. These logistical challenges have a main influence on the cost of crude oil; therefore, the opportunities to save cost in logistics still do exist. The large oil producing companies are undertaking future contracts through 'swaps or options' practice that saves their millions of dollars. The objective of this paper is to throw light on the supply chain challenges and opportunities in the oil industry and on swap practices which are widely employed by large oil producing companies around the world, such as Chevron Corporation, Saudi Arabian Oil Company, BP and Exxon Mobil.

Keywords: logistics, oil industry, swap practice, supply chain management

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Authors: Johnson Oladele Fatokun, I. P. Akpan

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In this paper, the one-dimensional time dependent Schrödinger equation is discretized by the method of lines using a second order finite difference approximation to replace the second order spatial derivative. The evolving system of stiff ordinary differential equation (ODE) in time is solved numerically by an L-stable trapezoidal-like integrator. Results show accuracy of relative maximum error of order 10-4 in the interval of consideration. The performance of the method as compared to an existing scheme is considered favorable.

Keywords: Schrodinger’s equation, partial differential equations, method of lines (MOL), stiff ODE, trapezoidal-like integrator

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Authors: Birome Holo Ba, Christian Prins, Caroline Prodhon

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Optimization is an important aspect of logistics management. It can reduce significantly logistics costs and also be a good tool for decision support. In this paper, we address a planning problem specific to biomass supply chain. We propose a new mixed integer linear programming (MILP) model dealing with different feed stock production operations such as harvesting, packing, storage, pre-processing and transportation, with the objective of minimizing the total logistic cost of the system on a regional basis. It determines the optimal number of harvesting machine, the fleet size of trucks for transportation and the amount of each type of biomass harvested, stored and pre-processed in each period to satisfy demands of refineries in each period. We illustrate the effectiveness of the proposal model with a numerical example, a case study in Aube (France department), which gives preliminary and interesting, results on a small test case.

Keywords: biomass logistics, supply chain, modelling, optimization, bioenergy, biofuels

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Authors: Ana Julia Acevedo Urquiaga, Jose A. Acevedo Suarez, Ana Julia Urquiaga Rodriguez, Neyfe Sablon Cossio

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Despite the progress made in logistics and supply chains fields, it is unavoidable the development of business models that use efficiently information to facilitate the integrated logistics flows management between partners. Collaborative management is an important tool for materializing the cooperation between companies, as a way to achieve the supply chain efficiency and effectiveness. The first face of this research was a comprehensive analysis of the collaborative planning on the Cuban companies. It is evident that they have difficulties in supply chains planning where production, supplies and replenishment planning are independent tasks, as well as logistics and distribution operations. Large inventories generate serious financial and organizational problems for entities, demanding increasing levels of working capital that cannot be financed. Problems were found in the efficient application of Information and Communication Technology on business management. The general objective of this work is to develop a methodology that allows the deployment of a planning and control system in a coordinated way on the medicine’s logistics system in Cuba. To achieve these objectives, several mechanisms of supply chain coordination, mathematical programming models, and other management techniques were analyzed to meet the requirements of collaborative logistics management in Cuba. One of the findings is the practical and theoretical inadequacies of the studied models to solve the current situation of the Cuban logistics systems management. To contribute to the tactical-operative management of logistics, the Collaborative Logistics Flow Management Model (CLFMM) is proposed as a tool for the balance of cycles, capacities, and inventories, always to meet the final customers’ demands in correspondence with the service level expected by these. The CLFMM has as center the supply chain planning and control system as a unique information system, which acts on the processes network. The development of the model is based on the empirical methods of analysis-synthesis and the study cases. Other finding is the demonstration of the use of a single information system to support the supply chain logistics management, allows determining the deadlines and quantities required in each process. This ensures that medications are always available to patients and there are no faults that put the population's health at risk. The simulation of planning and control with the CLFMM in medicines such as dipyrone and chlordiazepoxide, during 5 months of 2017, permitted to take measures to adjust the logistic flow, eliminate delayed processes and avoid shortages of the medicines studied. As a result, the logistics cycle efficiency can be increased to 91%, the inventory rotation would increase, and this results in a release of financial resources.

Keywords: collaborative management, medicine logistic system, supply chain planning, tactical-operative planning

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Authors: Müberra Yüksel, Ömer Faruk Görçün

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The purpose of the present study is to investigate the role of strategic human resource management (SHRM) in constructing "employer branding" in logistics. Prior research does not focus on internal stakeholders, that is, employees. Despite the fact that logistic sector has become customer-oriented, the focus is solely on service quality as the unique aspect of logistic companies for competitive advantage. With an increasing interest lately in internal marketing of the employer brand, the emphasis is on the value that human capital brings to the firm which cannot be imitated. `Employer branding` has been the application of branding and relationship marketing principles for competitive advantage in SHRM. Employer branding is an organizing framework for human resource managers since it represents an organization’s efforts to promote, both within and outside, a coherent view of what makes the firm different and desirable as an employer, i.e., the distinct “employer brand personality” and "employee value propositions" (EVP) offered. The presumption of employer branding enhanced by internal marketing is to make customer-conscious employees to handle services better by being aligned with business mission and goals. Starting from internal customers and analyzing the gaps of EVP by using analytical hierarchy process methodology (AHP) and inquiring whether these brand values are communicated and conceived well may be the initial steps in our proposal for employer branding in logistics sector. This empirical study aims to fill this research gap within the context of an emergent market- Turkey, which is located at a hub of transportation and logistics.

Keywords: Strategic Human Resource Management (SHRM), employer branding, Employee Value Propositions (EVP), Analytical Hierarchy Process (AHP), logistics

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Authors: Takashi Shimizu, Tomoaki Hashimoto

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Controlling the flow of fluids is a challenging problem that arises in many fields. Burgers’ equation is a fundamental equation for several flow phenomena such as traffic, shock waves, and turbulence. The optimal feedback control method, so-called model predictive control, has been proposed for Burgers’ equation. However, the model predictive control method is inapplicable to systems whose all state variables are not exactly known. In practical point of view, it is unusual that all the state variables of systems are exactly known, because the state variables of systems are measured through output sensors and limited parts of them can be only available. In fact, it is usual that flow velocities of fluid systems cannot be measured for all spatial domains. Hence, any practical feedback controller for fluid systems must incorporate some type of state estimator. To apply the model predictive control to the fluid systems described by Burgers’ equation, it is needed to establish a state estimation method for Burgers’ equation with limited measurable state variables. To this purpose, we apply unscented Kalman filter for estimating the state variables of fluid systems described by Burgers’ equation. The objective of this study is to establish a state estimation method based on unscented Kalman filter for Burgers’ equation. The effectiveness of the proposed method is verified by numerical simulations.

Keywords: observer systems, unscented Kalman filter, nonlinear systems, Burgers' equation

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Authors: Narumol Chintaganun

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In this paper we present the second-order central differencing scheme with the staggered version (STG) for solving the advection equation and Burger's equation. This scheme based on staggered evolution of the re-constructed cell averages. This scheme results in the second-order central differencing scheme, an extension along the lines of the first-order central scheme of Lax-Friedrichs (LxF) scheme. All numerical simulations presented in this paper are obtained by finite difference method (FDM) and STG. Numerical results are shown that the STG gives very good results and higher accuracy.

Keywords: central differencing scheme, STG, advection equation, burgers equation

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Authors: Siham Rahoui, Amr Mahfouz, Amr Arisha

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In a highly competitive environment characterised by uncertainty and disruptions, such as the recent COVID-19 outbreak, supply chains (SC) face the challenge of maintaining their cost at minimum levels while continuing to provide customers with high-quality products and services. More importantly, businesses in such an economic context strive to maintain survival by keeping the cost of undertaken activities (such as logistics) low and in-house. To do so, managers need to understand the costs associated with different products and services in order to have a clear vision of the SC performance, maintain profitability levels, and make strategic decisions. In this context, SC literature explored different costing models that sought to determine the costs of undertaking supply chain-related activities. While some cost accounting techniques have been extensively explored in the SC context, more contributions are needed to explore the potential of time driven activity-based costing (TDABC). More specifically, more applications are needed in the manufacturing context of the SC, where the debate is ongoing. The aim of the study is to assess the capability of the technique to assess the operational performance of the logistics function. Through a case study methodology applied to a manufacturing company operating in the automotive industry, TDABC evaluates the efficiency of the current configuration and its logistics processes. The study shows that monitoring the process efficiency and cost efficiency leads to strategic decisions that contributed to improve the overall efficiency of the logistics processes.

Keywords: efficiency, operational performance, supply chain costing, time driven activity based costing

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Authors: H. Ozbasaran

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IPN and IPE sections, which are commonly used European I shapes, are widely used in steel structures as cantilever beams to support overhangs. A considerable number of studies exist on calculating lateral torsional buckling load of I sections. However, most of them provide series solutions or complex closed-form equations. In this paper, a simple equation is presented to calculate lateral torsional buckling load of IPN and IPE section cantilever beams. First, differential equation of lateral torsional buckling is solved numerically for various loading cases. Then a parametric study is conducted on results to present an equation for lateral torsional buckling load of European IPN and IPE beams. Finally, results obtained by presented equation are compared to differential equation solutions and finite element model results. ABAQUS software is utilized to generate finite element models of beams. It is seen that the results obtained from presented equation coincide with differential equation solutions and ABAQUS software results. It can be suggested that presented formula can be safely used to calculate critical lateral torsional buckling load of European IPN and IPE section cantilevers.

Keywords: cantilever, IPN, IPE, lateral torsional buckling

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Authors: D. Garg, S. Luthra, A. Haleem

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Reverse logistics (RL) is supposed to be a systematic procedure that helps in improving the environmental hazards and maintain business sustainability for industries. Industries in Indian are now opting for adoption of RL techniques in business. But, RL practices are not popular in Indian industries because of many barriers for its successful implementation. Therefore, need arises to identify and evaluate the barriers to implement RL practices by taking an Indian industries perspective. Literature review approach and case study approach have been adapted to identify relevant barriers to implement RL practices. Further, Fuzzy Decision Making Trial and Evaluation Laboratory methodology has been brought into use for evaluating causal relationships among the barriers to implement RL practices. Seven barriers out of ten barriers have been categorized into the cause group and remaining into effect group. This research will help Indian industries to manage these barriers towards effective implementing RL practices.

Keywords: barriers, decision making trial and evaluation laboratory (DEMATEL), fuzzy set theory, Indian industries, reverse logistics (RL)

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Authors: H. Triki, Y. Hamaizi, A. El-Akrmi

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We consider the higher order nonlinear Schrödinger equation model with fourth-order dispersion, cubic-quintic terms, and self-steepening. This equation governs the propagation of fem to second pulses in optical fibers. We present new bright and dark solitary wave type solutions for such a model under certain parametric conditions. This kind of solution may be useful to explain some physical phenomena related to wave propagation in a nonlinear optical fiber systems supporting high-order nonlinear and dispersive effects.

Keywords: nonlinear Schrödinger equation, high-order effects, soliton solution

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Authors: Mishu Gupta, Rama Gupta

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It has been elucidated here that non- autonomous discrete non-linear Schrödinger equation is associated with saturable non-linearity through photo-refractive media. We have investigated the localized solution of non-autonomous saturable discrete non-linear Schrödinger equations. The similarity transformation has been involved in converting non-autonomous saturable discrete non-linear Schrödinger equation to constant-coefficient saturable discrete non-linear Schrödinger equation (SDNLSE), whose exact solution is already known. By back substitution, the solution of the non-autonomous version has been obtained. We have analysed our solution for the hyperbolic and periodic form of gain/loss term, and interesting results have been obtained. The most important characteristic role is that it helps us to analyse the propagation of electromagnetic waves in glass fibres and other optical wave mediums. Also, the usage of SDNLSE has been seen in tight binding for Bose-Einstein condensates in optical mediums. Even the solutions are interrelated, and its properties are prominently used in various physical aspects like optical waveguides, Bose-Einstein (B-E) condensates in optical mediums, Non-linear optics in photonic crystals, and non-linear kerr–type non-linearity effect and photo refracting medium.

Keywords: B-E-Bose-Einstein, DNLSE-Discrete non linear schrodinger equation, NLSE-non linear schrodinger equation, SDNLSE - saturable discrete non linear Schrodinger equation

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