Variable demand model for periodically reviewing with allowing refunding parts of the orders

Depending on a field study for one of the largest iron and paints warehouses in Egypt, this paper presents a new multi-item periodic review inventory model considering the refunding quantity cost. Through this field study, we found that the inventory level is monitored periodically at equal time intervals. Returning a part of the goods that were previously ordered is permitted. Also, a shortage is permissible to occur despite having orders, and it is a combination of the backorder and lost sales. This model has been applied in both crisp and fuzzy environments since the fuzzy case is more suitable for real-life than crisp. The Lagrange multiplier technique is used for solving the restricted mathematical model. Here, the demand is a random variable that follows the normal distribution with zero lead-time. Finally, the model is followed by a real application to clarify the model and prove its efficiency.

An effective localization algorithm for moving sources

By utilizing the time difference of arrival (TDOA), the frequency difference of arrival (FDOA), and the differential Doppler rate (DDR) measurements from sensors, this paper proposes an effective moving source localization algorithm with closed solutions. Instead of employing the traditional two-step weighted least squares (WLS) process, the Lagrange multiplier technique is employed in the first step to obtain the initial solution. This initial solution yields a better solution than the existing solution because the dependence among the variables are taken into account. The initial solution is further refined in the second step. The simulation results verify the effectiveness of the proposed algorithm when compared with the relevant existing algorithms.

New Numerical Algorithm to Solve Variable-Order Fractional Integrodifferential Equations in the Sense of Hilfer-Prabhakar Derivative

In this article, a numerical technique based on the Chebyshev cardinal functions (CCFs) and the Lagrange multiplier technique for the numerical approximation of the variable-order fractional integrodifferential equations are shown. The variable-order fractional derivative is considered in the sense of regularized Hilfer-Prabhakar and Hilfer-Prabhakar fractional derivatives. To solve the problem, first, we obtain the operational matrix of the regularized Hilfer-Prabhakar and Hilfer-Prabhakar fractional derivatives of CCFs. Then, this matrix and collocation method are used to reduce the solution of the nonlinear coupled variable-order fractional integrodifferential equations to a system of algebraic equations which is technically simpler for handling. Convergence and error analysis are examined. Finally, some examples are given to test the proposed numerical method to illustrate its accuracy and efficiency.

The optimal displacement control for fractional incommensurate mass-spring oscillators by Shifted Legendre polynomials

Based on the Riemann–Liouville fractional derivative, an optimal displacement control strategy for fractional incommensurate mass-spring oscillators has been presented. According to the calculus of variations and the Lagrange multiplier technique, the optimality conditions for the given problem are obtained. Using Shifted Legendre polynomials, the problem of solving differential equations is transformed into the problem of solving a set of algebraic equations. The validity, high efficiency and applicability of the proposed method are demonstrated through the simulation results.

Consideration of interlaminar strain–energy continuity in composite plate analysis using improved higher order theory

The main goal of this paper is to suggest an improved higher order refined theory for analysing perfectly bonded stacked composite laminates with the usual lamination configurations. The analysis incorporates continuous flexural and in-plane displacements at the interfaces. Furthermore, the transverse shear stress is continuous and constrained with the Lagrange multiplier technique by introducing 14 new unknown variables that are expressed in terms of the interfacial strain energy, which is assuming to be continuous throughout the thickness of the laminate. To determine the newly introduced flexural and in-plane unknown variables, the total potential energy is minimised using variational calculus. The numerical results are compared with those from existing reliable published papers. In general, the proposed approach is sufficient for analysing laminate structures with the required accuracy.

On the equivalence between different canonical forms of F(R) theory of gravity

Classical equivalence between Jordan’s and Einstein’s frame counterparts of [Formula: see text] theory of gravity has recently been questioned, since the two produce different Noether symmetries, which could not be translated back and forth using transformation relations. Here we add the Hamiltonian constraint equation, which is essentially the time–time component of Einstein’s equation, through a Lagrange multiplier to the existence condition for Noether symmetry and show that all the three different canonical structures of [Formula: see text] theory of gravity, including the one which follows from Lagrange multiplier technique, admit each and every available symmetry independently. This establishes classical equivalence.

Multiperiod Telser’s Safety-First Portfolio Selection with Regime Switching

This paper investigates a multiperiod Telser’s safety-first portfolio selection model with regime switching where the returns of the assets are assumed to depend on the market states modulated by a discrete-time Markov chain. The investor aims to maximize the expected terminal wealth and does not want the probability of the terminal wealth to fall short of a disaster level to exceed a predetermined number called the risk control level. Referring to Tchebycheff inequality, we modify Telser’s safety-first model to the case that aims to maximize the expected terminal wealth subject to a constraint where the upper bound of the disaster probability is less than the risk control level. By the Lagrange multiplier technique and the embedding method, we study in detail the existence of the optimal strategy and derive the closed-form optimal strategy. Finally, by mathematical and numerical analysis, we analyze the effects of the disaster level, the risk control level, the transition matrix of the Markov chain, the expected excess return, and the variance of the risky return.

Adaptive Mixed Finite Element Method for Elliptic problems with concentrated source terms

An adaptive mixed nite element method using the Lagrange multiplier technique are used to solve elliptic problems with Dirac delta source terms. The problem arises in the use of Chow-Anderssen linearfunctional methodology to recover coefficients locally in parameter estimation of elliptic equation from pointwise measurement. In this article, we use a posteriori error estimator based on averaging technique as refinement indicators to produce a cycle of mesh adaptation, which are experimentally shown to capture singularity phenomena. Our result shows that adaptive renement process is successfully rene elements around the center of the source terms and show that the global error estimation is better than uniform refinement process.

Numerical Simulation and Convergence Analysis of Fractional Optimization Problems With Right-Sided Caputo Fractional Derivative

This paper presents an efficient approximation schemes for the numerical solution of a fractional variational problem (FVP) and fractional optimal control problem (FOCP). As basis function for the trial solution, we employ the shifted Jacobi orthonormal polynomial. We state and derive a new operational matrix of right-sided Caputo fractional derivative of such polynomial. The new methodology of the present schemes is based on the derived operational matrix with the help of the Gauss–Lobatto quadrature formula and the Lagrange multiplier technique. Accordingly, the aforementioned problems are reduced into systems of algebraic equations. The error bound for the operational matrix of right-sided Caputo derivative is analyzed. In addition, the convergence of the proposed approaches is also included. The results obtained through numerical procedures and comparing our method with other methods demonstrate the high accuracy and powerful of the present approach.