Mathematical modeling for a multiproduct manufacturing system featuring postponement, external suppliers, overtime, and scrap

Manufacturing firms operating in today’s competitive global markets must continuously find the appropriate manufacturing scheme and strategies to effectively meet customer needs for various types of quality of merchandise under the constraints of short order lead-time and limited in-house capacity. Inspired by the offering of a decision-making model to aid smooth manufacturers’ operations, this study builds an analytical model to expose the influence of the outsourcing of common parts, postponement policies, overtime options, and random scrapped items on the optimal replenishment decision and various crucial system performance indices of the multiproduct problem. A two-stage fabrication scheme is presented to handle the products’ commonality and the uptime-reduced strategies to satisfy the short amount of time before the due dates of customers’ orders. A screening process helps identify and remove faulty items to ensure the finished lot’s anticipated quality. Mathematical derivation assists us in finding the manufacturing relevant total cost function. The differential calculus helps optimize the cost function and determine the optimal stock-replenishing rotation cycle policy. Lastly, a simulated numerical illustration helps validate our research result’s applicability and demonstrate the model’s capability to disclose the crucial managerial insights and facilitate manufacturing-relevant decision making.

Coverage enhancements of vehicles users using mobile stations at 5G cellular networks

High mobility requirements are one of the challenges face fifth-generation wireless (5G) cellular networks by providing acceptable wireless services to users traveling at speed up to 350 km/h. This paper presents a new scenario to increase the bit rate and coverage for passengers that use the vehicles for traveling through the installation a mobile station (MS) on these vehicles to provide a high-quality service to users. Based on signal to noise ratio (SNR’s) mathematical derivation and the outage probability of the user link, the proposed system is evaluated. Numerical results indicate an enhancement for users who received signal strength (RSS) from (-72 to -55) dBm and (15 to 38) Mbps in bit rate. Moreover, their number of users increased by proposed system adoption.

Reasoning Method Based on Intervals with Symmetric Truncated Normal Density

Error parameters are inevitable in systems. In formal verification, previous reasoning methods seldom considered the probability information of errors. In this article, errors are described as symmetric truncated normal intervals consisting of the intervals and symmetric truncated normal probability density. Furthermore, we also rigorously prove lemmas and a theorem to partially simplify the calculation process of truncated normal intervals and independently verify the formulas of variance and expectation of symmetric truncated interval given by some scholars. The mathematical derivation process or verification codes are provided for most of the key formulas in this article. Hence, we propose a new reasoning method that combines the probability information of errors with the previous statistical reasoning methods. Finally, an engineering example of the reasoning verification of train acceleration is provided. After simulating the large-scale cases, it is shown that the simulation results are consistent with the theoretical reasoning results. This method needs more calculation, while it is more effective in detecting non-error’s fault factors than other error reasoning methods.

An idealized 1½-layer isentropic model with convection and precipitation for satellite data assimilation research. Part II: model derivation

In this part II paper we present a fully consistent analytical derivation of the ‘dry’ isentropic 1½-layer shallow water model described and used in part I of this study, with no convection and precipitation. The mathematical derivation presented here is based on a combined asymptotic and slaved Hamiltonian analysis which is used to resolve an apparent inconsistency arising from the application of a rigid-lid approximation to an isentropic two-layer shallow water model. Real observations based on radiosonde data are used to justify the scaling assumptions used throughout the paper, as well as in part I. Eventually, a fully consistent isentropic 1½-layer model emerges from imposing fluid at rest (v1 = 0) and zero Montgomery potential (M1 = 0) in the upper layer of an isentropic two-layer model.

Convolution-Based Model-Solving Method for Three-Dimensional, Unsteady, Partial Differential Equations

Neural networks are increasingly used widely in the solution of partial differential equations (PDEs). This letter proposes 3D-PDE-Net to solve the three-dimensional PDE. We give a mathematical derivation of a three-dimensional convolution kernel that can approximate any order differential operator within the range of expressing ability and then conduct 3D-PDE-Net based on this theory. An optimum network is obtained by minimizing the normalized mean square error (NMSE) of training data, and L-BFGS is the optimized algorithm of second-order precision. Numerical experimental results show that 3D-PDE-Net can achieve the solution with good accuracy using few training samples, and it is of highly significant in solving linear and nonlinear unsteady PDEs.

Multi-Player Evolutionary Game of Network Attack and Defense Based on System Dynamics

We formalize the adversarial process between defender and attackers as a game and study the non-cooperative evolutionary game mechanism under bounded rationality. We analyze the long-term dynamic process between the attacking and defending parties using the evolutionary stable strategies derived from the evolutionary game model. First, we construct a multi-player evolutionary game model consisting of a defender and multiple attackers, formally describe the strategies, and construct a three-player game payoff matrix. Then, we propose two punishment schemes, i.e., static and dynamic ones. Moreover, through the combination of mathematical derivation with simulation, we obtain the evolutionary stable strategies of each player. Different from previous work, in this paper, we consider the influence of strategies among different attackers. The simulation shows that (1) in the static punishment scheme, increasing the penalty can quickly control the occurrence of network attacks in the short term; (2) in the dynamic punishment scheme, the game can be stabilized effectively, and the stable state and equilibrium values are not affected by the change of the initial values.

Splitting Physical Exergy by Its Feasible Working Ways

This paper analyzed the problems associated with physical exergy splitting, and based on this, presented a new splitting method. This new method splits the physical exergy into three parts according to the feasible working ways, i.e.,: the direct, indirect, and adaptive exergy. The computational method and the physical meaning of the three exergy parts were presented in detail in terms of graphic representation and mathematical derivation. Then, it was applied to the exergy analysis of a thermal power cycle. The results show that compared with the conventional method which splits the physical exergy into thermal and mechanical parts, the current exergy splitting method can better represent the change rule of the working ability of the real working stream in the cycle and the influence of some operation parameters, such as the turbine inlet temperature, on the real working ability. The study suggests that the new method can make the exergy analysis more helpful and guidable in its applications.

The impact of contract enforcement efficiency on debt maturity structure using mathematical derivation and comparative static analysis

In recent years, the systematic use of advanced mathematical methods to express, study and argue economic theories has become an important branch and research hotspot in economics. The choice of debt maturity structure is an interesting economics issue in corporate finance. The signing of debt financing contract is not only the enterprises’ independent behavior, but also will be affected by the contract environment. Differences in the contractual environment will inevitably lead to differences in the efficiency of contract enforcement between borrowers and lenders in debt contracts. This paper introduces the contract enforcement efficiency factor on the basis of the standard structure model constructed by Holmstrom and Tirole, and then theoretically investigates the influence mechanism of contract enforcement efficiency on debt maturity structure based on the mediating role of contract enforcement efficiency on the investors’ liquidation claims. By transforming the financing contract into a linear programming problem, and then solving the optimization model, mathematical derivation and static comparative analysis, the research shows that as the efficiency of contract enforcement increases, the amount of short-term debt and long-term debt increases, while the direction change in debt maturity structure is uncertain and the specific relationship between them is closely related to the magnitude of all exogenous variables.

DOA estimation method of spatial spectrum product for distributed coprime linear array

Coprime array isAsparse array composed of two uniform linear arrays with different spacing. When the two subarrays are inAnon-coherent distributed configuration, the direction of arrival (DOA) method based on the covariance analysis of the complete coprime array is no longer effective. According to the essential attribute that the distance between the elements of two subarrays can eliminate the angle ambiguity, based on the mathematical derivation, Aspatial spectral product DOA estimation method for incoherent distributed coprime arrays is proposed. Firstly, the spatial spectrum of each subarray is calculated by using the snapshot data of each subarray, and then the DOA estimation is realized by multiplying the spatial spectrum of each subarray. The simulation results show that the estimation accuracy and angle resolution of the present method are better than those of the traditional ambiguity resolution methods, and the estimation performance is good in the mutual coupling and low SNR environment, with the good adaptability and stability. Moreover, by using the flexibility of distributed array, the matching error is effectively solved through the rotation angle.

The Uniqueness of Solution to the Inverse Eigenvalue Problem for an Arrow-shaped Generalised Jacobi Matrix

This paper studies the inverse eigenvalue problem for an arrow-shaped generalised Jacobi matrix, inverting matrices through two eigen-pairs. In the paper, the existence and uniqueness of the solution to the problem are discussed, and mathematical expressions as well as a numerical example are given. Finally, the uniqueness theorem of its matrix is established by mathematical derivation.