Optimal Order Research Articles

Very high order finite volume solver for multi component two-phase flow with phase change using a posteriori Multi-dimensional Optimal Order Detection

Very high order finite volume solver for multi component two-phase flow with phase change using a posteriori Multi-dimensional Optimal Order Detection

Bayesian assessment of profitability for products with highly uncertain demand based on multiple samples

Abstract The achievable capacity index (ACI) is well suited to measuring the profitability of a newsboy-type product, wherein profitability is defined as the probability of achieving a target profit under the optimal order quantity. In retail/manufacturing situations where storage and production capacity are limited, profitability evaluation using ACI can be considered to select advantageous products. Although frequentist approaches are useful towards estimating the true ACI, the Bayesian approach may be preferable when prior information about the demand is available. In estimating the ACI, it may be necessary to deal with situations in which the demand is highly uncertain, the sample data consists of distinct subsets drawn from a demand population (i.e., multiple samples), and sampling error must be eliminated to avoid overestimates of profitability. This study seeks to overcome these issues by developing a Bayesian procedure for testing profitability based on multiple samples, focusing on exponentially distributed demand that can exhibit high uncertainty. The lower confidence bound of ACI is derived to express profitability estimates without sampling error. We also provide some tables to facilitate decision-making in evaluating profitability. We find that variations in confidence level and the evaluated criterion significantly influence the direction of decision-making, guiding managers to focus on controlling these factors. The practicality of the proposed method was demonstrated through a case study.

Two different eurozones: disentangling the labyrinth of the European economic dynamics

PurposeThis paper aims to analyze the possible interdependencies among fiscal, monetary and growth variables by applying multivariate Granger Causality and determining an ultimate “causality path” excluding redundant relationships based on a complex endogenous system for each country.Design/methodology/approachWe adopt a novel approach to test Granger Causality within the framework of Vector Autoregressive models. This approach enables us to expand the scope of relevant variables, which is typically limited to two or three, previously mentioned. Moreover, we employ graph-theoretic techniques for causal analysis, utilizing the PC algorithm (Colombo and Maathuis, 2014; Spirtes et al., 2000) to determine the optimal causal ordering among all statistically significant relationship.FindingsOur findings highlight the continued division between “core” and “peripheral” Euro area countries, with monetary policy variables playing a crucial role in the economic growth of “core” nations. Stable inflation contributes to sustained growth in these countries, while fiscal variables contribute to growth across most nations.Originality/valueThe literature concerning the relationship among different macroeconomic variables such as prices, output and monetary policy indicators such as interest rates and interest payments, may be incomplete or misguided due to the exclusion of relevant information because studies are mostly based on a bivariate or a trivariate framework dynamics. In this sense, one goal is the extension of the system, which may be crucial, because the omission of relevant variables may lead to biased results. Furthermore, we apply graph-theoretic methods for causal analysis by using the PC algorithm to determine the ultimate causal sequence among all possible ones and, finally, we aim to understand and disentangle the transmission process and the relationships among economic policies in a Euro area country-level analysis.

Entropy-based methods for formulating bottom-up ultra-coarse-grained models.

Bottom-up coarse-grained (CG) modeling is an effective means of bypassing the limited spatiotemporal scales of conventional atomistic molecular dynamics while retaining essential information from the atomistic model. A central challenge in CG modeling is the trade-off between accuracy and efficiency, as the inclusion of often pivotal many-body interaction terms in the CG force-field renders simulation markedly slower than simple pairwise models. The Ultra Coarse-Graining (UCG) method incorporates many-body terms through discrete internal state variables that modulate the CG force-field according to, e.g., changes in local environment when substantial chemical heterogeneities exist. However, assigning optimal internal states systematically from atomistic simulation data, as well as the practical application of bottom-up UCG theory to biomolecular systems, remain open problems. We develop two synergistic methods to aid in the development of UCG models that can capture inhomogeneities in atomistic systems such as those induced by phase coexistence. The first method establishes the systematic construction of UCG force-fields from a relative entropy minimization principle, while the second method utilizes machine-learning to obtain optimal local order parameters for enhanced model efficiency and transferability. We apply these methods to a methanol liquid-vapor interface and the ripple phase of a 1,2-dipalmitoyl-sn-glycero-3-phosphocholine lipid bilayer and demonstrate that UCG modeling alone recapitulates aspects of phase coexistence that are otherwise not observed in CG modeling.

Research on the Evaluation of Chinese Prefabricated Building Strategic Partners Based on Cloud Model and Improved Evidence Theory

In recent years, prefabricated buildings have developed rapidly in China. Compared with traditional buildings, prefabricated buildings require higher capabilities from partners in various aspects. However, due to the early stage of development of prefabricated buildings in China, the level of various enterprises varies greatly. How to evaluate partners scientifically and objectively is a realistic problem that needs to be solved urgently. In order to achieve economies of scale and promote the sustainable development of prefabricated buildings, this study proposes a novel evaluation model for strategic partner selection based on the cloud model and improved Dempster–Shafer (D-S) evidence theory. First, using a literature review and field research method, a strategic partner selection index system is developed that can reflect the characteristics of prefabricated buildings. To address the fuzziness and randomness of the traditional membership function, the cloud model is applied to calculate the membership value between the test samples and the benchmark cloud, which is subsequently transformed into basic probability distribution in the evidence theory. Furthermore, to mitigate the paradox of evidence fusion often encountered in traditional evidence theory, this model combines both the subjective and objective weights of evidence by game theory, and the conflicting evidence is corrected and fused according to the combination weight. Additionally, the Technique for Order Preference by Similarity to Ideal Solution (TOPSIS) method is used to further optimize the strategic partners of prefabricated buildings. Finally, the optimal order obtained from the case analysis is S1 > S2 > S4 > S3 > S5, and the evaluation results are consistent with the actual situation, which verifies the effectiveness and superiority of the proposed model in resolving the evidence conflict and selecting strategic partners. The research results have certain reference significance for optimizing the selection mechanism of prefabricated building strategic partners and guiding partners to establish long-term and stable cooperative relations.

A class of discontinuous Galerkin methods for nonlinear variational problems

In the context of discontinuous Galerkin methods, we study approximations of nonlinear variational problems. We propose element-wise nonconforming finite element methods to discretize the continuous minimisation problem. Using Γ \Gamma -convergence arguments we show that for convex energies the discrete minimisers converge to a minimiser of the continuous problem as the mesh parameter tends to zero, under the additional contribution of appropriately defined penalty terms at the level of the discrete energies. In addition, we provide error analysis in the case where the solution of the continuous minimization problem is smooth enough. Under appropriate assumptions we show local existence, uniqueness and corresponding optimal order error estimates for the discrete Euler-Lagrange equations of our scheme. We finally substantiate the feasibility of our methods by numerical examples.

The optimal ordering and packaging policies in e-commerce environment

Abstract Refunds pose a considerable challenge for e-tailers in China, and the primary cause of customer returns often stems from damage to goods attributed to improper logistics and shipping. However, employing appropriate packaging materials or techniques can significantly diminish the refund rate associated with commodity collision or crush. This paper concentrates on optimal ordering and packaging policies, wherein retailers allocate additional costs to enhance packaging techniques or materials, aiming to curtail the rate of damage to goods in transit. The theoretical findings indicate that retailers investing in new packaging materials or technologies can substantially impact the order quantity compared to scenarios where no such investments are made. An algorithm has been devised to investigate optimal ordering and packaging policies, with numerical examples illustrating the proposed model and algorithm. Through a sensitivity analysis, the paper explores the influence of four critical parameters—demand rate, setup cost, refund rate, and holding cost—on the optimal strategy. The discussion also provides managerial insights into the implications of the study.

Analysis of Soybean Raw Material Inventory Control for Production Sustainability at a Tofu Factory in Padang Cermin District, Pesawaran Regency

This study explores raw material inventory management at Bu Supi Tofu Factory in Padang Cermin, focusing on the Economic Order Quantity (EOQ) method to address challenges in soybean procurement. The factory uses a traditional purchasing system, leading to overstocking, increased costs, and reduced product quality. Through a qualitative-descriptive approach, the research evaluates the factory's current practices, calculates the optimal order quantity using the EOQ model, and compares it with the existing system. The results indicate that implementing EOQ can reduce ordering costs, storage expenses, and surplus stock while maintaining product quality and enhancing operational efficiency. This study highlights the potential benefits of applying modern inventory management techniques in small-scale industries to optimize resources and improve profitability.

Quickly Finding the Semantically Optimal Presentation Order for a Set of Text Artifacts

This study considers how to quickly find the order in which to present a set of text artifacts on mobile apps or websites such that those artifacts are maximally semantically separated. Semantic separation is desirable because it ensures that users experience as much novelty as possible from one item to the next, thereby improving user attention and engagement. Since an exhaustive search of all possible sequences of text items becomes increasingly infeasible as the length of the sequence grows, a new algorithm is proposed to quickly find the semantically optimal presentation order for a set of text artifacts. The performance of the proposed algorithm is evaluated using an extensive set of experiments involving three different types of text artifacts, seven different sequence lengths, and more than 600 experimental trials. The results demonstrate that the proposed algorithm can select statistically optimal sequences of text artifacts extremely quickly, regardless of the type of text artifacts being used as input or the length of the sequence. App and website developers who are seeking to hold users’ attention and improve user engagement may therefore find the proposed algorithm very attractive in comparison to an exhaustive search.

ANALISIS BIAYA PENJUALAN MENGGUNAKAN PERHITUNGAN POQ DALAM MERENCANAKAN DAN MENGENDALIKAN PERSEDIAAN POMPA AIR SUBMERSIBLE DI TOKO. XYZ

Optimal inventory management is one of the key elements in supply chain management, especially for companies focusing on products with fluctuating demand, such as submersible water pumps. This study aims to analyze the planning and control of submersible water pump inventory at PT. XYZ using the Period Order Quantity (POQ) method. The POQ method was chosen for its ability to determine the optimal order quantity based on actual demand periods, thereby minimizing inventory costs, including ordering and holding costs. The analysis process begins by identifying historical demand data, inventory costs, and other relevant parameters. Subsequently, the POQ method is applied to calculate the optimal order quantity for each period based on demand levels and the ordering cycle time. The study's findings indicate that implementing the POQ method can reduce total inventory costs compared to conventional methods employed by the company. Moreover, this method enhances inventory management efficiency by reducing ordering frequency and the risk of stockouts. In conclusion, the POQ method has proven effective in helping PT. XYZ manage submersible water pump inventory more efficiently and economically. The study recommends developing an integrated inventory information system to support the sustainable implementation of this method.

Research on the ordering strategy problem in supply chain with profit allocation under two-level price-fluctuation sales.

This paper investigates optimal ordering strategies in supply chains under two-level price fluctuations and initial profit allocation. By utilizing Copula functions to model the complex relationship between fluctuating prices and uncertain demand, the study develops both continuous and discrete decision models for practical applications. A discrete algorithm is proposed to approximate the optimal solution, with its convergence rigorously proven. Numerical experiments demonstrate that profit allocation ratios significantly impact optimal order quantities and overall supply chain profit. Price fluctuations, particularly at the discount level, present critical challenges, necessitating flexible and adaptive ordering strategies. The study also investigates the influence of different Copula relationships on optimal ordering decisions, revealing how varying market conditions-from moderate price sensitivity to high volatility-affect optimal order quantities. By examining ordering strategies in the context of profit allocation contracts, this research offers a new perspective on how supply chain members can collaboratively navigate uncertain markets. The findings provide actionable insights for managers to mitigate risks, improve coordination, and seize new opportunities. Extending traditional models to incorporate price fluctuations and profit allocation, this study makes theoretical and practical contributions to supply chain management, offering robust strategies to strengthen supply chain resilience.

Two‐Grid Finite Element Method for the Time‐Fractional Allen–Cahn Equation With the Logarithmic Potential

ABSTRACTIn this paper, we propose a two‐grid finite element method for solving the time‐fractional Allen–Cahn equation with the logarithmic potential. Firstly, with the L1 method to approximate Caputo fractional derivative, we solve the fully discrete time‐fractional Allen–Cahn equation on a coarse grid with mesh size and time step size . Then, we solve the linearized system with the nonlinear term replaced by the value of the first step on a fine grid with mesh size and the same time step size . We obtain the energy stability of the two‐grid finite element method and the optimal order of convergence of the two‐grid finite element method in the L2 norm when the mesh size satisfies . The theoretical results are confirmed by arithmetic examples, which indicate that the two‐grid finite element method can keep the same convergence rate and save the CPU time.

Application research of convolutional neural network and its optimization in lightning electric field waveform recognition

Quickly identifying and classifying lightning waveforms is the foundation of lightning forecasting and early warning. In this paper, based on the electric field observation of the Beijing lightning location website of the Institute of Atmospheric Physics, Chinese Academy of Sciences, a recognition and classification method of pulse signal waveform based on Convolutional Neural Network(CNN) algorithm is designed and implemented. The CNN network model and its parameters were optimized from three aspects: dataset, model parameters, and network structure, achieving a recognition rate of over 90%. The effects of various optimization terms and their different optimization orders on the training time of the model were studied. The results indicate that the CNN algorithm is suitable for the classification and recognition of lightning electric field (LEF) waveforms. Optimization can significantly improve recognition rate. The optimization method of fitting idealized waveforms can reduce noise in the dataset and significantly improve recognition rate, indicating that noise has a significant impact on waveform recognition. Therefore, it is necessary to perform noise preprocessing before recognition. The optimization has a huge impact on training efficiency, increasing training time by about 51% after optimization, but the influence of optimization order on it can be ignored.

Optimizing the Efficacy of Vaccine-Induced Immunotherapy in Melanomas.

Cancer therapeutic vaccines are used to strengthen a patient's own immune system by amplifying existing immune responses. Intralesional administration of the bacteria-based emm55 vaccine together with the PD1 checkpoint inhibitor produced a strong anti-tumor effect against the B16 melanoma murine model. However, it is not trivial to design an optimal order and frequency of injections for combination therapies. Here, we developed a coupled ordinary differential equations model calibrated to experimental data and used the mesh adaptive direct search method to optimize the treatment protocols of the emm55 vaccine and anti-PD1 combined therapy. This method determined that early consecutive vaccine injections combined with distributed anti-PD1 injections of decreasing separation time yielded the best tumor size reduction. The optimized protocols led to a twofold decrease in tumor area for the vaccine-alone treatment, and a fourfold decrease for the combined therapy. Our results reveal the tumor subpopulation dynamics in the optimal treatment condition, defining the path for efficacious treatment design. Similar computational frameworks can be applied to other tumors and other combination therapies to generate experimentally testable hypotheses in a fairly unrestricted and inexpensive setting.

Treatment of idiopathic granulomatous mastitis: a retrospective case series.

Idiopathic granulomatous mastitis (IGM) is a rare inflammatory disease of the breast. Various clinical management approaches have been described, but their efficacy and optimal sequential order remain uncertain. We describe the first Canadian cohort of patients with IGM, discuss treatment outcomes and outline a practical management approach. This retrospective study included patients diagnosed with biopsy-confirmed IGM between 2014 and 2023, aged over 18 years. Based on a scoping review of the literature, a diagnostic and management approach was developed, and we present here the disease course and outcomes using this approach. 22 females were included, with a mean age of 40 (24-65) years, mostly presenting with a breast lump (n =22, 100%) and breast pain (n = 15, 68%). Mean rheumatology follow-up was 28.7 months (range 3-79). Mean time from first symptom to diagnosis was 3.5 months (range 1-13). Corynebacterium kroppenstedtii was found in 8 patients. Treatment including lipophilic antibiotics, corticosteroids and disease modifying anti-rheumatic drugs (DMARDs), led to complete remission in 95% of patients, in a mean time of 11.6 months (range 1-36), and relapse in only 1 patient. 11 patients required DMARDs (50%), most commonly methotrexate (n=9). We highlight the variable severity of IGM and the benefits of a severity-based treatment approach. A diligent evaluation and work-up is essential to manage IGM. The proposed severity-based management approach with medical treatment and less aggressive surgical intervention led to complete remission in 95%.

Optimal second order boundary regularity for solutions to p-Laplace equations

Optimal second order boundary regularity for solutions to p-Laplace equations

Weak dependence and optimal quantitative self-normalized central limit theorems

Consider a stationary, weakly dependent sequence of random variables. Given only mild conditions, allowing for polynomial decay of the autocovariance function, we show a Berry–Esseen bound of optimal order n^{-1/2} for studentized (self-normalized) partial sums, both for the Kolmogorov and Wasserstein (and L^{p} ) distances. The results show that in general, (minimax) optimal estimators of the long-run variance lead to suboptimal bounds in the central limit theorem, that is, the rate n^{-1/2} cannot be reached, refuting a popular belief in the literature. This can be salvaged by simple methods. We reveal that in order to maintain the optimal speed of convergence n^{-1/2} , simple over-smoothing within a certain range is necessary and sufficient. The setup contains many prominent dynamical systems and time series models, including random walks on the general linear group, products of positive random matrices, functionals of GARCH models of any order, functionals of dynamical systems arising from stochastic differential equations, iterated random functions and many more.

An Optimal Three-point Eighth Order Iterative Method for Solving Non-linear Equations and The Attraction basins

An Optimal Three-point Eighth Order Iterative Method for Solving Non-linear Equations and The Attraction basins

Local Discontinuous Adaptive Finite Element Method for Steklov Eigenvalue Problems

Using the flexibility of the finite element method to solve the solution problems on different shaped and natured elements, the local discontinuous Galerkin method can handle very complex boundary problems. Using the local discontinuous Galerkin method to perform a priori error estimation for the Steklov eigenvalue problem, we obtain a reasonable error estimation subspace, which can effectively solve the validity and reliability of the eigenfunction indicator subspace and the reliability of the eigenvalue error estimation indicator. We use precise numerical data obtained from MATLAB experiments as the basis for judging whether the conclusion is reasonable. Finally, combining theoretical analysis, we show that the method achieves optimal convergence order.

ПРО ДЕЯКІ ОПТИМІЗАЦІЙНІ ВЛАСТИВОСТІ ОПЕРАТОРА ГАУССА–ВЕЄРШТРАССА

We consider the problem of the theory of function approximation concerning the analysis of linear summation methods of Fourier series, namely finding the optimal ones in one sense or another. To determine the optimal approximation order, the authors solve two important problems. First, the Gauss–Weierstrass operator is proved to be a saturated method, and its saturation order is found; second, saturation classes for this method are found. Keywords: optimization properties of functions, Gauss–Weierstrass operator, saturation order, saturation class.