Modeling and solving the multi-period inventory routing problem with constant demand rates

The inventory routing problem (IRP) is one of the challenging optimization problems in supply chain logistics. It combines inventory control and vehicle routing optimization. The main purpose of the IRP is to determine optimal delivery times and quantities to be delivered to customers, as well as optimal vehicle routes to distribute these quantities. The IRP is an underlying logistical optimization problem for supply chains implementing vendor-managed inventory (VMI) policies, in which the supplier takes responsibility for the management of the customers' inventory. In this paper, we consider a multi-period inventory routing problem assuming constant demand rates (MP-CIRP). The proposed model is formulated as a linear mixed-integer program and solved with a Lagrangian relaxation method. The solution obtained by the Lagrangian relaxation method is then used to generate a close to optimal feasible solution of the MP-CIRP by solving a series of assignment problems. The numerical experiments carried out so far show that the proposed Lagrangian relaxation approach nds quite good solutions for the MP-CIRP and in reasonable computation times

The existence of positive solution for an elliptic problem with critical growth and logarithmic perturbation

We consider the existence and nonexistence of positive solution for the following Br\'ezis-Nirenberg problem with logarithmic perturbation: \begin{equation*} \begin{cases} -\Delta u={\left|u\right|}^{{2}^{\ast }-2}u+\lambda u+\mu u\log {u}^{2} &x\in \Omega, \quad \;\:\, u=0& x\in \partial \Omega, \end{cases} \end{equation*} where $\Omega$ $\subset$ $\R^N$ is a bounded smooth domain, $\lambda, \mu \in \R$, $N\ge3$ and ${2}^{\ast }:=\frac{2N}{N-2}$ is the critical Sobolev exponent for the embedding $H^1_{0}(\Omega)\hookrightarrow L^{2^\ast}(\Omega)$. The uncertainty of the sign of $s\log s^2$ in $(0, +\infty)$ has some interest in itself. We will show the existence of positive ground state solution which is of mountain pass type provided $\lambda\in \R, \mu>0$ and $N\geq 4$. While the case of $\mu<0$ is thornier. However, for $N=3,4$ $\lambda\in (-\infty, \lambda_1(\Omega))$, we can also establish the existence of positive solution under some further suitable assumptions. And a nonexistence result is also obtained for $\mu<0$ and $-\frac{(N-2)\mu}{2}+\frac{(N-2)\mu}{2}\log(-\frac{(N-2)\mu}{2})+\lambda-\lambda_1(\Omega)\geq 0$ if $N\geq 3$. Comparing with the results in Br\'ezis, H. and Nirenberg, L. (Comm. Pure Appl. Math. 1983), some new interesting phenomenon occurs when the parameter $\mu$ on logarithmic perturbation is not zero

An exact algorithm for the single-vehicle cyclic inventory routing problem

The single-vehicle cyclic inventory routing problem (SV CIRP) consists of a repetitive distribution of a product from a single depot to a selected subset of customers. For each customer that is selected for replenishments, the supplier collects a corresponding xed reward. The objective is to determine the subset of customers to replenish, the quantity of the product to be delivered to each, and to design the vehicle route so that the resulting pro t (di erence between the total reward and the total logistical cost) is maximized while preventing stockouts at each of the selected customers. In this paper, the SV CIRP is formulated as a mixed-integer program with a nonlinear objective function. After an e cient analysis of the problem, an exact algorithm for its solution is proposed. This exact algorithm requires only solutions of linear mixed-integer programs. Values of an insertion-based heuristic for this problem are compared to the optimal values obtained for a set of some test problems. In general the gap may get as large as 25%, which justi es the e ort to continue exploring and developing exact and approximation algorithms for the SV CIRP.Postprint (published version

Open-Vocabulary Argument Role Prediction for Event Extraction

The argument role in event extraction refers to the relation between an event and an argument participating in it. Despite the great progress in event extraction, existing studies still depend on roles pre-defined by domain experts. These studies expose obvious weakness when extending to emerging event types or new domains without available roles. Therefore, more attention and effort needs to be devoted to automatically customizing argument roles. In this paper, we define this essential but under-explored task: open-vocabulary argument role prediction. The goal of this task is to infer a set of argument roles for a given event type. We propose a novel unsupervised framework, RolePred for this task. Specifically, we formulate the role prediction problem as an in-filling task and construct prompts for a pre-trained language model to generate candidate roles. By extracting and analyzing the candidate arguments, the event-specific roles are further merged and selected. To standardize the research of this task, we collect a new event extraction dataset from WikiPpedia including 142 customized argument roles with rich semantics. On this dataset, RolePred outperforms the existing methods by a large margin. Source code and dataset are available on our GitHub repository: https://github.com/yzjiao/RolePredComment: EMNLP 2022 Finding

Analysis of factors affecting the effectiveness of oil spill clean-up: A bayesian entwork approach

Ship-related marine oil spills pose a significant threat to the environment, and while it may not be possible to prevent such incidents entirely, effective clean-up efforts can minimize their impact on the environment. The success of these clean-up efforts is influenced by various factors, including accident-related factors such as the type of accident, location, and environmental weather conditions, as well as emergency response-related factors such as available resources and response actions. To improve targeted and effective responses to oil spills resulting from ship accidents and enhance oil spill emergency response methods, it is essential to understand the factors that affect their effectiveness. In this study, a data-driven Bayesian network (TAN) analysis approach was used with data from the U.S. Coast Guard (USCG) to identify the key accident-related factors that impact oil spill clean-up performance. The analysis found that the amount of discharge, severity, and the location of the accident are the most critical factors affecting the clean-up ratio. These findings are significant for emergency management and planning oil spill clean-up efforts.Postprint (published version

Author Correction: Magnesium intake and mortality due to liver diseases: Results from the Third National Health and Nutrition Examination Survey Cohort

A correction to this article has been published and is linked from the HTML and PDF versions of this paper. The error has been fixed in the paper

Senescence risk score: a multifaceted prognostic tool predicting outcomes, stemness, and immune responses in colorectal cancer

Colorectal cancer (CRC) remains a primary cause of cancer mortality globally, necessitating precise prognostic indicators for effective clinical management. Our study introduces the Senescence Risk Score (SRRS), based on several senescence-related genes (SRGs), a potent prognostic tool designed to measure cellular senescence in CRC. The higher SRRS predicts a poorer prognosis, providing a novel and efficient approach to patient stratification. Notably, we found that SRRS correlates with methylation and mutation variations, and increased immune infiltration in the tumor microenvironment, thus revealing potential therapeutic targets. We also discovered an inverse relationship between SRRS and cell stemness, which could have significant implications for cancer treatment strategies. Utilizing bioinformatics resources and machine learning, we identified LIMK1 and WRN as key genes associated with SRRS, further enhancing its prognostic value. Importantly, the modulation of these genes significantly impacts cellular senescence, proliferation, and stemness in CRC cells. In summary, our development of SRRS offers a powerful tool for CRC prognosis and paves the way for novel therapeutic strategies, underscoring its potential in transforming CRC patient management

Influence of Audiovisual Training on Horizontal Sound Localization and Its Related ERP Response

The objective was to investigate the influence of audiovisual training on horizontal sound localization and the underlying neurological mechanisms using a combination of psychoacoustic and electrophysiological (i.e., event-related potential, ERP) measurements on sound localization. Audiovisual stimuli were used in the training group, whilst the control group was trained using auditory stimuli only. Training sessions were undertaken once per day for three consecutive days. Sound localization accuracy was evaluated daily after training, using psychoacoustic tests. ERP responses were measured on the first and last day of tasks. Sound localization was significantly improved in the audiovisual training group when compared to the control group. Moreover, a significantly greater reduction in front-back confusion ratio for both trained and untrained angles was found between pre- and post-test in the audiovisual training group. ERP measurement showed a decrease in N1 amplitude and an increase in P2 amplitude in both groups. However, changes in late components were only found in the audiovisual training group, with an increase in P400 amplitude and decrease in N500 amplitude. These results suggest that the interactive effect of audiovisual localization training is likely to be mediated at a relatively late cognitive processing stage