A Multi-echelon Inventory System with Supplier Selection and Order Allocation under Stochastic Demand

This article addresses the development of an integrated supplier selection and inventory control problems in supply chain management by developing a mathematical model for a multi-echelon system. In particular, a buyer firm that consists of one warehouse and N identical retailers wants to procure a type of product from a group of potential suppliers, which may require different price, ordering cost, lead time and have restriction on minimum and maximum total order size, to satisfy the stochastic demand. A continuous review system that implements the order quantity, reorder point (Q, R) inventory policy is considered in the model. The objective of the model is to select suppliers and to determine the optimal inventory policy that coordinates stock level between each echelon of the system while properly allocating orders among selected suppliers to maximize the expected profit. The model has been solved by decomposing the mixed integer nonlinear programming model into two sub-models. Numerical experiments are conducted to evaluate the model and some managerial insights are obtained by performing some sensitivity analysis

A novel feature selection framework for incomplete data

Feature selection on incomplete datasets is an exceptionally challenging task. Existing methods address this challenge by first employing imputation methods to complete the incomplete data and then conducting feature selection based on the imputed data. Since imputation and feature selection are entirely independent steps, the importance of features cannot be considered during imputation. However, in real-world scenarios or datasets, different features have varying degrees of importance. To address this, we propose a novel incomplete data feature selection framework that considers feature importance. The framework mainly consists of two alternating iterative stages: the M-stage and the W-stage. In the M-stage, missing values are imputed based on a given feature importance vector and multiple initial imputation results. In the W-stage, an improved reliefF algorithm is employed to learn the feature importance vector based on the imputed data. Specifically, the feature importance vector obtained in the current iteration of the W-stage serves as input for the next iteration of the M-stage. Experimental results on both artificially generated and real incomplete datasets demonstrate that the proposed method outperforms other approaches significantly

Effective Multi-echelon Inventory Systems for Supplier Selection and Order Allocation

Successful supply chain management requires an effective sourcing strategy to counteract uncertainties in both the suppliers and demands. Therefore, determining a better sourcing policy is critical in most of industries. Supplier selection is an essential task within the sourcing strategy. A well-selected set of suppliers makes a strategic difference to an organization\u27s ability to reduce costs and improve the quality of its end products. To discover the cost structure of selecting a supplier, it is more interesting to further determine appropriate levels of inventory in each echelon for different suppliers. This dissertation focuses on the study of the integrated supplier selection, order allocation and inventory control problems in a multi-echelon supply chain. First, we investigate a non-order-splitting inventory system in supply chain management. In particular, a buyer firm that consists of one warehouse and N identical retailers procures a type of product from a group of potential suppliers, which may have different prices, ordering costs, lead times and have restriction on minimum and maximum total order size, to satisfy stochastic demand. A continuous review system that implements the order quantity, reorder point (Q, R) inventory policy is considered in the proposed model. The model is solved by decomposing the mixed integer nonlinear programming model into two sub-models. Numerical experiments are conducted to evaluate the model and some managerial insights are obtained with sensitivity analysis. In the next place, we extend the study to consider the multi-echelon system with the order-splitting policy. In particular, the warehouse acquisition takes place when the inventory level depletes to a reorder point R, and the order Q is simultaneously split among m selected suppliers. This consideration is important since it could pool lead time risks by splitting replenishment orders among multiple suppliers simultaneously. We develop an exact analysis for the order-splitting model in the multi-echelon system, and formulate the problem in a Mixed Integer Nonlinear Programming (MINLP) model. To demonstrate the solvability and the effectiveness of the model, we conduct several numerical analyses, and further conduct simulation models to verify the correctness of the proposed mathematical model

Vorticity wave interaction and exceptional points in shear flow instabilities

We establish a link between vorticity wave interaction and $\mathcal{PT}$-symmetry breaking in shear flow instabilities. The minimal dynamical system for two coupled counter-propagating vorticity waves is shown to be a non-Hermitian system that exhibits a saddle-node exceptional point. The mechanism of phase-locking and mutual growth of vorticity waves is then related to the Krein collision and the breaking of $\mathcal{PT}$-symmetry through the exceptional point. The key parameter that leads the system to spontaneous $\mathcal{PT}$-symmetry breaking is the ratio between frequency detuning and coupling strength of the vorticity waves. The critical behavior near the exceptional point is described as a transition between phase-locking and phase-slip dynamics of the vorticity waves. The phase-slip dynamics lead to non-modal, transient growth of perturbations in the regime of unbroken $\mathcal{PT}$-symmetry, and the phase-slip frequency $\Omega \propto |k-k_c|^{1/2}$ shares the same critical exponent with the phase rigidity of system eigenvectors. The results can be readily extended to the interaction of multiple vorticity waves with multiple exceptional points and rich transient dynamics.Comment: 10 pages, 13 figure