Zhiqing Meng

A tri-level programming model based on Conditional Value-at-Risk for three-stage supply chain management

For the problem of supply chain management, the existing literature mainly focuses on the research of the single-stage supply chain or the two-stage supply chain that consists of a manufacturer and a retailer. To our best knowledge, little attention has been paid to the study of a more extensive supply chain that consists of a material supplier, a manufacturer and a retailer, which is a more practical and interesting case. Therefore, based on the Conditional Value-at-Risk (CVaR) measure of risk management, this paper proposes a tri-level programming model for the three-stage supply chain management. In this model, the material supplier and the manufacturer maximize their own profit while the retailer maximize his/her CVaR of expected profit. Further, we show that the proposed tri-level programming model can be transferred into a bilevel programming model, which can be solved by the existing methods. Numerical results show that the proposed model is efficient for improving the risk management of the three-stage supply chain.

On the Smoothing of the Square-Root Exact Penalty Function for Inequality Constrained Optimization

In this paper we propose two methods for smoothing a nonsmooth square-root exact penalty function for inequality constrained optimization. Error estimations are obtained among the optimal objective function values of the smoothed penalty problem, of the nonsmooth penalty problem and of the original optimization problem. We develop an algorithm for solving the optimization problem based on the smoothed penalty function and prove the convergence of the algorithm. The efficiency of the smoothed penalty function is illustrated with some numerical examples, which show that the algorithm seems efficient.

An objective penalty function method for nonlinear programming

In this paper, we propose a novel objective penalty function for inequality constrained optimization problems. The objective penalty function differs from any existing penalty function and also has two desired features: exactness and smoothness if the constraints and objective function are differentiable. An exact penalty result is proved for the objective penalty function. In addition to these results, based on the objective penalty function, we develop an algorithm for solving the original problem and show its convergence under some mild conditions.

A second-order smooth penalty function algorithm for constrained optimization problems

This paper introduces a second-order differentiability smoothing technique to the classical l1 exact penalty function for constrained optimization problems(COP). Error estimations among the optimal objective values of the nonsmooth penalty problem, the smoothed penalty problem and the original optimization problem are obtained. Based on the smoothed problem, an algorithm for solving COP is proposed and some preliminary numerical results indicate that the algorithm is quite promising.

Exactness and algorithm of an objective penalty function

Penalty function is an important tool in solving many constrained optimization problems in areas such as industrial design and management. In this paper, we study exactness and algorithm of an objective penalty function for inequality constrained optimization. In terms of exactness, this objective penalty function is at least as good as traditional exact penalty functions. Especially, in the case of a global solution, the exactness of the proposed objective penalty function shows a significant advantage. The sufficient and necessary stability condition used to determine whether the objective penalty function is exact for a global solution is proved. Based on the objective penalty function, an algorithm is developed for finding a global solution to an inequality constrained optimization problem and its global convergence is also proved under some conditions. Furthermore, the sufficient and necessary calmness condition on the exactness of the objective penalty function is proved for a local solution. An algorithm is presented in the paper in finding a local solution, with its convergence proved under some conditions. Finally, numerical experiments show that a satisfactory approximate optimal solution can be obtained by the proposed algorithm.

A penalty function method based on smoothing lower order penalty function

The paper introduces a smoothing technique for a lower order penalty function for constrained optimization problems (COP). It is proved that the optimal solution to the smoothed penalty optimization problem is a @e2-approximate optimal solution to the original optimization problem under some mild assumptions. Based on the smoothed penalty function, an algorithm for solving COP is proposed and some numerical examples are given.

A Smoothing Support Vector Machine Based on Quarter Penalty Function

It is very important to find out a smoothing support vec- tor machine. This paper studies a smoothing support vec- tor machine (SVM) by using quarter penalty function. We introduce the optimization problem of SVM with an uncon- strained and nonsmooth optimization problem via quarter penalty function. Then, we define a one-order differentiable function to approximately smooth the penalty function, and get an unconstrained and smooth optimization problem. By error analysis, we may obtain approximate solution of SVM by solving its approximately smooth penalty optimization problem without constraints. The numerical experiment shows that our smoothing SVM is efficient.

A Smoothing Objective Penalty Function Algorithm for Inequality Constrained Optimization Problems

In this article, a smoothing objective penalty function for inequality constrained optimization problems is presented. The article proves that this type of the smoothing objective penalty functions has good properties in helping to solve inequality constrained optimization problems. Moreover, based on the penalty function, an algorithm is presented to solve the inequality constrained optimization problems, with its convergence under some conditions proved. Two numerical experiments show that a satisfactory approximate optimal solution can be obtained by the proposed algorithm.

On the newsvendor model with conditional Value-at-Risk of opportunity loss

To manage the risk arising from uncertainty in market demand, this paper introduces the Conditional Value-at-Risk (CVaR) measure into the decision framework of the newsvendor who aims to minimise his opportunity loss. It is found under the CVaR measure that the newsvendor’s optimal order quantity is increasing in the confidence level when the understock loss is bigger than the overstock loss. This implies that an over-ordering may be even more caused by the newsvendor’s risk aversion about opportunity loss than risk seeking behaviour. Under this optimal order quantity, it is proved that the newsvendor’s expected profit and expected opportunity loss are decreasing and increasing in the confidence level, respectively. Furthermore, some management insights are presented to facilitate the risk management of the newsvendor model.

Coordination between a supplier and a retailer in terms of profit concession for a two-stage supply chain

This paper introduces a coordination model that copes with the conflicts between a supplier and a retailer in a two-stage supply chain. In this model, the supplier aims to maximise his/her profit, while the retailer aims to maximise his/her expected profit under a stochastic demand. To solve this model, an -coordination solution to this model is introduced, which implies the supplier and the retailer both will make a same concession in their profits to cooperate with each other. Further, we show that each feasible solution to this model is an -coordination solution for a sufficiently large value , while the -optimum coordination solution gives the minimum concession for the supplier and the retailer. Besides, it is proved that the -optimum coordination solution can be obtained by solving a mathematical programming problem. At last, a numerical example and sensitivity analysis are given to show the performance of the proposed method.