Table of Content

15 December 2010, Volume 14 Issue 4

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Original Articles

Influence of Real Interest Rate Volatilities  on Long-term Asset Allocation

XIE Yao, Liang-Zhi-An

2010, 14(4):  1-10. 

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For one-period investors, fixed income securities without default are risk-free asset, because the return of these securities can be determined at the beginning of investment period. However, considering long-term investment, investors are able to adjust their portfolio since fixed income securities would have risk of interest rate volatilities from reinvestment. So fixed income securities are no longer risk-free. This paper discusses long-term asset allocation under a frame of special ``habit formation" utility function. Under some assumption for simplicities, we derive the influence of real interest rate volatilities on weight of risky asset allocation, and provide theoretical basis and algorithm for calculating real optimal long-term asset allocation.

Parallel-batch Scheduling on Unrelated Machines  to Minimize the Sum Objectives

MIAO Cui-Xia, Zhang-Yu-Zhong, WANG Cheng-Fei

2010, 14(4):  11-20. 

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In this paper, we consider the parallel-batch scheduling problems on unrelated parallel machines. For the unbounded parallel-batch model,we discuss the special case: the processing times are agreeable, i.e.,$p_{ij}\leq p_{ik}$ for all $i=1, \cdots, m $, $1\leq j\neq k\leq n$, where $m$ and $n$ is the number of machines and jobs, respectively, and we design a dynamic programming algorithm to minimize the total completion time in polynomal time when $m$ is constant. For the bounded parallel-batch model, we discuss the case with $p_{ij}=p_{i}$ for $i=1, \cdots, m $ and $j=1,\cdots, n$, give an optimal algorithm for the general schedule to minimize the total weighted completion time, and design a pseudo-polynomial time algorithm for the case with rejection  to minimize the sum of the total weighted completion time of the accepted jobs and the total penalty of the rejected jobs.

A Conic Programming Approach for Robust Portfolio Optimization Problems

BAI Yan-Qin, SHU Xuan-Yu, ZHANG Hong-Jie

2010, 14(4):  21-31. 

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This paper deals with the robust portfolio optimization problems with linear transaction costs. The model is based on the worst-case Conditional Value-at-Risk (CVaR) risk measure and uncertainty for the portfolio return distribution. We show that the robust portfolio optimization problems with box uncertainty  and ellipsoidal uncertainty structures can be reformulated as linear programming and second-order cone programming, respectively. Moreover, we illustrate our model by an example of market data simulation.  

The Properties of Subdifferential for Set-Valued Mappings and Applications

GUO Xiao-Le, LI Sheng-Jie, LI Zhong-Wei

2010, 14(4):  32-40. 

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In this paper, some different properties of the subdifferential for set-valued mappings, which has been introduced in ``Subgradient of S-convex set-valued mappings and weak efficient solutions"(Appl. Math. J. Chinese Univ., 1998, 13(4): 463-472)  are discussed. Moreover, in virtue of the property of the contingent derivative, some exact calculus rules of the subdifferential for calculating the subdifferential for the sum, composition and intersection of two set-valued mappings. Finally, a necessary and sufficient optimality condition of set-valued optimization problems is discussed.  

Tardiness penalty and earliness award with learning effect processing time

YU Ying, SUN Shi-Jie, WANG Kai, HE Long-Min

2010, 14(4):  41-52. 

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In this paper, we consider a single-machine scheduling model with a given due date and learning effect processing time. The objective function is the total weighted tardiness penalty and earliness award. Our aim is to find an optimal sequence so as to minimize the objective function. As the problem is NP-hard, we give some polynomial time solvable cases of this problem. A branch and bound algorithm was given for general case of the problem based on a rapid method for estimating the lower bound.  

 The Feedback Control of the Control System of Prices Long-term Volatility in Efficient Stock Markets

ZOU Hui-Wen

2010, 14(4):  53-65. 

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The feedback control of the control system of prices long-term volatility in efficient stock markets is discussed. The control  system model of prices long-term volatility in efficient stock markets is built. According  to the conditions of system complete accomplishability, both of the following issues are  discussed respectively: issue of taking stock market policies as single-control nput  collocating poles, and that of taking listed corporations policies as single-control  input collocating poles. According to the conditions of system incomplete accomplishability,  the equanimity problems are respectively discussed both when the stock markets don't develop  and when the stock market doesn't carry out macro-regulation. A dimension-minus state observer   is designed to estimate stocks' intrinsic value. By choosing the stocks' corresponding average    intrinsic value when the listed corporations are increasing in equilibrium as the target value,   we design linear multi-variables adjustor to make the closed-loop system become stable gradually   and the output of the system  track that target value. Through the feedback control we can improve  the interior structure and performance of the control system, and arrive at the purpose of regulating the stock markets.  

 A New Model with Parameter for Ranking Efficient Units in Data Envelopment Analysis

WANG Jin-Shan, NI Min

2010, 14(4):  68-74. 

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 This paper pursues the measuring the efficient unit in DEA (data envelopment analysis), developing a rinking model with parameter by defining the most efficiency and the most unefficiency, which could rink the efficient unit. The paper gives the valuable strategic rinking rule and proves the advantage of the model. Some characteristics of our models are proposed. Applying this approach, the paper examines an example.

 Pollutant Emission Quota Allocation Based on DEA

BIAN Yi-Wen

2010, 14(4):  75-83. 

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  This paper describes a typical environment management problem, i.e., environment will be improved by allocating pollutant emission quotas. After analyzing the characteristics of the problem, a DEA-based approach is developed to address the problem. In the proposed approach, the pollutant emission quota is a type of decision variables in the proposed DEA model and it is allocated to decision making units (DMUs) by optimizing it when solving the proposed model. The approach, which is applied to 32 paper mills along the Huai River in China, indicates that the paper mill system's overall eco-efficiency is effectively improved. Since the proposed approach can improve the system's eco-efficiency by llocation the pollutant emission quota, it can provide more veracious information for environment management.  

 Preemptive Scheduling to Minimize  Maximum Earliness Cost

ZHONG Xue-Ling, WANG Guo-Qing, CHENG Ming-Bao, LI Xiao-Chun

2010, 14(4):  83-91. 

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This paper discusses the problem that $n$ jobs with their own deadlines and precedence constraints have to be processed on a single machine considering the idle insert. The objective is to find a preemptive job sequence and determine jobs' starting times so as to minimize the maximum earliness cost. Firstly, we consider two special cases: (1) common deadline and precedence constraints; (2) arbitrary deadlines and no precedence constraint. The $O(n^2)$ algorithms are provided respectively. Then the general case of arbitrary deadlines and precedence constraints is considered based on the two special cases, and an $O(n^2)$ algorithm is developed too. Since tardy jobs are prohibited, it's possible that there is no feasible sequence for the problem. We consider the feasibility primarily.

Investment Strategies in the Presence of a Minimum Performance Guarantee under Stochastic Interest Rate

LIU Fu-Bing, LIU Hai-Long

2010, 14(4):  92-100. 

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Under the stochastic interest rate environment, we consider fund manager’s optimal investment problem with a minimum performance guarantee. Using martingale method, we derive the explicit solution. The result shows that the optimal investment strategies include three parts: one is the speculative portfolio strategy, another is the hedge strategy for stochastic interest rate, the other is the replicating strategy for the benchmark portfolio which is used as the minimum performance guarantee. In addition, the optimal investment strategies at any time are equivalent to the strategies which are to invest in a portfolio which generates the amount of benchmark portfolio at the final date and to invest remainder of one’s wealth as if unconstrained

An Artificial Intelligence-Algebraic Algorithm for the Linear Goal Dimensional Resources Allocation Problems in  Programming and the Linear Programming

SUN Huan-Chun

2010, 14(4):  101-111. 

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So far the modified simplex method and simplex method have been used for the solution of the linear goal programming and linear programming respectively. Of course, these methods are effective and successful, but they are some what trouble and time-consuming when the scale of problem is larger. Recently author discovered that and artificial intelligence-algebraic algorithm can be used for solving this two kinds of problem. The main idea of this algorithm is that based on the practical background of the problem man's wisdom is used to analyse which of the inequality constraints should be equalties to make the optimized goal function or the objective function optimum. Asuming that there are $m'$ of equalities in $m$ inequality constraints, in which only $n$ decision variables are ncluded and so there are $n-m'$ of decision variables should be zeros to make the optimized goal function or the objective function optimum. The optimality condition is used to determine which of decision variables equal to zeros. At last, the optimum solution or the satistactory solution can be solved from the $m'$ equality equations including $m'$ decision variables. Many examples we collected show that this algorithm is very simple, rapid and effective and the results obtained by this algorithm and by the traditional simplex method are almost all consistent, exception of a few examples due to mistakes happened in the calculation of simplex methods. And so this algorithm posseses considerably wide applicability. But the universal applicability didn't be proved theretically yet. Therefore an important aim of this paper is to attract readers to investigate with us the problem of whether this algorithm posseses universal applicability.

 The Optimization of Four Ordinal Activities Pairs with Random Slack

WANG Jing, LI Xing-Mei, QI Jian-Xun

2010, 14(4):  112-120. 

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It is one of resource constrained project scheduling problems, which selecting 2\emph{m} activities from \emph{n} parallel activities to make \emph{m} ordinal activities pairs and minimize the affection on the project duration. In order to provide theories and methods for such problem, in this paper, we study the optimization problem that how to select eight parallel activities from \emph{n} ones to make four ordinal activities pairs. Based on present theory, optimal row-mate theorem is given, and founded on them, standard-criterion algorithm is designed and proved theoretically. Finally, an example is given to illustrate the feasibility of the algorithm.  

An Inexact Alternating Directions Method for Solving  Double Objective Optimization Problems

ZENG Yu-Hua, PENG Zheng

2010, 14(4):  121-128. 

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 In this paper,  a direct method,  namely  the  inexact alternating directions method, is proposed for solving double objective optimization problems. The convergence property of the proposed method is proved.  Some primary numerical results are presented to show that the proposed method is available and applicable.