Tighter Bounds for the Gap and Non-IRUP Constructions in the One-dimensional Cutting Stock Problem

The one-dimensional cutting stock problem is investigated with respect to the difference between the optimal function values of the integer programming problem and its continuous relaxation. A tighter bound for this gap is presented, followed by some non-IRUP constructions. Finally, instances with gap 7/6 are constructed, the largest gap known so far.     

Heuristic for the rectangular two-dimensional single stock size cutting stock problem with two-staged patterns

Two-staged patterns are often used in manufacturing industries to divide stock plates into rectangular items. A heuristic algorithm is presented to solve the rectangular two-dimensional single stock size cutting stock problem with two-staged patterns. It uses the column-generation method to solve the residual problems repeatedly, until the demands of all items are satisfied. Each pattern is generated using a procedure for the constrained single large object placement problem to guarantee the convergence of the algorithm. The computational results of benchmark and practical instances indicate the following: (1) the algorithm can solve most instances to optimality, with the gap to optimality being at most one plate for those solutions whose optimality is not proven and (2) for the instances tested, the algorithm is more efficient (on average) in reducing the number of plates used than a published algorithm and a commercial stock cutting software package.     

Large gaps in one-dimensional cutting stock problems

Its linear relaxation is often solved instead of the one-dimensional cutting stock problem (1CSP). This causes a difference between the optimal objective function values of the original problem and its relaxation, called a gap. The size of this gap is considered in this paper with the aim to formulate principles for the construction of instances of the 1CSP with large gaps. These principles are complemented by examples for such instances.     

The three-factor model and artificial neural networks: predicting stock price movement in China

Since the establishment of the Shanghai Stock Exchange (SHSE) in 1990 and the Shenzhen Stock Exchange (SZSE) in 1991, China’s stock markets have expanded rapidly. Although this rapid growth has attracted considerable academic interest, few studies have examined the ability of conventional financial models to predict the share price movements of Chinese stock. This gap in the literature is significant, given the volatility of the Chinese stock markets and the added risk that arises from the Chinese legal and regulatory environment. In this paper we address this research gap by examining the predictive ability of several well-established forecasting models, including dynamic versions of a single-factor CAPM-based model and Fama and French’s three-factor model. In addition, we compare the forecasting ability of each of these models with that of an artificial neural network (ANN) model that contains the same predictor variables but relaxes the assumption of model linearity. Surprisingly, we find no statistical differences in the forecasting accuracy of the CAPM and three-factor model, a result that may reflect the emerging nature of the Chinese stock markets. We also find that each ANN model outperforms the corresponding linear model, indicating that neural networks may be a useful tool for stock price prediction in emerging markets.     

The cutting stock problem for large sections in the iron and steel industries

The characteristics of a cutting stock problem for large sections in the iron and steel industries are as follows:(1) There is a variety of criterions such as maximizing yield and increasing effeciency of production lines. (2) A cutting stock problem is accompanied by an optimal stock selection problem. A two-phase algorithm is developed, using an heuristic method. This algorithm gives nearly optimal solutions in real time. It is applied to both batch-solving and on-line solving of one-dimensional cutting of large section. The new algorithm has played an important role in a large-section production system to increase the yield by approximately 2.5%.     

中国股市收益率与异质波动性关系研究

本文研究了中国股票市场的异质波动性问题。主要从异质波动性的识别与分布,异质波动性与股票收益率之间的关系,以及异质波动性是否被充分定价等三方面进行探讨。研究的目的在于分析股票异质波动性问题在中国股票市场中的特殊地位,这其中也包括异质波动性对股票收益影响问题。结合中国股票市场的数据,采用广义矩估计(GMM)的数量方法,显著地得到了中国股票市场中异质波动性水平,并以此分析了异质波动性与股票收益之间的关系,证明股票异质波动性水平是投资者进行决策时需要考虑的重要因素之一。     

Decision making in stock trading: An application of PROMETHEE

The key issue for decision making in stock trading is selection of the right stock at the right time. In order to select the superior stocks (alternatives) for investment, a finite number of alternatives have to be ranked considering several and sometimes conflicting criteria. Therefore, we are faced with a special multicriteria decision-making problem. The purpose of this paper is to develop a decision-making model for selecting superior stocks in stock exchange and a model is provided in order to structure this problem. The proposed model is structured around two pillars: Industry evaluation and Company evaluation. The preference ranking organization method for enrichment evaluation (PROMETHEE) has been used for solving the problem. The model has been applied at Tehran Stock Exchange (TSE) as a real case and a survey from the experts in order to determine the effective criteria for industry evaluation and company evaluation has been conducted.     

随机执行日经理股票期权的定价及激励效用分析

针对标准支付型经理股票期权执行日确定的问题,提出具有随机执行日的支付型经理股票期权的定价公式;选择期权价值对股票价格的敏感性(delta)、期权价值对股票收益波动率的敏感性(vega)对经理股票期权进行激励效用分析;并通过改变部分参数的值,分析期权对经理激励作用的变化.     

The one-dimensional cutting stock problem with usable leftovers – A survey

In this article, we review published studies that consider the solution of the one-dimensional cutting stock problem (1DCSP) with the possibility of using leftovers to meet future demands, if long enough. The one-dimensional cutting stock problem with usable leftovers (1DCSPUL) is a problem frequently encountered in practical settings but often, it is not dealt with in an explicit manner. For each work reviewed, we present the application, the mathematical model if one is proposed and comments on the computational results obtained. The approaches are organized into three classes: heuristics, item-oriented, or cutting pattern-oriented.     

关于半无限规划的对偶间隙

该文对半无限凸规划（Ｐ）提出了一个对偶问题（Ｄ１），证明了（Ｄ１）与（Ｐ）无对偶间隙当且仅当Ｌａｇｒａｎｇｅ对偶问题（Ｄ）与（Ｐ）之间无对偶间隙，作者还利用方向导数给出一个新的刻划鞍点准则的方法。     

The combined cutting stock and lot-sizing problem in industrial processes

Despite its great applicability in several industries, the combined cutting stock and lot-sizing problem has not been sufficiently studied because of its great complexity. This paper analyses the trade-off that arises when we solve the cutting stock problem by taking into account the production planning for various periods. An optimal solution for the combined problem probably contains non-optimal solutions for the cutting stock and lot-sizing problems considered separately. The goal here is to minimize the trim loss, the storage and setup costs. With a view to this, we formulate a mathematical model of the combined cutting stock and lot-sizing problem and propose a solution method based on an analogy with the network shortest path problem. Some computational results comparing the combined problem solutions with those obtained by the method generally used in industry—first solve the lot-sizing problem and then solve the cutting stock problem—are presented. These results demonstrate that by combining the problems it is possible to obtain benefits of up to 28% profit. Finally, for small instances we analyze the quality of the solutions obtained by the network shortest path approach compared to the optimal solutions obtained by the commercial package AMPL.     

含交易费用的投资组合问题的新模型及其求解途径

本文提出了证券投资组合的一个新模型.该模型综合考虑了证券的收益率、证券分红和证券价格的关系,并将证券分红和证券价格作为系统的随机参数处理,建立了证券投资组合的随机规划模型.利用机会约束规划方法,我们研究了将所建立的随机规划模型转化为普通光滑优化问题求解的方法,得到了该类问题求解的有效途径.     

Mean–variance efficiency of DC pension plan under stochastic interest rate and mean-reverting returns

This paper studies the optimization problem of DC pension plan under mean–variance criterion. The financial market consists of cash, bond and stock. Similar to Guan and Liang (2014), we assume that the instantaneous interest rate is an affine process including the Cox–Ingersoll–Ross (CIR) model and Vasicek model. However, we assume that the expected return of the stock follows a completely different mean-reverting process, which can well display the bear and bull features of the market, and the market price of the stock index is the Ornstein–Uhlenbeck process. The pension manager thus has to undertake the risks of interest rate and market price of stock index. Besides, a special stochastic contribution rate is formulated. The goal of the pension manager is to maximize the expected terminal value and minimize the variance of terminal value. We will use the technique developed by Guan and Liang (2014) to tackle this problem and derive the closed-forms of efficient frontier and strategies. Numerical analysis is given in the end of this paper to show the economic behavior of the efficient frontier and strategies.     

Gap functions for generalized vector equilibrium problems via conjugate duality and applications

In this article, gap functions for a generalized vector equilibrium problem (GVEP) with explicit constraints are investigated. Under a concept of supremum/infimum of a set, defined in terms of a closure of the set, three kinds of conjugate dual problems are investigated by considering the different perturbations to GVEP. Then, gap functions for GVEP are established by using the weak and strong duality results. As application, the proposed approach is applied to construct gap functions for a vector optimization problem and a generalized vector variational inequality problem.     

Stochastic volatility asymptotics of stock loans: Valuation and optimal stopping

A stock loan, or equity security lending service, is a loan which uses stocks as collateral. The borrower has the right to repay the principal with interest and regain the stock, or make no repayment and surrender the stock. Therefore, the valuation of stock loan is an optimal stopping problem related to a perpetual American option with a negative effective interest rate. The negative effective interest rate makes standard techniques for perpetual American option pricing failure. Using a fast mean-reverting stochastic volatility model, we applied a perturbation technique to the free-boundary value problem for the stock loan price. An analytical pricing formula and optimal exercise boundary are derived by means of asymptotic expansion.     

A hybrid approach based on genetic algorithms to solve the problem of cutting structural beams in a metalwork company

This work presents a hybrid approach based on the use of genetic algorithms to solve efficiently the problem of cutting structural beams arising in a local metalwork company. The problem belongs to the class of one-dimensional multiple stock sizes cutting stock problem, namely 1-dimensional multiple stock sizes cutting stock problem. The proposed approach handles overproduction and underproduction of beams and embodies the reusability of remnants in the optimization process. Along with genetic algorithms, the approach incorporates other novel refinement algorithms that are based on different search and clustering strategies. Moreover, a new encoding with a variable number of genes is developed for cutting patterns in order to make possible the application of genetic operators. The approach is experimentally tested on a set of instances similar to those of the local metalwork company. In particular, comparative results show that the proposed approach substantially improves the performance of previous heuristics.     

A matching approach for replenishing rectangular stock sizes

Consider a replenishment problem in which several different rectangular sizes of material are stocked. Customers order rectangles of the material, but the rectangles ordered have a range on specified width as well as on specified length. To satisfy the customer requirements, the stock material can be cut once longitudinally in order to satisfy two customer requirements or not cut at all, that is, an entire stock piece of material is used to satisfy one customer requirement. If an exact match is impossible in the current planning period, the unused material must be returned to stock— an expensive and undesirable situation. In this paper, a nonbipartite weighted matching problem formulation will be given for determining the replenishment requirements of rectangular stock sizes. Then, a hybrid solution approach, capable of solving real applications (typically up to 3000 nodes) efficiently, will be discussed. This solution was implemented in September 1998 and has operated successfully since then.     

Enhanced lateral transshipments in a multi-location inventory system

In managing an inventory network, two approaches to the pooling of stock have been proposed. Reactive transshipments respond to shortages at a location by moving inventory from elsewhere within the network, while proactive stock redistribution seeks to minimize the chance of future stockouts. This paper is the first to propose an enhanced reactive approach in which individual transshipments are viewed as an opportunity for proactive stock redistribution. We adopt a quasi-myopic approach to the development of a strongly performing enhanced reactive transshipment policy. In comparison to a purely reactive approach to transshipment, service levels are improved while a reduction in safety stock levels is achieved. The aggregate costs incurred in managing the system are significantly reduced, especially so for large networks. Moreover, an optimal policy is determined for small networks and it is shown that the enhanced reactive policy substantially closes the gap to optimality.     

Tightening a copositive relaxation for standard quadratic optimization problems

We focus in this paper the problem of improving the semidefinite programming (SDP) relaxations for the standard quadratic optimization problem (standard QP in short) that concerns with minimizing a quadratic form over a simplex. We first analyze the duality gap between the standard QP and one of its SDP relaxations known as “strengthened Shor’s relaxation”. To estimate the duality gap, we utilize the duality information of the SDP relaxation to construct a graph G ^?. The estimation can be then reduced to a two-phase problem of enumerating first all the minimal vertex covers of G ^? and solving next a family of second-order cone programming problems. When there is a nonzero duality gap, this duality gap estimation can lead to a strictly tighter lower bound than the strengthened Shor’s SDP bound. With the duality gap estimation improving scheme, we develop further a heuristic algorithm for obtaining a good approximate solution for standard QP.     

Characterization of duality for a generalized quasi-equilibrium problem

In this paper, the duality theory of a generalized quasi-equilibrium problem (also called generalized Ky Fan quasi-inequality) is investigated by using the image space approach. Generalized quasi-equilibrium problem is transformed into a minimization problem. The minimization problem is further reformulated as an image problem by virtue of linear/nonlinear separation function. The dual problem of the image problem is constructed in the image space, then zero duality gap between the image problem and its dual problem is derived under saddle point condition as well as the equivalent regular linear/nonlinear separation condition. Finally, some more sufficient conditions guaranteeing zero duality gap are also proposed.