Dual Objective Segmentation to Improve Targetability: An Evolutionary Algorithm Approach**

Cluster‐based segmentation usually involves two sets of variables: (i) the needs‐based variables (referred to as the bases variables), which are used in developing the original segments to identify the value, and (ii) the classification or background variables, which are used to profile or target the customers. The managers’ goal is to utilize these two sets of variables in the most efficient manner. Pragmatic managerial interests recognize the underlying need to start shifting from methodologies that obtain highly precise value‐based segments but may be of limited practical use as they provide less targetable segments. Consequently, the imperative is to shift toward newer segmentation approaches that provide greater focus on targetable segments while maintaining homogeneity. This requires dual objective segmentation, which is a combinatorially difficult problem. Hence, we propose and examine a new evolutionary methodology based on genetic algorithms to address this problem. We show, based on a large‐scale Monte Carlo simulation and a case study, that the proposed approach consistently outperforms the existing methods for a wide variety of problem instances. We are able to obtain statistically significant and managerially important improvements in targetability with little diminution in the identifiability of value‐based segments. Moreover, the proposed methodology provides a set of good solutions, unlike existing methodologies that provide a single solution. We also show how these good solutions can be used to plot an efficient Pareto frontier. Finally, we present useful insights that would help managers in implementing the proposed solution approach effectively.     

Efficient frontiers for electricity procurement by an LDC with multiple purchase options

In meeting its retail sales obligations, management of a local distribution company (LDC) must determine the extent to which it should rely on spot markets, forward contracts, and the increasingly popular long-term tolling agreements under which it pays a fee to reserve generator capacity. We address these issues by solving a mathematical programming model to derive the efficient frontier that summarizes the optimal tradeoffs available to the LDC between procurement risk and expected cost. To illustrate the approach, we estimate the expected procurement costs and associated variances that proxy for risk through a spot-price regression for the spot-purchase alternative and a variable-cost regression for the tolling-agreement alternative. The estimated regressions yield the estimates required to determine the efficient frontier. We develop several such frontiers under alternative assumptions as to the forward-contract price and the tolling agreement's capacity payment, and discuss the implications of our results for LDC management.     

Centralized resource allocation based on efficiency analysis for step-by-step improvement paths

The existing centralized resource allocation models often assume that all of the DMUs are efficient after resource allocation. For the DMU with a very low efficiency score, it means the dramatic reduction of the resources, which can cause the organizational resistance. In addition, in reality, it is particularly difficult for the DMUs to achieve their target efficiencies in a single step, especially when they are far from the efficient frontier. Thus, gradual progress towards benchmarking targets is gaining importance. In this paper, we present a new approach for resource allocation based on efficiency analysis under a centralized decision-making environment. Through our approach, the central decision-maker can obtain a sequence of intermediate benchmark targets based on efficiency analysis, which provide a level-wise improvement path to direct the DMUs to reach their ultimate targets on the efficient frontier in an implementable and realistic manner. Numerical examples are presented to illustrate the application procedure of the proposed approach.     

Portfolio optimization: New capabilities and future methods

Summary  This paper addresses the problem of portfolio selection in finance. In many cases, currently available software to compute the efficient frontier runs into difficulty in problems with more than about 600 securities. To proceed beyond this size, it is often necessary to modify the problem in which case there is typically a loss of information. In this paper, we discuss a computer capability that can exactly compute mean-variance efficient frontiers of problems with up to 2,000 securities in very reasonable time (even if a problem’s covariance matrix is 100% dense). The paper also discusses an augmentation to the theory of portfolio selection that allows multiple objectives (such as dividends, liquidity, social responsibility, amount invested in R&D, and so forth) to be incorporated into the portfolio selection process. In such problems, the efficient set is no longer a “frontier,” but is now best described as a “surface” with the interesting property that it is composed of platelets (like on the back of a turtle). Moreover, the computer capability that can compute the exact efficient frontier of a mean-variance problem with up to 2,000 securities also has, after additional coding, the ability to compute exactly all platelets of the efficient surface of a tri-criterion portfolio problem with up to 400 securities.

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Zusammenfassung  In dieser Arbeit stellen wir einen leistungsf?higen Rechenalgorithmus vor, um den effizienten Rand (die nichtdominierten Alternativen) von Portfolio-Auswahlproblemen in der Finanzierung zu bestimmen. Wir bezeichnen den Berechnungsalgorithmus, der in Java programmiert ist, mit MPQ (multi-parametric quadratic programming). MPQ weist gegenüber bisherigen Berechnungsverfahren eine Reihe von Vorteilen auf: Es kann für umfangreiche Anwendungsf?lle genutzt werden, ist durch passable Rechenzeiten charakterisiert und kann die Menge effizienter Alternativen in einem Bruchteil bisher üblicher Rechenzeiten bestimmen.

     

奇导协方差矩阵和任意收益率分布下均值-CVaR模型的有效边界特征

本文利用现代主流风险度量技术CVaR代替方差或VaR,建立了均值-CVaR模型,在任意收益率分布下,利用无套利均衡分析的方法研究了奇异协方差矩阵情形的投资组合问题,得到了模型有效边界的本质特征,最后作为结论的直接应用和说明,我们给出了一个具体的算例分析。     

考虑交易成本的投资组合效率估计方法

投资组合绩效评价是学术界研究的热点问题。本文在经典的经济学框架下,基于真实前沿面,给出了投资组合效率的明确定义。由于实际投资环境的影响,投资组合优化模型非常复杂,难以获得真实前沿面的解析解,这给投资组合效率的应用带来了很大的困难。本文基于投资组合理论,在投资组合模型所对应的前沿面为凹函数的情况下,采用基于数据的投资组合DEA评价模型构造前沿面来逼近真实的前沿面,从而估计一般情形下投资组合的效率。在此基础上研究了考虑交易成本的投资组合效率评价问题,并用实例说明了本文方法的合理性与可行性。     

不确定终止时间的多阶段最优投资组合

研究了当终止时间不确定时的多阶段最优投资组合问题.假定终止时间是个服从某分布的随机变量,将不确定终止时间的问题转化为确定时间的问题,应用动态规划求解模型,得到最优投资策略以及有效边界的解析形式.实例证明所得的结论是对确定终止时间情形的推广,最优投资策略受终止时间分布的影响.     

Using branch-and-price approach to solve the directed network design problem with relays

We present node-arc and arc-path formulations, and develop a branch-and-price approach for the directed network design problem with relays (DNDR). The DNDR problem can be used to model many network design problems in transportation, service, and telecommunication system, where relay points are necessary. The DNDR problem consists of introducing a subset of arcs and locating relays on a subset of nodes such that in the resulting network, the total cost (arc cost plus relay cost) is minimized, and there exists a directed path linking the origin and destination of each commodity, in which the distances between the origin and the first relay, any two consecutive relays, and the last relay and the destination do not exceed a predefined distance limit. With the node-arc formulation, we can directly solve small DNDR instances using mixed integer programming solver. With the arc-path formulation, we design a branch-and-price approach, which is a variant of branch-and-bound with bounds provided by solving linear programs using column generation at each node of the branch-and-bound tree. We design two methods to efficiently price out columns and present computational results on a set of 290 generated instances. Results demonstrate that our proposed branch-and-price approach is a computationally efficient procedure for solving the DNDR problem.     

Solution Procedures for the Lot-Streaming Problem

Lot streaming is the process of splitting a job into sublots so its operations can be overlapped and its progress accelerated. We present a computationally efficient procedure for solving the m-machine, two-sublot problem, and we discuss the bottleneck insights that emerge from the analysis. We also examine heuristic approaches for more than two sublots and discuss computational results for these procedures.     

A new two-party bargaining mechanism

If resources and facilities from different partners need to be engaged for a large-scale project with a huge number of tasks, any of which is indivisible, decision on the number of tasks assigned to any collaborating partner often requires a certain amount of coordination and bargaining among these partners so that the ultimate task allocation can be accepted by any partner in a business union for the project. In the current global financial crisis, such cases may appear frequently. In this paper, we first investigate the behavior of such a discrete bargaining model often faced by service-based organizations. In particular, we address the general situation of two partners, where the finite Pareto efficient (profit allocation) set does not possess any convenient assumption for deriving a bargaining solution, namely a final profit allocation (corresponding to a task assignment) acceptable to both partners. We show that it is not appropriate for our discrete bargaining model to offer the union only one profit allocation. Modifying the original optimization problem used to derive the Nash Bargaining Solution (NBS), we develop a bargaining mechanism and define a related bargaining solution set to fulfil one type of needs on balance between profit-earning efficiency and profit-earning fairness. We then show that our mechanism can also suit both Nash’s original concave bargaining model and its continuous extension without the concavity of Pareto efficient frontier on profit allocation.     

基于Copula-APD-GARCH模型的投资组合有效前沿分析

根据ES风险度量方法,拓展了马克维茨均值-方差资产组合模型,研究均值-ES准则下的资产组合问题.用APD-GARCH模型刻画风险资产收益率序列,以多元Copula函数描述风险资产间的相关结构信息,构造灵活的Copula-APDG-ARCH模型.利用该模型,借助Monte Carlo模拟,分别研究相关结构是多元正态Copula函数、多元t-Copula函数和多元Clayton Copula函数的风险资产组合的均值一ES有效前沿,并进行比较.实证研究表明,在有效组合范围内,正态Copula函数明显高估了资产的组合风险;当期望收益较小时,t-Copula函数对应的风险值最小,但随着期望收益的增加,多元Clayton Copula函数时应的有效前沿表现最好.     

Multi-objective machine-component grouping in cellular manufacturing: A genetic algorithm

The cellular manufacturing system (CMS) is an important group technology (GT) application. The first step of CMS design is cell formation, generally known as machinecell formation (MCF) or machine-component (MCG). A genetic algorithm (GA) is a robust adaptive optimization method based on principles of natural evolution and is appropriate for the MCG problem, which is an NP complete complex problem. In this study, we propose a GA-based procedure to solve the MCG problem. More specifically, this study aims to minimize (1) total cost, which includes intercell and intracell part transportation costs and machines investment cots; (2) intracell machine loading imbalance; and (3) intercell machine loading imbalance under many realistic considerations. An illustrative example and comparisons demonstrate the effectiveness of this procedure. The proposed procedure is extremely adaptive, flexible, efficient and can be used to solve real MCG problems in factories by providing robust manufacturing cell formation in a short execution time.     

基于最近距离投影的DEA两阶段效率评价方法研究

数据包络分析是进行效率评价最重要的方法之一。传统的数据包络分析理论主要寻找有效前沿面上的最远距离投影，在极大化无效性指数的同时也面临着效率改进的巨大难度和高额成本。对于具有两阶段内部生产结构的决策单元，本文从考虑最小改进难度的视角出发，提出了最近距离投影的两阶段效率评价方法。该方法首先得到所有强有效决策单元的线性组合，且这些组合均占优于被评价的两阶段决策单元。然后建立了两阶段范围调整效率评价模型，在确定具有最近投影距离的占优组合的同时，得到了两阶段评价效率。最后，本文运用我国32家上市银行的年度数据对所提出方法进行了应用验证。     

Portfolio rebalancing with an investment horizon and transaction costs

In this paper we consider the problem of rebalancing an existing financial portfolio, where transaction costs have to be paid if we change the amount held of any asset. These transaction costs can be fixed (so paid irrespective of the amount traded provided a trade occurs) and/or variable (related to the amount traded). We indicate the importance of the investment horizon when rebalancing such a portfolio and illustrate the nature of the efficient frontier that results when we have transaction costs. We model the problem as a mixed-integer quadratic programme with an explicit constraint on the amount that can be paid in transaction cost. Our model incorporates the interplay between optimal portfolio allocation, transaction costs and investment horizon. We indicate how to extend our model to include cardinality constraints and present a number of enhancements to the model to improve computational performance. Results are presented for the solution of publicly available test problems involving up to 1317 assets.     

效用函数意义下投资组合有效选择问题的研究

我们知道,每个投资者在进行投资过程中,都有自己对收益与风险的偏好程度,即投资活动要遵循一个关于收益与风险的效用函数。按照古典经济学的分析,这个效用函数称为无差异曲线 (IDC),它是用均值 -方差来表现风险 -回报率相互替换的大小和形式的。每个投资者都拥有一条无差异曲线来表示他对于预期回报率和标准差的偏好。那么投资者如何确定他的一条无差异曲线,使他的最佳资产组合位于这条无差异曲线上 ?本文运用自己独创的一种几何方法解决了这个难题。本文首先把Markowitz模型的有效前沿用投资组合的权重向量表示出来,然后将无差异曲线也用抽资组合的权重向量表示出来,再由资产组合的有效选择原则就求出这个无差异曲线了。     

The determination of the least distance to the strongly efficient frontier in Data Envelopment Analysis oriented models: Modelling and computational aspects

Determining the least distance to the efficient frontier for estimating technical inefficiency, with the consequent determination of closest targets, has been one of the relevant issues in recent Data Envelopment Analysis literature. This new paradigm contrasts with traditional approaches, which yield furthest targets. In this respect, some techniques have been proposed in order to implement the new paradigm. A group of these techniques is based on identifying all the efficient faces of the polyhedral production possibility set and, therefore, is associated with the resolution of a NP-hard problem. In contrast, a second group proposes different models and particular algorithms to solve the problem avoiding the explicit identification of all these faces. These techniques have been applied more or less successfully. Nonetheless, the new paradigm is still unsatisfactory and incomplete to a certain extent. One of these challenges is that related to measuring technical inefficiency in the context of oriented models, i.e., models that aim at changing inputs or outputs but not both. In this paper, we show that existing specific techniques for determining the least distance without identifying explicitly the frontier structure for graph measures, which change inputs and outputs at the same time, do not work for oriented models. Consequently, a new methodology for satisfactorily implementing these situations is proposed. Finally, the new approach is empirically checked by using a recent PISA database consisting of 902 schools.     

On the max-weight edge coloring problem

We study the following generalization of the classical edge coloring problem: Given a weighted graph, find a partition of its edges into matchings (colors), each one of weight equal to the maximum weight of its edges, so that the total weight of the partition is minimized. We explore the frontier between polynomial and NP-hard variants of the problem, with respect to the class of the underlying graph, as well as the approximability of NP-hard variants. In particular, we present polynomial algorithms for bounded degree trees and star of chains, as well as an approximation algorithm for bipartite graphs of maximum degree at most twelve which beats the best known approximation ratios.     

Closest targets and strong monotonicity on the strongly efficient frontier in DEA

The determination of closest efficient targets has attracted increasing interest of researchers in recent Data Envelopment Analysis (DEA) literature. Several methods have been introduced in this respect. However, only a few attempts exist that analyze the implications of using closest targets on the technical inefficiency measurement. In particular, least distance measures based on Hölder norms satisfy neither weak nor strong monotonicity on the strongly efficient frontier. In this paper, we study Hölder distance functions and show why strong monotonicity fails. Along this line, we provide a solution for output-oriented models that allows assuring strong monotonicity on the strongly efficient frontier. Our approach may also be extended to the most general case, i.e. non-oriented models, under some conditions of regularity.     

A multi-criteria approach to fair and efficient bandwidth allocation

In systems which serve many users there is a need to respect some fairness rules while looking for the overall efficiency. This applies among others to network design where a central issue is how to allocate bandwidth to flows efficiently and fairly. The so-called max–min fairness is widely used to meet these goals. However, allocating the bandwidth to optimize the worst performance may cause a large worsening of the overall throughput of the network. In this paper we show how the concepts of mult-criteria equitable optimization can effectively be used to generate various fair and efficient allocation schemes. We introduce a multi-criteria model equivalent to equitable optimization and we develop a corresponding reference point procedure to generate fair and efficient bandwidth allocations. Our analysis is focused on the nominal network design for elastic traffic that is currently the most significant traffic of IP networks. The procedure is tested on a sample network dimensioning problem for elastic traffic and its abilities to model various preferences are demonstrated.     

Removing the impact of environment with units-invariant efficient frontier analysis: An illustrative case study with intertemporal panel data

The four-stage methodology consists of a units-invariant efficient frontier analysis followed by Tobit regression, adjustment of data, and a repeat of the efficient frontier analysis. The outlined methodology is an improvement over existing similar approaches because the playing field can be levelled by adjusting data based on input as well as output slacks for managers who may have been advantaged or disadvantaged by their environments. The accompanying case study investigates the influence of the general level of interest rates on bank efficiency using intertemporal panel data spanning 8 years and two countries. Key findings support the assertion that changes in interest rates can distort measurement of bank efficiency.