Robust portfolio modeling with incomplete cost information and project interdependencies

Robust portfolio modeling (RPM) [Liesiö, J., Mild, P., Salo, A., 2007. Preference programming for robust portfolio modeling and project selection. European Journal of Operational Research 181, 1488–1505] supports project portfolio selection in the presence of multiple evaluation criteria and incomplete information. In this paper, we extend RPM to account for project interdependencies, incomplete cost information and variable budget levels. These extensions lead to a multi-objective zero-one linear programming problem with interval-valued objective function coefficients for which all non-dominated solutions are determined by a tailored algorithm. The extended RPM framework permits more comprehensive modeling of portfolio problems and provides support for advanced benefit–cost analyses. It retains the key features of RPM by providing robust project and portfolio recommendations and by identifying projects on which further attention should be focused. The extended framework is illustrated with an example on product release planning.     

Scenario-based portfolio selection of investment projects with incomplete probability and utility information

In the selection of investment projects, it is important to account for exogenous uncertainties (such as macroeconomic developments) which may impact the performance of projects. These uncertainties can be addressed by examining how the projects perform across several scenarios; but it may be difficult to assign well-founded probabilities to such scenarios, or to characterize the decision makers’ risk preferences through a uniquely defined utility function. Motivated by these considerations, we develop a portfolio selection framework which (i) uses set inclusion to capture incomplete information about scenario probabilities and utility functions, (ii) identifies all the non-dominated project portfolios in view of this information, and (iii) offers decision support for rejection and selection of projects. The proposed framework enables interactive decision support processes where the implications of additional probability and utility information or further risk constraints are shown in terms of corresponding decision recommendations.     

Robust optimization for performance tuning of modern database systems

Issues regarding design and management of database systems have been studied by applying operations research (OR) techniques. The purpose of this study is to propose a new alternative towards database performance tuning for query-processing needs of modern database systems from the perspective of operations research using robust optimization. We use a query-driven approach to specify database structures (schema) so that they are robust to uncertainty and dynamics of queries in a changing environment and allow fast and timely information retrieval and exchange. Instead of applying hardware tuning or traditional database tuning techniques, we examine queries by their types and properties to derive database structures that are robust at efficiently processing future queries of any type. This query-driven approach improves the efficiency of processing queries by setting up database structures based on the queries’ information needs. This new methodology provides a new approach of tuning database performance that is robust to unexpected changes and dynamics. To further demonstrate the idea, we develop a robust optimization model using a non-linear von Neumann–Morgenstern expected utility function and present two computational examples.     

A robustness approach to uncapacitated network design problems

In this paper, we address uncapacitated network design problems characterised by uncertainty in the input data. Network design choices have a determinant impact on the effectiveness of the system. Design decisions are frequently made with a great degree of uncertainty about the conditions under which the system will be required to operate. Instead of finding optimal designs for a given future scenario, designers often search for network configurations that are “good” for a variety of likely future scenarios. This approach is referred to as the “robustness” approach to system design. We present a formal definition of “robustness” for the uncapacitated network design problem, and develop algorithms aimed at finding robust network designs. These algorithms are adaptations of the Benders decomposition methodology that are tailored so they can efficiently identify robust network designs. We tested the proposed algorithms on a set of randomly generated problems. Our computational experiments showed two important properties. First, robust solutions are abundant in uncapacitated network design problems, and second, the proposed algorithms performance is satisfactory in terms of cost and number of robust network designs obtained.     

Robust Model Averaging Method Based on LOF Algorithm

Model averaging is a good alternative to model selection, which can deal with the uncertainty from model selection process and make full use of the information from various candidate models. However, most of the existing model averaging criteria do not consider the influence of outliers on the estimation procedures. The purpose of this paper is to develop a robust model averaging approach based on the local outlier factor (LOF) algorithm which can downweight the outliers in the covariates. Asymptotic optimality of the proposed robust model averaging estimator is derived under some regularity conditions. Further, we prove the consistency of the LOF-based weight estimator tending to the theoretically optimal weight vector. Numerical studies including Monte Carlo simulations and a real data example are provided to illustrate our proposed methodology.     

A fuzzy approach to R&D project portfolio selection

A major advance in the development of project selection tools came with the application of options reasoning in the field of Research and Development (R&D). The options approach to project evaluation seeks to correct the deficiencies of traditional methods of valuation through the recognition that managerial flexibility can bring significant value to projects. Our main concern is how to deal with non-statistical imprecision we encounter when judging or estimating future cash flows. In this paper, we develop a methodology for valuing options on R&D projects, when future cash flows are estimated by trapezoidal fuzzy numbers. In particular, we present a fuzzy mixed integer programming model for the R&D optimal portfolio selection problem, and discuss how our methodology can be used to build decision support tools for optimal R&D project selection in a corporate environment.     

奖惩机制下零售商信息分享对闭环供应链的影响研究

研究奖惩机制下零售商的信息分享策略以及对闭环供应链的影响,建立了由制造商和零售商以及消费者组成的闭环供应链,其中制造商负责回收废旧产品并进行再制造。分别研究了集中式决策的情形和分散式决策下零售商信息分享和不分享的情形。研究发现,若政府在社会总福利目标中不考虑奖惩成本且回收难度较小时,零售商信息分享使社会总福利提高,反之,导致社会总福利降低;零售商信息分享总会使消费者剩余的期望值降低,但能够提高废旧产品的回收率。最后,针对零售商信息分享引起社会福利提高的情况设计了回收责任分担契约激励零售商分享信息。关键词:信息分享;奖惩机制;闭环供应链;社会福利;消费者剩余     

Cost-efficiency analysis of weapon system portfolios

Decisions about the acquisition and maintenance of military equipment serve to build long-term capabilities in preparation of military conflicts. Typically, these decisions involve large investments which need to be supported by adequate cost-efficiency analyses. Yet the cost-efficiency analysis of weapon systems involves several challenges: for example, it is necessary to account for the possible interactions among different weapon systems; the relevance of several impact criteria; and the variety of combat situations in which these systems may be used. In this paper, we develop a portfolio methodology where these challenges are addressed by evaluating the cost-efficiencies of entire portfolios consisting of individual weapon systems. Our methodology accounts for possible interactions among systems by synthesizing impact assessment results that are either generated by combat simulation models or elicited from experts. It also admits incomplete preference information about the relative importance of different impact criteria. This methodology guides decision making by identifying which combinations of weapon systems are efficient with respect to multiple evaluation criteria in different combat situations at different cost levels. It can also be extended to settings where multiple combat situations are addressed simultaneously. The methodology is generic and can therefore be applied also in civilian settings when portfolios of activities (such as mitigation of harmful environmental emissions) may exhibit interactions.     

Robust spectral risk optimization when the subjective risk aversion is ambiguous: a moment-type approach

Choice of a risk measure for quantifying risk of an investment portfolio depends on the decision maker’s risk preference. In this paper, we consider the case when such a preference can be described by a law invariant coherent risk measure but the choice of a specific risk measure is ambiguous. We propose a robust spectral risk approach to address such ambiguity. Differing from Wang and Xu (SIAM J Optim 30(4):3198–3229, 2020), the new robust model allows one to elicit the decision maker’s risk preference through pairwise comparisons and use the elicited preference information to construct an ambiguity set of risk spectra. The robust spectral risk measure (RSRM) is based on the worst case risk spectrum from the set. To calculate RSRM and solve the associated optimal decision making problem, we use a technique from Acerbi and Simonetti (Portfolio optimization with spectral measures of risk. Working paper, 2002) to develop a new computational approach which is independent of order statistics and reformulate the robust spectral risk optimization problem as a single deterministic convex programming problem when the risk spectra in the ambiguity set are step-like. Moreover, we propose an approximation scheme when the risk spectra are not step-like and derive a bound for the model approximation error and its propagation to the optimal decision making problems. Some preliminary numerical test results are reported about the performance of the robust model and the computational scheme.

     

On Statistical Inference Based on Record Values

We develop methodology for conducting inference based on record values and record times derived from a sequence of independent and identically distributed random variables. The advantage of using information about record times as well as record values is stressed. This point is a subtle one, since if the sampling distribution F is continuous then there is no information at all about F in the record times alone; the joint distribution of any number of them does not depend on F. However, the record times and record values jointly contain considerably more information about F than do the record values alone. Indeed, in the case of a distribution with regularly varying tails, the rate of convergence of the exponent of regular variation is two orders of magnitude faster if information about record times is included. Optimal estimators and convergence rates are derived under simple, specific models, and shown to be surprisingly robust against significant departures from those models. However, even under our special models the estimators have irregular properties, including an undefined information matrix. To some extent these difficulties may be alleviated by conditioning and by considering the relationship between maximum likelihood and maximum probability estimators.     

A framework for sensitivity analysis of decision trees

In the paper, we consider sequential decision problems with uncertainty, represented as decision trees. Sensitivity analysis is always a crucial element of decision making and in decision trees it often focuses on probabilities. In the stochastic model considered, the user often has only limited information about the true values of probabilities. We develop a framework for performing sensitivity analysis of optimal strategies accounting for this distributional uncertainty. We design this robust optimization approach in an intuitive and not overly technical way, to make it simple to apply in daily managerial practice. The proposed framework allows for (1) analysis of the stability of the expected-value-maximizing strategy and (2) identification of strategies which are robust with respect to pessimistic/optimistic/mode-favoring perturbations of probabilities. We verify the properties of our approach in two cases: (a) probabilities in a tree are the primitives of the model and can be modified independently; (b) probabilities in a tree reflect some underlying, structural probabilities, and are interrelated. We provide a free software tool implementing the methods described.

     

A robust optimization approach to wine grape harvesting scheduling

Optimization models are increasingly being used in agricultural planning. However, the inherent uncertainties present in agriculture make it difficult. In recent years, robust optimization has emerged as a methodology that allows dealing with uncertainty in optimization models, even when probabilistic knowledge of the phenomenon is incomplete. In this paper, we consider a wine grape harvesting scheduling optimization problem subject to several uncertainties, such as the actual productivity that can be achieved when harvesting. We study how effective robust optimization is solving this problem in practice. We develop alternative robust models and show results for some test problems obtained from actual wine industry problems.     

A mixed-method optimisation and simulation framework for supporting logistical decisions during offshore wind farm installations

With a typical investment in excess of £100 million for each project, the installation phase of offshore wind farms (OWFs) is an area where substantial cost-reductions can be achieved; however, to-date there have been relatively few studies exploring this. In this paper, we develop a mixed-method framework which exploits the complementary strengths of two decision-support methods: discrete-event simulation and robust optimisation. The simulation component allows developers to estimate the impact of user-defined asset selections on the likely cost and duration of the full or partial completion of the installation process. The optimisation component provides developers with an installation schedule that is robust to changes in operation durations due to weather uncertainties. The combined framework provides a decision-support tool which enhances the individual capability of both models by feedback channels between the two, and provides a mechanism to address current OWF installation projects. The combined framework, verified and validated by external experts, was applied to an installation case study to illustrate the application of the combined approach. An installation schedule was identified which accounted for seasonal uncertainties and optimised the ordering of activities.     

Interactive outranking approaches for multicriteria decision-making problems with imprecise information

PROMETHEE is a powerful method, which can solve many multiple criteria decision making (MCDM) problems. It involves sophisticated preference modelling techniques but requires too much a priori precise information about parameter values (such as criterion weights and thresholds). In this paper, we consider a MCDM problem where alternatives are evaluated on several conflicting criteria, and the criterion weights and/or thresholds are imprecise or unknown to the decision maker (DM). We build robust outranking relations among the alternatives in order to help the DM to rank the alternatives and select the best alternative. We propose interactive approaches based on PROMETHEE method. We develop a decision aid tool called INTOUR, which implements the developed approaches.     

Constructing and evaluating balanced portfolios of R&D projects with interactions: A DEA based methodology

We propose and demonstrate a methodology for the construction and analysis of efficient, effective and balanced portfolios of R&D projects with interactions. The methodology is based on an extended data envelopment analysis (DEA) model that quantifies some the qualitative concepts embedded in the balanced scorecard (BSC) approach. The methodology includes a resource allocation scheme, an evaluation of individual projects, screening of projects based on their relative values and on portfolio requirements, and finally a construction and evaluation of portfolios. The DEA–BSC model is employed in two versions, first to evaluate individual R&D projects, and then to evaluate alternative R&D portfolios. To generate portfolio alternatives, we apply a branch-and-bound algorithm, and use an accumulation function that accounts for possible interactions among projects. The entire methodology is illustrated via an example in the context of a governmental agency charged with selecting technological projects.     

Stochastic multiobjective acceptability analysis for the Choquet integral preference model and the scale construction problem

The Choquet integral preference model is adopted in Multiple Criteria Decision Aiding (MCDA) to deal with interactions between criteria, while the Stochastic Multiobjective Acceptability Analysis (SMAA) is an MCDA methodology considered to take into account uncertainty or imprecision on the considered data and preference parameters. In this paper, we propose to combine the Choquet integral preference model with the SMAA methodology in order to get robust recommendations taking into account all parameters compatible with the preference information provided by the Decision Maker (DM). In case the criteria are on a common scale, one has to elicit only a set of non-additive weights, technically a capacity, compatible with the DM’s preference information. Instead, if the criteria are on different scales, besides the capacity, one has to elicit also a common scale compatible with the preferences given by the DM. Our approach permits to explore the whole space of capacities and common scales compatible with the DM’s preference information.     

Optimal project portfolio selection with carryover constraint

In a typical capital rationing problem, a project portfolio is selected to maximize expected return on investment while adhering to the capital budget constraint. Sometimes projects may be delayed and they have to be funded beyond their planned completion time. This type of ‘unplanned carryovers’ represents a financial obligation to the company. If future years' capital budgets cannot be expanded to cover such obligations, future projects may be cancelled or postponed to fund the unplanned carryover. In this paper, we develop a methodology based on multi-attribute utility theory and chance-constrained programming to optimize portfolio selection subject to the constraints that the selected portfolio does not exceed the available budget and that the carryover of the unspent funds to the next fiscal year does not exceed predetermined limits. We use this technique to select an optimal project portfolio for Lockheed Martin Space Systems' infrastructure investments.     

US Coast Guard air station location with respect to distress calls: A spatial statistics and optimization based methodology

We study the problem of suitably locating US Coast Guard air stations to respond to emergency distress calls. Our goal is to identify robust locations in the presence of uncertainty in distress call locations. Our analysis differs from the literature primarily in the way we model this uncertainty. In our optimization and simulation based methodology, we develop a statistical model and demonstrate our procedure using a real data set of distress calls. In addition to guiding strategic decisions of placement of various stations, our methodology is also able to provide guidance on how the resources should be allocated across stations.     

政府奖惩机制下零售商主导的闭环供应链微分博弈策略

本文在考虑政府奖惩机制下,研究零售商主导的闭环供应链中成员的动态均衡策略,其中制造商负责回收再制造,回收率随时间动态变化。分别构建了三种模式下的Stackelberg微分博弈模型:政府不对制造商和零售商实施奖惩机制、政府只对制造商实施奖惩机制以及政府同时对制造商和零售商实施奖惩机制。运用贝尔曼连续型动态规划理论,求解了三种模式下制造商和零售商的决策均衡结果并进行了对比分析,从消费者剩余价值和成员利润的视角证明了政府实施奖惩机制的有效性。最后通过算例对成员均衡策略进行了稳态分析和非稳态分析。研究结果表明:政府的奖惩机制能够正确引导闭环供应链成员做出最优决策,有利于减缓分散决策所带来的双重边际效应,提高消费者剩余价值。零售商分担回收责任会削减政府对制造商回收的激励作用,降低闭环供应链整体利润。相比之下,政府只对制造商实施奖惩机制是最优模式选择,可以同时提高经济和环保双重效益。     

Subagging for credit scoring models

The logistic regression framework has been for long time the most used statistical method when assessing customer credit risk. Recently, a more pragmatic approach has been adopted, where the first issue is credit risk prediction, instead of explanation. In this context, several classification techniques have been shown to perform well on credit scoring, such as support vector machines among others. While the investigation of better classifiers is an important research topic, the specific methodology chosen in real world applications has to deal with the challenges arising from the real world data collected in the industry. Such data are often highly unbalanced, part of the information can be missing and some common hypotheses, such as the i.i.d. one, can be violated. In this paper we present a case study based on a sample of IBM Italian customers, which presents all the challenges mentioned above. The main objective is to build and validate robust models, able to handle missing information, class unbalancedness and non-iid data points. We define a missing data imputation method and propose the use of an ensemble classification technique, subagging, particularly suitable for highly unbalanced data, such as credit scoring data. Both the imputation and subagging steps are embedded in a customized cross-validation loop, which handles dependencies between different credit requests. The methodology has been applied using several classifiers (kernel support vector machines, nearest neighbors, decision trees, Adaboost) and their subagged versions. The use of subagging improves the performance of the base classifier and we will show that subagging decision trees achieve better performance, still keeping the model simple and reasonably interpretable.