Miguel A. Lejeune

An Exact Solution Approach for Portfolio Optimization Problems Under Stochastic and Integer Constraints

In this paper, we study extensions of the classical Markowitz mean-variance portfolio optimization model. First, we consider that the expected asset returns are stochastic by introducing a probabilistic constraint, which imposes that the expected return of the constructed portfolio must exceed a prescribed return threshold with a high confidence level. We study the deterministic equivalents of these models. In particular, we define under which types of probability distributions the deterministic equivalents are second-order cone programs and give closed-form formulations. Second, we account for real-world trading constraints (such as the need to diversify the investments in a number of industrial sectors, the nonprofitability of holding small positions, and the constraint of buying stocks by lots) modeled with integer variables. To solve the resulting problems, we propose an exact solution approach in which the uncertainty in the estimate of the expected returns and the integer trading restrictions are simultaneously considered. The proposed algorithmic approach rests on a nonlinear branch-and-bound algorithm that features two new branching rules. The first one is a static rule, called idiosyncratic risk branching, while the second one is dynamic and is called portfolio risk branching. The two branching rules are implemented and tested using the open-source Bonmin framework. The comparison of the computational results obtained with state-of-the-art MINLP solvers ( MINLP_BB and CPLEX ) and with our approach shows the effectiveness of the latter, which permits to solve to optimality problems with up to 200 assets in a reasonable amount of time. The practicality of the approach is illustrated through its use for the construction of four fund-of-funds now available on the major trading markets.

Measuring the impact of data mining on churn management

Churn management is a fundamental concern for businesses and the emergence of the digital economy has made the problem even more acute. Companies’ initiatives to handle churn and customers’ profitability issues have been directed to more customer‐oriented strategies. In this paper, we present a customer relationship management framework based on the integration of the electronic channel. This framework is constituted of four tools that should provide an appropriate collection, treatment and analysis of data. From this perspective, we pay special attention to some of the latest data mining developments which, we believe, are destined to play a central role in churn management. Relying on sensitivity analysis, we propose an analysis framework able to prefigure the possible impact induced by the ongoing data mining enhancements on churn management and on the decision‐making process.

A variable neighborhood decomposition search method for supply chain management planning problems

Abstract Few models have been developed for the integrated planning and scheduling of the inventory, production and distribution functions. In this paper, we consider a three-stage supply chain, for which a sustainable inventory–production–distribution plan over a multi-period horizon is constructed. The associated program takes the form of a general mixed-integer program, for which the sole reliance upon exact methods is shown to be insufficient. We use a solution algorithm based on the variable neighborhood decomposition search metaheuristics, that can be seen as a stagewise exploration of increasingly large neighborhoods. The stages are related to the decomposition scheme, i.e., the order on which integrality conditions are restored. Within each stage, a sequence of neighborhoods is defined relying on the variable neighborhood search metaheuristics, while the exploration of the successive neighborhoods is performed using a branch-and-bound algorithm. The methodology is validated through its application to a problem faced by a large supply chain. Empirical results show that (i) the methodology performs best when the decomposition scheme accounts for the possibility of resources bottleneck, (ii) the primary source of savings originates from the distribution function and (iii) congestion must be defined with respect to the availability of the distribution resources at the periods with high requirements.

MIP reformulations of the probabilistic set covering problem

In this paper, we address the following probabilistic version (PSC) of the set covering problem:

Stochastic network design for disaster preparedness

{\min\{cx\,|\,{\mathbb P}(Ax \ge \xi) \ge p, x \in \{0, 1\}^N\}}

A logical analysis of banks' financial strength ratings

where A is a 0-1 matrix,

Mathematical programming approaches for generating p-efficient points

{\xi}