Juan Pérez

Cost-based feature selection for Support Vector Machines: An application in credit scoring

In this work we propose two formulations based on Support Vector Machines for simultaneous classification and feature selection that explicitly incorporate attribute acquisition costs. This is a challenging task for two main reasons: the estimation of the acquisition costs is not straightforward and may depend on multivariate factors, and the inter-dependence between variables must be taken into account for the modelling process since companies usually acquire groups of related variables rather than acquiring them individually. Mixed-integer linear programming models are proposed for constructing classifiers that constrain acquisition costs while classifying adequately. Experimental results using credit scoring datasets demonstrate the effectiveness of our methods in terms of predictive performance at a low cost compared to well-known feature selection approaches.

jPhase: an object-oriented tool for modeling phase-type distributions

Phase-Type distributions are a powerful tool in stochastic modeling of real systems. In this paper, we describe an object-oriented tool used to represent and manipulate these distributions as computational objects. It allows the computation of multiple closure properties that can be used when modeling large systems with multiple interactions. The tool also includes procedures for fitting the parameter of a distribution from a data set and capabilities for generating random numbers from a specified distribution. This framework is built in a flexible and expandable way, and, therefore, it is not limited to the algorithms provided.

Pricing and composition of bundles with constrained multinomial logit

In this paper, we propose an extension of the problem of bundling with multinomial logit, making an explicit inclusion of the consumers’ maximum willingness to pay (MWTP) by means of the constrained multinomial logit (CMNL). In the bundling problem, we determine the price and the composition of bundles offered for a single segment of consumers by a firm, which is competing with others in the market, and we compare this result to a base case in which the consumers’ MWTP is not considered. We assume these consumers as rational since they choose the bundle that maximise their utility and the bundle price is within their MWTP. The resulting model is a non-linear mixed integer programme which is solved in two steps: (i) pricing is the first step; the prices are numerically determined in a fixed point equations system and (ii) in the second step the composition of the bundle is determined by explicit enumeration. The results show that the price obtained is less than the one got in the case without CMNL (and bigger than the costs), and the composition of the offered bundle is different as well. It is possible to conclude that not considering the consumers’ MWTP in the context of the problem of bundling will imply an overestimation of the firm’s profit. We have analysed as well the results for a Chilean telecommunications company. These results show the importance of including the MWTP in the pricing and composition process.

A fast Newton's iteration for M/G/1-type and GI/M/1-type Markov chains

In this article we revisit Newtons iteration as a method to find the G or R matrix in M/G/1-type and GI/M/1-type Markov chains. We start by reconsidering the method proposed in Ref.[ 15 ], which required O(m 6 + Nm 4) time per iteration, and show that it can be reduced to O(Nm 4), where m is the block size and N the number of blocks. Moreover, we show how this method is able to further reduce this time complexity to O(Nr 3 + Nm 2 r 2 + m 3 r) when A 0 has rank r < m. In addition, we consider the case where [A 1 A 2…A N ] is of rank r < m and propose a new Newtons iteration method which is proven to converge quadratically and that has a time complexity of O(Nm 3 + Nm 2 r 2 + mr 3) per iteration. The computational gains in all the cases are illustrated through numerical examples.

Integrated framework for profit-based feature selection and SVM classification in credit scoring

Abstract In this paper, we propose a profit-driven approach for classifier construction and simultaneous variable selection based on linear Support Vector Machines. The main goal is to incorporate business-related information such as the variable acquisition costs, the Types I and II error costs, and the profit generated by correctly classified instances, into the modeling process. Our proposal incorporates a group penalty function in the SVM formulation in order to penalize the variables simultaneously that belong to the same group, assuming that companies often acquire groups of related variables for a given cost rather than acquiring them individually. The proposed framework was studied in a credit scoring problem for a Chilean bank, and led to superior performance with respect to business-related goals.

A reconfiguration of fire station and fleet locations for the Santiago Fire Department

The geographical distribution of the population of the city of Santiago, Chile, has changed significantly in recent years. In spite of this fact, the location of the fire stations has remained unchanged. We propose a model for the optimal location of the fire stations and a fleet assignment for the Santiago Fire Department (SFD), aimed at maximising the number of events attended to with a predefined standard response. The results of the model are compared with respect to the current location of fire stations and fleet assignment in the SFD. There are different types of resources (stations and vehicles), and different types of events in which the same types of vehicles are used. We analyse various possible current and future scenarios, using a forecast based on historical data. Our results show that by optimally reallocating the resources a 10–30% increase can be achieved in the number of emergency calls that are attended to with an adequate response in time and number of vehicles, without the need for additional fire stations or vehicles. Thus our contribution is empirical and relies on the real world application which is being considered by Chilean government.

Impact of Dampening Demand Variability in a Production/Inventory System with Multiple Retailers

We study a supply chain consisting of a single manufacturer and two retailers. The manufacturer produces goods on a make-to-order basis, while both retailers maintain an inventory and use a periodic replenishment rule. As opposed to the traditional (r, S) policy, where a retailer at the end of each period orders the demand seen during the previous period, we assume that the retailers dampen their demand variability by smoothing the order size. More specifically, the order placed at the end of a period is equal to β times the demand seen during the last period plus (1 − β) times the previous order size, with β ∈ (0, 1] the smoothing parameter. We develop a GI/M/1-type Markov chain with only two nonzero blocks A 0 and A d to analyze this supply chain. The dimension of these blocks prohibits us from computing its rate matrix R in order to obtain the steady state probabilities. Instead we rely on fast numerical methods that exploit the structure of the matrices A 0 and A d , i.e., the power method, the Gauss–Seidel iteration, and GMRES, to approximate the steady state probabilities. Finally, we provide various numerical examples that indicate that the smoothing parameters can be set in such a manner that all the involved parties benefit from smoothing. We consider both homogeneous and heterogeneous settings for the smoothing parameters.

The impact of dampening demand variability in a production/inventory system with multiple retailers (abstract only)

We study a supply chain consisting of a single manufacturer and two retailers. The manufacturer produces goods on a make-to-order basis, while both retailers maintain an inventory and use a periodic replenishment rule. As opposed to the traditional (r, S) policy, where a retailer at the end of each period orders the demand seen during the previous period, we assume that the retailers dampen their demand variability by smoothing the order size. More specifically, the order placed at the end of a period is equal to ß times the demand seen during the last period plus (1?ß) times the previous order size, with ß ? (0, 1] the smoothing parameter.n We develop a GI/M/1-type Markov chain with only two nonzero blocks A0 and Ad to analyze this supply chain. The dimension of these blocks prohibits us from computing its rate matrix R in order to obtain the steady state probabilities. Instead we rely on fast numerical methods that exploit the structure of the matrices A0 and Ad, i.e., the power method, the Gauss-Seidel iteration and GMRES, to approximate the steady state probabilities.n Finally, we provide various numerical examples that indicate that the smoothing parameters can be set in such a manner that all the involved parties benefit from smoothing. We consider both homogeneous and heterogeneous settings for the smoothing parameters.

jMarkov package: a stochastic modeling tool

When analyzing real life stochastic systems in most cases is easier, cheaper and more effective to use analytical models rather than studying the physical system or a simulation model of it. The stochastic modeling is a powerful tool that helps the analysis and optimization of stochastic systems.n However the use of stochastic modeling is not widely spread in todays industries and among practitioners. This lack of acceptance is caused by two main reasons the first being the curse of dimensionality, which is defined by the number of states required to describe a system. This number grows exponentially as the size of the system increases. The second reason is the lack of user-friendly and efficient software packages that allow the modeling of the problem without involving the user with the implementation of the solution algorithms to solve it.n The curse of dimensionality is a constant problem that has been addressed by different approaches through time, but it is not intended within the scope of our work; our focus is on the latter issue. We propose a generic solver that enables the user to focus on modeling without getting involved in the complexity required by the solution methods.n We design an object oriented framework for stochastic modeling with four components namely, jMarkov which models Markov Chains, jQBD which models Quasi Birth and Death Processes, jPhase which models Phase Types Distributions and jMDP which models Markov Decision Processes. We concentrate all our effort on creating a software that allows the user to model any kind of system like a Markov Chain, QBD or MDP with fairly basic knowledge of programming. To this end we separate the modeling part from the solution algorithms; therefore the user only needs to mathematically model the problem and the software will do the rest. However, we leave the package with the possibility that experienced users can code their own solution algorithms; this is done since the package only contains the most common algorithms found in the literature.n The software does not use external plain files like .txt or .dat written with specific commands, but rather it is based on OOP (Object Oriented Programming). The main advantages of it include implementation in Java framework, which allows the computational representation of the model to be very similar to its mathematical representation such that it would become natural to pass from one to another. Also the program possesses the usual characteristics of Java such as the use of inheritance and abstraction. Finally, Java is a high level computational language so the user doesnt need to be concerned about technical problems.