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    <title>Mathematical Methods and Programming</title>
    <link>http://repub.eur.nl/res/concept/jel-C6/</link>
    <description>Recent publications classified by JEL Code C6</description>
    <language>en</language>
    <image>
      <url>http://repub.eur.nl/static-eur/img/logo.png</url>
      <title>RePub, Erasmus University Rotterdam</title>
      <link>http://repub.eur.nl</link>
    </image>
    <item>
      <title>Optimal investment in learning-curve technologies (Article)</title>
      <link>http://repub.eur.nl/res/pub/33018/</link>
      <pubDate>2012-10-01T00:00:00Z</pubDate>
      <description>
        
        We study optimal investment in technologies characterized by the learning curve. There are two investment patterns depending on the shape of the learning curve. If the learning process is slow, firms invest relatively late and on a larger scale. If the curve is steep, firms invest earlier and on a smaller scale. We further demonstrate that learning investment differs greatly from investment in technologies without learning effects. Learning investments generate substantial initial losses and are very sensitive to downside risk. We show that the most susceptible to losses and risk are technologies with intermediate speed of learning. 
      </description>
      <author>Della Seta, M.</author> <author>Gryglewicz, S.</author> <author>Kort, P.M.</author>
    </item> <item>
      <title>Solving Weighted Voting Game Design Problems Optimally: Representations, Synthesis, and Enumeration (Research Paper)</title>
      <link>http://repub.eur.nl/res/pub/32170/</link>
      <pubDate>2012-05-01T00:00:00Z</pubDate>
      <description>
        
        We study the inverse power index problem for weighted voting games: the problem of finding a weighted voting game in which the power of the players is as close as possible to a certain target distribution. Our goal is to find algorithms that solve this problem exactly. Thereto, we study various subclasses of simple games, and their associated representation methods. We survey algorithms and impossibility results for the synthesis problem, i.e., converting a representation of a simple game into another representation. We contribute to the synthesis problem by showing that it is impossible to compute in polynomial time the list of ceiling coalitions of a game from its list of roof coalitions, and vice versa. Then, we proceed by studying the problem of enumerating the set of weighted voting games. We present first a naive algorithm for this, running in doubly exponential time. Using our knowledge of the synthesis problem, we then improve on this naive algorithm, and we obtain an enumeration algorithm that runs in quadratic exponential time. Moreover, we show that this algorithm runs in output-polynomial time, making it the best possible enumeration algorithm up to a polynomial factor. Finally, we propose an exact anytime algorithm for the inverse power index problem that runs in exponential time. By the genericity of our approach, our algorithm can be used to find a weighted voting game that optimizes any exponential time computable function. We implement our algorithm for the case of the normalized Banzhaf index, and we perform experiments in order to study performance and error convergence.
      </description>
      <author>Keijzer, B. de</author> <author>Klos, T.B.</author> <author>Zhang, Y.</author>
    </item> <item>
      <title>Power Structures and Adaptation: How to Distribute Power within a Group (Research Paper)</title>
      <link>http://repub.eur.nl/res/pub/30573/</link>
      <pubDate>2011-11-21T00:00:00Z</pubDate>
      <description>
        
        How steep should a hierarchy be, or should there be a hierarchical stratification at all? Research on power, divided between two main research streams (i.e., functionalist and conflict theories of power), reports discrepant answers to this question. This paper suggests that the choice between groups with low, high, and moderate power disparity depends on whether power assignment is based on competency or not. Problem complexity, group size, and size of the difference between high and low power are also proposed as moderators in comparing different power models. The present paper extends earlier work by conceptualizing power simultaneously as a relational capacity, behaviors emanating from this capacity, and exercise of power in the form of influence. Additionally, it goes beyond the formal organizational design perspective where power is confined to formal and stable hierarchies, and allows for informal power structures and evolutionary dynamics.
      </description>
      <author>Tarakci, M.</author> <author>Groenen, P.J.F.</author>
    </item> <item>
      <title>Modelling Issues in Kernel Ridge Regression (Research Paper)</title>
      <link>http://repub.eur.nl/res/pub/26508/</link>
      <pubDate>2011-09-01T00:00:00Z</pubDate>
      <description>
        
        Kernel ridge regression is gaining popularity as a data-rich nonlinear forecasting tool, which is applicable in many different contexts. This paper investigates the influence of the choice of kernel and the setting of tuning parameters on forecast accuracy. We review several popular kernels, including polynomial kernels, the Gaussian kernel, and the Sinc kernel. We interpret the latter two kernels in terms of their smoothing properties, and we relate the tuning parameters associated to all these kernels to smoothness measures of the prediction function and to the signal-to-noise ratio. Based on these interpretations, we provide guidelines for selecting the tuning parameters from small grids using cross-validation. A Monte Carlo study confirms the practical usefulness of these rules of thumb. Finally, the flexible and smooth functional forms provided by the Gaussian and Sinc kernels makes them widely applicable, and we recommend their use instead of the pop ular polynomial kernels in general settings, in which no information on the data-generating process is available.
      </description>
      <author>Exterkate, P.</author>
    </item> <item>
      <title>Time Slot Management in Attended Home Delivery (Article)</title>
      <link>http://repub.eur.nl/res/pub/25987/</link>
      <pubDate>2011-08-01T00:00:00Z</pubDate>
      <description>
        
        Many e-tailers providing attended home delivery, especially e-grocers, offer narrow delivery time slots to ensure satisfactory customer service. The choice of delivery time slots has to balance marketing and operational considerations, which results in a complex planning problem. We study the problem of selecting the set of time slots to offer in each of the zip codes in a service region. The selection needs to facilitate cost-effective delivery routes, but also needs to ensure an acceptable level of service to the customer. We present a fully automated approach that is capable of producing high-quality delivery time slot offerings in a short amount of time. Computational experiments reveal the value of this approach and the impact of the environment on the underlying trade-offs. 
 

      </description>
      <author>Savelsbergh, M.W.P.</author> <author>Fleischmann, M.</author> <author>Agatz, N.A.H.</author> <author>Campbell, A.</author>
    </item> <item>
      <title>Time Slot Management in Attended Home Delivery (Article)</title>
      <link>http://repub.eur.nl/res/pub/25988/</link>
      <pubDate>2011-08-01T00:00:00Z</pubDate>
      <description>
        
        Many e-tailers providing attended home delivery, especially e-grocers, offer narrow delivery time slots to ensure satisfactory customer service. The choice of delivery time slots has to balance marketing and operational considerations, which results in a complex planning problem. We study the problem of selecting the set of time slots to offer in each of the zip codes in a service region. The selection needs to facilitate cost-effective delivery routes, but also needs to ensure an acceptable level of service to the customer. We present a fully automated approach that is capable of producing high-quality delivery time slot offerings in a short amount of time. Computational experiments reveal the value of this approach and the impact of the environment on the underlying trade-offs. 
 

      </description>
      <author>Savelsbergh, M.W.P.</author> <author>Fleischmann, M.</author> <author>Agatz, N.A.H.</author> <author>Campbell, A.</author>
    </item> <item>
      <title>Prospect theory for continuous distributions: A preference foundation (Article)</title>
      <link>http://repub.eur.nl/res/pub/23265/</link>
      <pubDate>2011-06-01T00:00:00Z</pubDate>
      <description>
        
        Preference foundations give necessary and sufficient conditions for a decision model, stated directly in terms of the empirical primitive: the preference relation. For the most popular descriptive model for decision making under risk and uncertainty today, prospect theory, preference foundations have as yet been provided only for prospects taking finitely many values. In applications, however, prospects often are complex and involve infinitely many values, as in normal and lognormal distributions. This paper provides a preference foundation of prospect theory for such complex prospects. We allow for unbounded utility and only require finite additivity of the underlying probability distributions, leaving the restriction to countably additive distributions optional. As corollaries, we generalize previously obtained preference foundations for special cases of prospect theory (rank-dependent utility and Choquet expected utility) that all required countable additivity. We now obtain genuine generalizations of de Finetti’s and Savage’s finitely additive setups to unbounded utility.
      </description>
      <author>Kothiyal, A.</author> <author>Spinu, V.</author>
    </item> <item>
      <title>An Alternative Bayesian Approach to Structural Breaks in Time Series Models (Research Paper)</title>
      <link>http://repub.eur.nl/res/pub/22551/</link>
      <pubDate>2011-02-07T00:00:00Z</pubDate>
      <description>
        
        We propose a new approach to deal with structural breaks in time series models. The key contribution is an alternative dynamic stochastic specification for the model parameters which describes potential breaks. After a break new parameter values are generated from a so-called baseline prior distribution. Modeling boils down to the choice of a parametric likelihood specification and a baseline prior with the proper support for the parameters. The approach accounts in a natural way for potential out-of-sample breaks where the number of breaks is stochastic. Posterior inference involves simple computations that are less demanding than existing methods. The approach is illustrated on nonlinear discrete time series models and models with restrictions on the parameter space.
      </description>
      <author>Hauwe, S. van den</author> <author>Paap, R.</author> <author>Dijk, D.J.C. van</author>
    </item> <item>
      <title>Nonlinear Forecasting with Many Predictors using Kernel Ridge Regression (Research Paper)</title>
      <link>http://repub.eur.nl/res/pub/22335/</link>
      <pubDate>2011-01-04T00:00:00Z</pubDate>
      <description>
        
        This paper puts forward kernel ridge regression as an approach for forecasting with many predictors that are related nonlinearly to the target variable. In kernel ridge regression, the observed predictor variables are mapped nonlinearly into a high-dimensional space, where estimation of the predictive regression model is based on a shrinkage estimator to avoid overfitting. We extend the kernel ridge regression methodology to enable its use for economic time-series forecasting, by including lags of the dependent variable or other individual variables as predictors, as is typically desired in macroeconomic and financial applications. Monte Carlo simulations as well as an empirical application to various key measures of real economic activity confirm that kernel ridge regression can produce more accurate forecasts than traditional linear methods for dealing with many predictors based on principal component regression.
      </description>
      <author>Exterkate, P.</author> <author>Groenen, P.J.F.</author> <author>Heij, C.</author> <author>Dijk, D.J.C. van</author>
    </item> <item>
      <title>Global Stochastic Properties of Dynamic Models and their Linear Approximations (Research Paper)</title>
      <link>http://repub.eur.nl/res/pub/20748/</link>
      <pubDate>2010-09-01T00:00:00Z</pubDate>
      <description>
        
        The dynamic properties of micro based stochastic macro models are often analyzed through a linearization around the associated deterministic steady state. Recent literature has investigated the error made by such a deterministic approximation. Complementary to this literature we investigate how the linearization affects the stochastic properties of the original model. We consider a simple real business cycle model with noisy learning by doing. The solution has a stationary distribution that exhibits moment failure and has an unbounded support. The linear approximation, however, yields a stationary distribution with possibly a bounded support and all moments finite.
      </description>
      <author>Babus, A.M.</author> <author>Vries, C.G. de</author>
    </item> <item>
      <title>A Model for Evaluating Pharmaceutical R&amp;D Investment Projects under Technical and Economic Uncertainties (Research Paper)</title>
      <link>http://repub.eur.nl/res/pub/18211/</link>
      <pubDate>2010-02-18T00:00:00Z</pubDate>
      <description>
        
        This study sets up a compound option approach for evaluating pharmaceutical R&amp;D investment projects in the presence of technical and economic uncertainties. Technical uncertainty is modeled as a Poisson jump that allows for failure and thus abandonment of the drug development. Economic uncertainty is modeled as a standard di¤usion process which incorporates both up-and downward shocks. Practical application of this method is emphasized through a case analysis. We show that both uncertainties have a positive impact on the R&amp;D option value. Moreover, from the sensitivity analysis, we nd that the sensitivity of the option with respect to economic uncertainty and market introduction cost decreases when technical uncertainty increases.
      </description>
      <author>Pennings, H.P.G.</author> <author>Sereno, L.</author>
    </item> <item>
      <title>A comparison of biased simulation schemes for stochastic volatility models (Article)</title>
      <link>http://repub.eur.nl/res/pub/18571/</link>
      <pubDate>2010-02-01T00:00:00Z</pubDate>
      <description>
        
        Using an Euler discretization to simulate a mean-reverting CEV process gives rise to the problem that while the process itself is guaranteed to be nonnegative, the discretization is not. Although an exact and efficient simulation algorithm exists for this process, at present this is not the case for the CEV-SV stochastic volatility model, with the Heston model as a special case, where the variance is modelled as a mean-reverting CEV process. Consequently, when using an Euler discretization, one must carefully think about how to fix negative variances. Our contribution is threefold. Firstly, we unify all Euler fixes into a single general framework. Secondly, we introduce the new full truncation scheme, tailored to minimize the positive bias found when pricing European options. Thirdly and finally, we numerically compare all Euler fixes to recent quasi-second order schemes of Kahl and Jckel, and Ninomiya and Victoir, as well as to the exact scheme of Broadie and Kaya. The choice of fix is found to be extremely important. The full truncation scheme outperforms all considered biased schemes in terms of bias and root-mean-squared error
      </description>
      <author>Lord, R.</author> <author>Koekkoek, R.</author> <author>Dijk, D.J.C. van</author>
    </item> <item>
      <title>Flexible decision support in dynamic inter-organisational networks (Article)</title>
      <link>http://repub.eur.nl/res/pub/21712/</link>
      <pubDate>2010-01-01T00:00:00Z</pubDate>
      <description>
        
        An effective Decision Support System (DSS) should help its users improve decision making in complex, information-rich environments. We present a feature gap analysis that shows that current decision support technologies lack important qualities for a new generation of agile business models that require easy, temporary integration across organisational boundaries. We enumerate these qualities as DSS Desiderata, properties that can contribute both effectiveness and flexibility to users in such environments. To address this gap, we describe a new design approach that enables users to compose decision behaviours from separate, configurable components, and allows dynamic construction of analysis and modelling tools from small, single-purpose evaluator services. The result is what we call an ‘evaluator service network’ that can easily be configured to test hypotheses and analyse the impact of various choices for elements of decision processes. We have implemented and tested this design in an interactive version of the MinneTAC trading agent, an agent designed for the Trading Agent Competition for Supply Chain Management.
      </description>
      <author>Collins, J.</author> <author>Ketter, W.</author> <author>Gini, M.</author>
    </item> <item>
      <title>Stochastic Dominance: Convexity and Some Efficiency Tests (Research Paper)</title>
      <link>http://repub.eur.nl/res/pub/17495/</link>
      <pubDate>2009-11-01T00:00:00Z</pubDate>
      <description>
        
        This paper points out the importance of Stochastic Dominance (SD) efficient sets being convex. We review classic convexity and efficient set characterization results on SD efficiency of a given portfolio relative to a diversified set of assets and generalize them in the following aspects. First, we broaden the class of individual utilities in Rubinstein (1974) that lead to two-fund separation. Secondly, we propose a linear programming SSD test that is more efficient than that of Post (2003) and expand the SSD efficiency criteria developed by Dybvig and Ross (1982) onto the Third Order Stochastic Dominance and further to Decreasing Absolute and Increasing Relative Risk Aversion Stochastic Dominance. The efficient sets for those are finite unions of convex sets.
      </description>
      <author>Lizyayev, A.M.</author>
    </item> <item>
      <title>Demand-driven scheduling of movies in a multiplex (Article)</title>
      <link>http://repub.eur.nl/res/pub/16070/</link>
      <pubDate>2009-06-01T00:00:00Z</pubDate>
      <description>
        
        This paper is about a marketing decision support system in the movie industry. The decision support system of interest is a model that generates weekly movie schedules in a multiplex movie theater. A movie schedule specifies, for each day of the week, on which screen(s) different movies will be played, and at which time(s). The model integrates elements from marketing (the generation of demand figures) with approaches from operations research (the optimization procedure). Therefore, it consists of two parts: (i) conditional forecasts of the number of visitors per show for any possible starting time, and (ii) a scheduling procedure that quickly finds a near optimal schedule (which can be demonstrated to be close to the optimal schedule). To generate this schedule, we formulate the "movie scheduling problem" as a generalized set partitioning problem. The latter is solved with an algorithm based on column generation techniques. We tested the combined demand forecasting/schedule optimization procedure in a multiplex in Amsterdam, generating movie schedules for fourteen weeks. The proposed model not only makes movie scheduling easier and less time consuming, but also generates schedules that attract more visitors than current "intuition-based" schedules.
      </description>
      <author>Eliashberg, J.</author> <author>Hegie, Q.</author> <author>Ho, J.</author> <author>Huisman, D.</author> <author>Miller, S.J.</author> <author>Swami, S.</author> <author>Weinberg, C.B.</author> <author>Wierenga, B.</author>
    </item> <item>
      <title>Dynamic Factor Models with Smooth Loadings for Analyzing the Term Structure of Interest Rates (Research Paper)</title>
      <link>http://repub.eur.nl/res/pub/16299/</link>
      <pubDate>2009-05-01T00:00:00Z</pubDate>
      <description>
        
        We propose a new approach to the modelling of the term structure of interest rates. We consider the general dynamic factor model and show how to impose smoothness restrictions on the factor loadings. We further present a statistical procedure based on Wald tests that can be used to find a suitable set of such restrictions. We present these developments in the context of term structure models, but they are also applicable in other settings. We perform an empirical study using a data set of unsmoothed Fama-Bliss zero yields for US treasuries of different maturities. The general dynamic factor model with and without smooth loadings is considered in this study together with models that are associated with Nelson-Siegel and arbitrage-free frameworks. These existing models can be regarded as special cases of the dynamic factor model with restrictions on the model parameters. For all model candidates, we consider both stationary and nonstationary autoregressive processes (with different numbers of lags) for the latent factors. Finally, we perform statistical hypothesis tests to verify whether the restrictions imposed by the models are supported by the data. Our main conclusion is that smoothness restrictions can be imposed on the loadings of dynamic factor models for the term structure of US interest rates but that the restrictions implied by a number of popular term structure models are rejected.
      </description>
      <author>Jungbacker, B.</author> <author>Koopman, S.J.</author> <author>Wel, M. van der</author>
    </item> <item>
      <title>Nash Game Model for Optimizing Market Strategies, Configuration of Platform Products in a Vendor Managed Inventory (VMI) Supply Chain for a Product Family (Research Paper)</title>
      <link>http://repub.eur.nl/res/pub/15029/</link>
      <pubDate>2009-03-02T00:00:00Z</pubDate>
      <description>
        
        This paper discusses how a manufacturer and its retailers interact with each other to optimize their product marketing strategies, platform product configuration and inventory policies in a VMI (Vendor Managed Inventory) supply chain. The manufacturer procures raw materials from multiple suppliers to produce a family of products sold to multiple retailers. Multiple types of products are substitutable each other to end customers. The manufacturer makes its decision on raw materials’ procurement, platform product configuration, product replenishment policies to retailers with VMI, price discount rate, and advertising investment to maximize its profit. Retailers in turn consider the optimal local advertising and retail price to maximize their profits. This problem is modeled as a dual simultaneous non-cooperative game (as a Nash game) model with two sub-games. One is between the retailers serving in competing retail markets and the other is between the manufacturer and the retailers. This paper combines analytical, iterative and GA (genetic algorithm) methods to develop a game solution algorithm to find the Nash equilibrium. A numerical example is conducted to test the proposed model and algorithm, and gain managerial implications.
      </description>
      <author>Yu, Y.</author> <author>Huang, G.Q.</author>
    </item> <item>
      <title>Open Location Management in Automated Warehousing Systems (Research Paper)</title>
      <link>http://repub.eur.nl/res/pub/14615/</link>
      <pubDate>2009-01-30T00:00:00Z</pubDate>
      <description>
        
        A warehouse needs to have sufficient open locations to be able to store incoming shipments of various sizes. In combination with ongoing load retrievals open locations gradually spread over the storage area. Unfavorable positions of open locations negatively impact the average load retrieval times. This paper presents a new method to manage these open locations such that the average system travel time for processing a block of storage and retrieval jobs in an automated warehousing system is minimized. We introduce the effective storage area (ESA), a well-defined part of the locations closest to the depot; where only a part of the open locations –the effective open locations-, together with all the products, are stored. We determine the optimal number of effective open locations and the ESA boundary minimizing the average travel time. Using the ESA policy, the travel time of a pair of storage and retrieval jobs can be reduced by more than 10% on average. Its performance depends hardly on the number or the sequence of retrievals. In fact, in case of only one retrieval, applying the policy leads already to beneficial results. Application is also easy; the ESA size can be changed dynamically during storage and retrieval operations.
      </description>
      <author>Yu, Y.</author> <author>Koster, M.B.M. de</author>
    </item> <item>
      <title>Flexible Decision Support in Dynamic Interorganizational Networks (Research Paper)</title>
      <link>http://repub.eur.nl/res/pub/14082/</link>
      <pubDate>2008-12-05T00:00:00Z</pubDate>
      <description>
        
        An effective Decision Support System (DSS) should help its users improve decision-making in complex, information-rich, environments. We present a feature gap analysis that shows that current decision support technologies lack important qualities for a new generation of agile business models that require easy, temporary integration across organisational boundaries. We enumerate these qualities as DSS Desiderata, properties that can contribute both effectiveness and flexibility to users in such environments. To address this gap, we describe a new design approach that enables users to compose decision behaviours from separate, configurable components, and allows dynamic construction of analysis and modelling tools from small, single-purpose evaluator services. The result is what we call an “evaluator service network” that can easily be configured to test hypotheses and analyse the impact of various choices for elements of decision processes. We have implemented and tested this design in an interactive version of the MinneTAC trading agent, an agent designed for the Trading Agent Competition for Supply Chain Management.
      </description>
      <author>Collins, J.</author> <author>Ketter, W.</author> <author>Gini, M.</author>
    </item> <item>
      <title>How Much is Location Information Worth? A Competitive Analysis of the Online Traveling Salesman Problem with Two Disclosure Dates (Research Paper)</title>
      <link>http://repub.eur.nl/res/pub/13837/</link>
      <pubDate>2008-11-13T00:00:00Z</pubDate>
      <description>
        
        In this paper we derive the worst-case ratio of an online algorithm for the Traveling Salesman Problem (TSP) with two disclosure dates. This problem, a variant of the online TSP with release dates, is characterized by the disclosure of a job’s location at one point in time followed by the disclosure of that job’s release date at a later point in time. We present an online algorithm for this problem restricted to the positive real number line. We then derive the worst-case ratio of our algorithm and show that it is best-possible in two contexts – the first, one in which the amount of time between the disclosure events and release time are fixed and equal for all jobs; and a second in which the time between disclosure events varies for each job. We conclude that the value of advanced information can be attributed to the location information alone – yielding an optimal solution in favorable instances.
      </description>
      <author>Srour, F.J.</author> <author>Zuidwijk, R.A.</author>
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