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Matus, O., Barrera, J., Moreno, E., & Rubino, G. (2019). On the Marshall-Olkin Copula Model for Network Reliability Under Dependent Failures. IEEE Trans. Reliab., 68(2), 451–461.
Abstract: The Marshall-Olkin (MO) copulamodel has emerged as the standard tool for capturing dependence between components in failure analysis in reliability. In this model, shocks arise at exponential random times, that affect one or several components inducing a natural correlation in the failure process. However, because the number of parameter of the model grows exponentially with the number of components, MO suffers of the “curse of dimensionality.” MO models are usually intended to be applied to design a network before its construction; therefore, it is natural to assume that only partial information about failure behavior can be gathered, mostly from similar existing networks. To construct such an MO model, we propose an optimization approach to define the shock's parameters in the MO copula, in order to match marginal failures probabilities and correlations between these failures. To deal with the exponential number of parameters of this problem, we use a column-generation technique. We also discuss additional criteria that can be incorporated to obtain a suitable model. Our computational experiments show that the resulting MO model produces a close estimation of the network reliability, especially when the correlation between component failures is significant.
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Rojas, F., & Leiva, V. (2016). Inventory management in food companies with statistically dependent demand. Acad.-Rev. Latinoam. Adm., 29(4), 450–485.
Abstract: Purpose – The objective of this paper is to propose a methodology based on random demand inventory models and dependence structures for a set of raw materials, referred to as “components”, used by food services that produce food rations referred to as “menus”. Design/methodology/approach – The contribution margins of food services that produce menus are optimised using random dependent demand inventory models. The statistical dependence between the demand for components and/or menus is incorporated into the model through the multivariate Gaussian (or normal) distribution. The contribution margins are optimised by using probabilistic inventory models for each component and stochastic programming with a differential evolution algorithm. Findings – When compared to the non-optimised system previously used by the company, the (average) expected contribution margin increases by 18.32 per cent when using a continuous review inventory model for groceries and uniperiodic models for perishable components (optimised system). Research limitations/implications – The multivariate modeling can be improved by using (a) other non-Gaussian (marginal) univariate probability distributions, by means of the copula method that considers more complex statistical dependence structures; (b) time-dependence, through autoregressive time-series structures and moving average; (c) random modelling of lead-time; and (d) demands for components with values equal to zero using zero-inflated or adjusted probability distribution. Practical implications – Professional management of the supply chain allows the users to register data concerning component identification, demand, and stock levels to subsequently be used with the proposed methodology, which must be implemented computationally. Originality/value – The proposed multivariate methodology allows it to describe demand dependence structures through inventory models applicable to components used to produce menus in food services.
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