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Lot Sizing Decisions Under Uncertain Demand Considering Skewness and Kurtosis

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Part of the Lecture Notes in Networks and Systems book series (LNNS,volume 405)

Abstract

The lot sizing model is useful for supply making decisions based on probabilistic modeling of demand, using two-stage stochastic programming, calculating the optimal costs of a supply model. In this paper, we study this model by using simulated scenarios subject to different degrees of skewness and kurtosis to model demand, considering univariate Weibull statistical distribution described by a generalized additive models of location, scale and shape (GAMLSS).

We carried out a simulation study of 10,000 different demand scenarios with different degrees of skewness and kurtosis, evaluating relationships between total costs, lot size decisions, expected stock and out of stock respect to coefficients of demand skewness and kurtosis.

In this study it has been shown that the coefficients of skewness and kurtosis impact on the total costs of supplying an item. The results also allow generating a predictive pattern of the first and second stage decisions, that is, the expected quantities in stock and shortages for the use of stochastic lot sizing. Our results indicate that the higher total cost of supply and greater shortage are related to demand patterns with more negative symmetry and lower kurtosis.

Keywords

  • GAMLSS
  • kurtosis
  • Lot sizing
  • Statistical moments
  • Skewness
  • Weibull statistical distribution

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Acknowledgment

This research was carried out thanks to the funding of the Fondecyt initiation project code: 11190004, Chile.

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Correspondence to Fernando Rojas .

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Rojas, F. (2022). Lot Sizing Decisions Under Uncertain Demand Considering Skewness and Kurtosis. In: Botto-Tobar, M., Cruz, H., Díaz Cadena, A., Durakovic, B. (eds) Emerging Research in Intelligent Systems. CIT 2021. Lecture Notes in Networks and Systems, vol 405. Springer, Cham. https://doi.org/10.1007/978-3-030-96043-8_1

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