### Resumen

In the classical stochastic continuous review, (Q; r) model [18, 19], the inventory cost c(Q; r) has an averaging term which is given as an integral of the expected costs over the different inventory positions during the lead time on any given cycle. The main objective of the article is to study risk averse optimization in the classical (Q; r) model using CV aR_{α} as a coherent risk measure with respect to the probability distribution of the demand D on inventory position costs (the sum of the inventory holding and backorder penality cost), for any given (generic) confidence level α ∈ [0, 1). We show that the objective function is jointly convex in (Q; r). We also compare the risk averse solution and some other solutions in both analytical and computational ways. Additionally, some general and useful results are obtained.

Idioma original | Inglés |
---|---|

Páginas (desde-hasta) | 135-146 |

Número de páginas | 12 |

Publicación | Journal of Industrial and Management Optimization |

Volumen | 13 |

N.º | 1 |

DOI | |

Estado | Publicada - 1 ene 2017 |

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### Citar esto

_{a}R

_{α}of costs minimization.

*Journal of Industrial and Management Optimization*,

*13*(1), 135-146. https://doi.org/10.3934/jimo.2016008

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_{a}R

_{α}of costs minimization',

*Journal of Industrial and Management Optimization*, vol. 13, n.º 1, pp. 135-146. https://doi.org/10.3934/jimo.2016008

**(Q; r) model with Cv _{a}R_{α} of costs minimization.** / Serna, María Andrea Arias; Yepes, Maŕa Eugenia Puerta; Coterio, Céesar Edinson Escalante; Ospina, Gerardo Arango.

Resultado de la investigación: Contribución a una revista › Artículo › Investigación › revisión exhaustiva

TY - JOUR

T1 - (Q; r) model with Cv aRα of costs minimization

AU - Serna, María Andrea Arias

AU - Yepes, Maŕa Eugenia Puerta

AU - Coterio, Céesar Edinson Escalante

AU - Ospina, Gerardo Arango

PY - 2017/1/1

Y1 - 2017/1/1

N2 - In the classical stochastic continuous review, (Q; r) model [18, 19], the inventory cost c(Q; r) has an averaging term which is given as an integral of the expected costs over the different inventory positions during the lead time on any given cycle. The main objective of the article is to study risk averse optimization in the classical (Q; r) model using CV aRα as a coherent risk measure with respect to the probability distribution of the demand D on inventory position costs (the sum of the inventory holding and backorder penality cost), for any given (generic) confidence level α ∈ [0, 1). We show that the objective function is jointly convex in (Q; r). We also compare the risk averse solution and some other solutions in both analytical and computational ways. Additionally, some general and useful results are obtained.

AB - In the classical stochastic continuous review, (Q; r) model [18, 19], the inventory cost c(Q; r) has an averaging term which is given as an integral of the expected costs over the different inventory positions during the lead time on any given cycle. The main objective of the article is to study risk averse optimization in the classical (Q; r) model using CV aRα as a coherent risk measure with respect to the probability distribution of the demand D on inventory position costs (the sum of the inventory holding and backorder penality cost), for any given (generic) confidence level α ∈ [0, 1). We show that the objective function is jointly convex in (Q; r). We also compare the risk averse solution and some other solutions in both analytical and computational ways. Additionally, some general and useful results are obtained.

KW - (Q,r) model

KW - CVaR

KW - Inventory models

KW - Risk averse optimization

KW - Risk measure

UR - http://www.scopus.com/inward/record.url?scp=85054589723&partnerID=8YFLogxK

U2 - 10.3934/jimo.2016008

DO - 10.3934/jimo.2016008

M3 - Artículo

VL - 13

SP - 135

EP - 146

JO - Journal of Industrial and Management Optimization

JF - Journal of Industrial and Management Optimization

SN - 1547-5816

IS - 1

ER -

_{a}R

_{α}of costs minimization. Journal of Industrial and Management Optimization. 2017 ene 1;13(1):135-146. https://doi.org/10.3934/jimo.2016008