### Abstract

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.

Original language | English |
---|---|

Pages (from-to) | 135-146 |

Number of pages | 12 |

Journal | Journal of Industrial and Management Optimization |

Volume | 13 |

Issue number | 1 |

DOIs | |

State | Published - 1 Jan 2017 |

### Keywords

- (Q,r) model
- CVaR
- Inventory models
- Risk averse optimization
- Risk measure

## Fingerprint Dive into the research topics of '(Q; r) model with Cv <sub>a</sub>R<sub>α</sub> of costs minimization'. Together they form a unique fingerprint.

## Cite this

_{a}R

_{α}of costs minimization.

*Journal of Industrial and Management Optimization*,

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