The φ-divergence-based robust optimization model of a single-period inventory under CVaR

QIU Ruo-zhen, YUAN Hong-tao, LI Xiang, ZHU Zhu

Systems Engineering - Theory & Practice ›› 2015, Vol. 35 ›› Issue (12) : 3056-3064.

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Systems Engineering - Theory & Practice ›› 2015, Vol. 35 ›› Issue (12) : 3056-3064. DOI: 10.12011/1000-6788(2015)12-3056

The φ-divergence-based robust optimization model of a single-period inventory under CVaR

  • QIU Ruo-zhen1, YUAN Hong-tao1, LI Xiang2, ZHU Zhu3
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Abstract

The robust optimization model of a single-period inventory based on conditional value-at-risk (CVaR) is established for risk-aversion inventory managers under the discrete stochastic demand with uncertain probability. Using φ-divergence, the confidence region of the uncertain demand probability with a certain confidence level is constructed based on statistical theory when only knowing discrete demand scenarios. The robust optimization model of a single period inventory is transformed into a tractable one by Lagrange dual theory. Specially, an inventory strategy based on data-driven is proposed in the setting of only demand scenarios are known. At last, some numerical examples are executed to analyze the impacts of the degree of risk-aversion, the different forms of φ-divergence and the number of sampling on inventory strategy and managers' performance. The results show that the robust inventory strategy based on φ-divergence is robust to restrain the effects of the uncertain demand probability on the inventory performance. Furthermore, comparing with the results derived by data-driven method, the robust inventory strategy based on φ-divergence can ensure inventory managers to get a more ideal performance which indicates that the mining for statistical information implicit in demand data can effectively improve the inventory managers' operation performance.

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inventory strategy / conditional value-at-risk / φ-divergence / robust optimization / data-driven

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QIU Ruo-zhen , YUAN Hong-tao , LI Xiang , ZHU Zhu. The φ-divergence-based robust optimization model of a single-period inventory under CVaR. Systems Engineering - Theory & Practice, 2015, 35(12): 3056-3064 https://doi.org/10.12011/1000-6788(2015)12-3056

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