Robust optimisation for risk-averse multi-period inventory decision with partial demand distribution information

Abstract

We study robust multi-period inventory decisions for risk-averse managers with incomplete demand information for products with a short life cycle. The three inventory models we developed aim respectively to maximise expected profit, maximise conditional value-at-risk-based profit, and balance between the two objectives. We formulate each objective into an associated robust counterpart model under the assumption of ellipsoid distribution and again under the box distribution. The ellipsoid distribution-based robust model can be mathematically transformed into a non-linear programming which can be solved by finding solutions to some second-order cone programs, while the box distribution-based model can be converted into a general piecewise linear optimisation problem. We prove that the transformed versions are equivalent to the original ones and that both transformed models can be solved efficiently. Numerical examples are given to demonstrate the practicability of the proposed approach for dealing with uncertain demands. We find that the proposed optimisation approaches are robust under both the ellipsoid and box distributions. Finally, sensitivity analysis on the risk-averse degree and optimism index is conducted to validate the proposed models and solution approaches.

Keywords:

• robustness and sensitivity analysis
• conditional value-at-risk (CVaR)
• risk-averse
• multi-period inventory
• uncertainty distribution

Acknowledgements

 

Notes

This research is partly supported by the National Nature Science Foundation of China (71372186), The Ministry of Education General Research Project in Humanities and Social Sciences (11YJC630165).