A practical assessment of risk-averse approaches in production lot-sizing problems

ABSTRACT

This paper presents an empirical assessment of four state-of-the-art risk-averse approaches to deal with the capacitated lot-sizing problem under stochastic demand. We analyse two mean-risk models based on the semideviation and on the conditional value-at-risk risk measures, and alternate first and second-order stochastic dominance approaches. The extensive computational experiments based on different instances characteristics and on a case-study suggest that CVaR exhibits a good trade-off between risk and performance, followed by the semideviation and first-order stochastic dominance approach. For all approaches, enforcing risk-aversion helps to reduce the cost-standard deviation substantially, which is usually accomplished via increasing production rates. Overall, we can say that very risk-averse decision-makers would be willing to pay an increased price to have a much less risky solution given by CVaR. In less risk-averse settings, though, semideviation and first-order stochastic dominance can be appealing alternatives to provide significantly more stable production planning costs with a marginal increase of the expected costs.

Keywords:

• lot-sizing
• two-stage stochastic programming
• risk-aversion
• CVaR
• semideviation
• first-order stochastic dominance
• second-order stochastic dominance

Acknowledgments

We would like to thank Prof. Eli Angela Vitor Toso from Universidade Federal de São Carlos (Production Engineering Department) for sharing her views on how to construct an interesting research methodology in quantitative modelling. We thank both reviewers for carefully reading the manuscript and for their valuable comments and suggestions that have helped us to emphasise our contributions and overall methodology, which further improved the readability of the paper.

Disclosure statement

No potential conflict of interest was reported by the authors.

Correction Statement

This article has been republished with minor changes. These changes do not impact the academic content of the article.