Robust policies for a multi-stage production/inventory problem with switching costs and uncertain demand

Abstract

In this paper, we seek robust policies for a multi-stage production/inventory problem to minimise total costs, including switching, production, inventory or shortage costs. While minimising switching costs often leads to non-convexity in the model, 0–1 variables are introduced to linearise the objective function. Considering the impossibility of obtaining the exact distribution of uncertain demand, we study the production/inventory problem under worst cases to resist uncertainty. In contrast to traditional inventory problems, unexpected yields in production are considered. Robust support vector regression is developed to approximate the yields of each unit. A mixed-integer linear programming is proposed, employing the duality theory to address the min–max model. A practical case study from cold rolling is considered. Experiments on the actual steel production data are reported to illustrate the validity of the proposed approach.

Keywords:

• multi-stage inventory
• switching costs
• machine learning
• robust optimisation
• MILP

Acknowledgements

We thank the referees and editors, whose comments significantly helped the presentation and analysis in this paper.

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

This research was supported by the National Key Research and Development Program of China [grant number 2016YFB0901900]; the Fund for the National Natural Science Foundation of China [grant number 61374203]; the Fund for Innovative Research Groups of the National Natural Science Foundation of China [grant number 71621061]; the Major International Joint Research Project of the National Natural Science Foundation of China [grant number 71520107004], and the 111 Project (B16009).