Optimal control of inventory level for perishable goods with uncertain decay factor and uncertain forecast information: a new robust MPC approach

Abstract

This paper deals with the inventory control in supply chains under the following assumptions: (1) perishable goods with uncertain deteriorating factor, (2) a future uncertain customer demand that, over a limited prediction horizon, belongs to a known compact set. The problem is to define a smooth control policy maximising the fulfilled customer demand and minimising the inventory level. This problem is here solved through a new Robust Model Predictive Control (RMPC) approach. This implies solving a min–max optimisation problem with hard constraints on the control effort (i.e. the sequence of replenishment orders). To drastically reduce the numerical complexity of this problem, the control signal is sought in the space of B-spline functions, which are known to be universal approximators admitting a parsimonious parametric representation. This allows us: (1) to reduce the number of both decision variables and constraints involved in the optimisation procedure, (2) to reformulate the numerically demanding minimisation of the worst case cost functional as a simpler Weighted Constrained Robust Least Squares (WCRLS) estimation problem. The WCRLS algorithm can be efficiently solved using interior point methods. A rigorous analysis of stability and feasibility conditions is provided.

Keywords:

• Supply chain
• optimal inventory management
• model predictive control
• min–max optimisation

Data availability statement

The authors declare that the data supporting the findings of this study have been generated by simulation. Data are available from the corresponding author [V.O.] on request.

Disclosure statement

No potential conflict of interest was reported by the author(s).

Notes

1 The customer demand has been generated as the sum of bounded white noise with two S-shaped curve membership functions obtained through the smf function of Matlab.

Additional information

Funding

This work was supported by MIUR.

Notes on contributors

Beatrice Ietto

Beatrice Ietto is a post-doctoral researcher at the Department of Management of the Università Politecnica delle Marche, Ancona, Italy currently working as a visiting researcher at the Einstein Center Digital Future (Berlin), participating on the research project Blockchain: a blockchain-based participation platform to enable more transparency and participation in urban development. Her research interests include the impact of digitalisation on intangibles within the Industry 4.0 context, human-centered digital innovation and Industry 4.0, blockchain for citizens participation in urban development, supply chain management and consumer social media engagement behaviors. She has published in national and international peer reviewed journals, such as the Journal of Customer Knowledge Management. She has a PhD in Media, Music and Cultural Studies form Macquarie University (Sydney, Australia) and a Master Degree in International Marketing from the University of Technology (Sydney, Australia).

Valentina Orsini

Valentina Orsini received the Laurea degree in Electronic Engineering in 2003 and the Ph.D. in “Artificial Intelligence Systems” in 2006 from Università Politecnica delle Marche (Ancona, Italy). She is currently Associate Professor in Automatic Control at Università Politecnica delle Marche and Associate Editor of Asian Journal of Control. Her research interests are mainly focused on linear time varying systems, switching systems, robust control, LPV control, event based sporadic control, model inversion, model predictive control, decoupling/decentralized control. Currently she is interested in supply chain management through optimal control methods. She published more than 50 papers in international journals and conferences.