Voluntary environmental effort under (s,S) inventory policy*

Abstract

Prior research on inventory control has been wide ranging, yet the environmental implications of an $\left(s,S\right)$ inventory policy remain uninvestigated. This paper seeks to bridge the gap by characterising a firm’s voluntary environmental policy in the setup of an $\left(s,S\right)$ inventory control policy. We suggest a mixed model structure wherein, due to the presence of fixed production costs, the inventory is determined continuously by sales and impulsively with ordering decisions obeying an optimal stopping process, while the uncertain sales process is controlled by continuous-time environmental goodwill-related decisions. We show that a firm should successively use voluntary environmental efforts to stimulate its sales when there is inventory and to increase backlogging to improve its production efficiency. Given the recurrent pattern of this policy, we conclude that voluntary environmental efforts under an $\left(s,S\right)$ inventory control is not compatible with using these efforts as a means to generate ephemeral reputation insurance.

KEYWORDS:

• Inventory control
• environmental protection management
• stochastic demand
• voluntary programmes
• quasi-variational inequalities

Acknowledgements

The authors acknowledge helpful comments from two anonymous referees.

Disclosure statement

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

Data availability statement

Data sharing is not applicable to this article as no new data were created or analysed in this study.

Notes

1 https://www.shell.com/shellenergy/othersolutions/welcome-to-shell-environmental-products/working-with-customers-to-compensate-for-their-emissions.html.

2 https://www.reliableplant.com/view/22448/land-rover-offsets-co2.

3 https://climatechampions.unfccc.int/unilever-and-the-race-to-halve-emissions-by-2030/.

4 https://cen.acs.org/materials/Chemex-goes-global-carbon-neutral/98/i42.

5 A similar approach can be found in, e.g., Khmelnitsky and Singer (2015) and Herbon (2021).

6 Earlier surveys are notably Aggarwal (1974) and Porteus (1990).

7 Note that the impulse times refer to the times when the inventory is modified. So if production takes some time, for example a fixed amount of time, the stopping time will be the time of delivery.

Additional information

Funding

This work was supported by National Science Foundation (USA): [grant number NSF-DMS 2204795].

Notes on contributors

Alain Bensoussan

 Alain Bensoussan is Lars Magnus Ericsson Chair and the Director of ICDRiA (International Center for Decision and Risk Analysis) at the University of Texas at Dallas. He is also Chair Professor of Risk and Decision Analysis at the City University Hong Kong. He has been for 4 years World Class University Distinguished Professor at Ajou University, Korea. He is Professor Emeritus at the University Paris Dauphine. Professor Bensoussan served as President of National Institute for Research in Computer Science and Control (INRIA) from 1984 to 1996; President of the French Space Agency (CNES) from 1996 to 2003; and Chairman of the European Space Agency (ESA) Council from 1999 to 2002. He is a member of the French Academy of Sciences, French Academy of Technology, Academia Europaea, and International Academy of Astronautics. His distinctions include AMS Fellow, IEEE Fellow, SIAM Fellow, Von Humboldt award, and the NASA public service medal. Professor Bensoussan is a decorated Officer of Legion d’Honneur, Commandeur Ordre National du Merite from France and Officer Bundes Verdienst Kreuz from Germany. He has received the W.T. and Idalia Reid Prize from SIAM in 2014. He has an extensive research background in stochastic control, risk analysis and decision-making. He has published 13 books and more than 400 papers and proceedings. He develops a comprehensive approach to Risk Analysis, to apprehend technical and socio-economic risks simultaneously. He has experience in aerospace and information technology industries. His main focus is presently in the energy sector.

Fouad El Ouardighi

 Fouad El Ouardighi teaches operations and supply chain management as well as optimal control theory and continuous-time dynamic games at ESSEC Business School. His main research interests are in the interface of operations and marketing management, in R&D competition, environmental economics and management, and epidemic control. He visited many foreign academic institutions as University of Washington in Seattle, HEC-Montreal, McGill University, Bar-Ilan University, HEC-Paris, Technical University of Vienna, etc. Fouad was former academic director of various Advanced Masters programmes in Operations Management. He is currently the coordinator of the Operations Management and Operations Research concentration of the ESSEC PhD programme.