The newsvendor problem with GHG emissions from waste disposal under cap-and-trade regulation

Abstract

We study a newsvendor problem with greenhouse gas (GHG) emissions at the disposal stage regulated by a cap-and-trade policy. We first consider a synchronous version of the problem where the replenishment period and the emission assessment period are the same. For this problem, we propose simple algorithms to derive the optimal quantity and cost for both continuous and discrete demand distributions. We show that ignoring the carbon tax may lead to large overcost, especially when the GHG quota is small. For a normally distributed demand, we also show that the demand standard deviation has a non-linear and non-monotonic effect on the order quantity. We then investigate an asynchronous version of the problem where replenishment decisions occur at a higher frequency than the quota allocation. We formulate this lot sizing problem as a Markov decision process and solve it with a dynamic programming algorithm whose complexity is assessed. Through a numerical experimentation and theoretical results, we demonstrate how and when the flexibility of the optimal dynamic replenishment decisions allows to reduce costs. When approaching the end of the time horizon, the uncertainty reduction allows the decision maker to adopt a riskier policy and order larger quantities.

KEYWORDS:

• Newsvendor
• GHG emissions
• cap-and-trade
• lot-sizing
• dynamic programming

Acknowledgments

The authors would like to thank Professor Nabil Absi for his gracious and helpful contribution to the problem statement.

Data availability statement

The data supporting the findings of this study are available within the article.

Disclosure statement

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

Additional information

Funding

This research was financed by the French government IDEX-ISITE initiative [grant number 16-IDEX-0001 (CAP 20-25)] and by the Auvergne-Rhône-Alpes region under the program ‘Pack Ambition Recherche’.

Notes on contributors

Jean-Philippe Gayon

Jean-Philippe Gayon is a full professor in the department of computer science at Clermont Auvergne INP. His research interests are in operations management and operations research with a special focus on stochastic models.

Michael Hassoun

Michael Hassoun is a lecturer in the Industrial Engineering Department at the Ariel University Center, Israel. His research interests focus on modelling and management of production systems, with an emphasis on Semiconductor manufacturing, and operations research in sustainability. He earned his PhD and MSc in Industrial Engineering from Ben-Gurion University of the Negev, Israel, and his BSc in Mechanical Engineering from the Technion, Israel.