Optimizing production-inventory replenishment and lead time decisions under a fill rate constraint in a two-echelon sustainable supply chain with quality issues

Abstract

This paper considers a single vendor-single buyer coordinated supply chain under stochastic demand. GHG emissions arise from the vendor's production process. A carbon tax and penalties for exceeding multiple emissions limits are considered. A random number of defectives characterises the batch received by the buyer, who performs an inspection activity. Setup and transportation times are controllable through a capital investment, whose outcome is uncertain. An optimisation problem is formulated under the minimax distribution-free approach. The objective is to find the production-inventory replenishment policy and the length of setup and transportation times that minimise the long-run expected total system cost rate considering a fill rate constraint. Several properties of the cost function are demonstrated, and an optimisation method is developed. Finally, numerical experiments are carried out to draw insights on the effect of the model parameters, including different legislation schemes concerning GHG emissions, on the optimal system performance. The novelty of the paper consists into investigating the effect of a controllable lead time on coordinated supply chain decisions in presence of GHG emissions and quality issues, in a stochastic environment. A major finding is that controlling lead time enhances both the overall cost efficiency and the environmental sustainability of the system.

Keywords:

• Supply chain
• inventory
• stochastic
• optimisation
• sustainability
• quality

Disclosure statement

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

Data availability statement

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

Additional information

Notes on contributors

Davide Castellano

Davide Castellano graduated in 2010 in Management Engineering at Università di Pisa (Italy). In 2015, he obtained a PhD in Mechanical Engineering at the same university with specialisation in Operations Management. In 2015, he was Research Associate at Università di Pisa. Between 2016 and 2020 he was Research Assistant at Università degli Studi di Napoli ‘Federico II’ (Italy), where he became Assistant Professor (non-tenure track) from 2020 to 2021. At present, he is a tenure-track Assistant Professor in Industrial Systems Engineering at the same university. His research activity concerns maintenance management, systems reliability, production management, logistics, and inventory management. He is the author of more than 40 technical papers published in international journals or conference proceedings.

Roberto Gabbrielli

Roberto Gabbrielli graduated with honours in Mechanical Engineering at the University of Pisa (Italy). He has a PhD in Energy Power Systems and is Associate Professor in Industrial Systems Engineering at the Department of Civil and Industrial Engineering of the University of Pisa (Italy). His current research activity concerns the production planning and control, lean methods for material management, the development of decision support systems for industrial investments, and the material logistics. To this purpose, novel management methods and mathematical models have been introduced for the performance improvement of the logistic systems. He is author of more than 40 papers published in scientific international journals with peer review.

Mosè Gallo

Mosè Gallo serves as Associate Professor of Industrial Systems Engineering at Department of Chemical, Materials and Production Engineering of the University of Naples Federico II (Italy). He is a mechanical engineer and received Ph.D. degree in ‘Production Technologies and Systems’ from University of Naples Federico II in 2008. His research interests are related to design and management problems of production systems. Specifically, he has tackled issues concerning quality, maintenance, production planning, environmental sustainability and soft computing techniques applied to industrial fields. He has authored several research papers and book chapters. He is a member of editorial boards of several international scientific Journals.

Bibhas C. Giri

Bibhas C. Giri is a Professor in the Department of Mathematics, Jadavpur University, Kolkata, India. His research interests include inventory/supply chain management, production planning and scheduling, and multi-criteria decision making. He has published papers in reputed international journals including the European Journal of Operational Research, International Journal of Production Research, International Journal of Production Economics, OMEGA, Journal of the Operational Research Society, and others.

Sumon Sarkar

Sumon Sarkar is a Ph.D. scholar in the Department of Mathematics, Jadavpur University, Kolkata, India. He received his B.S. degree in Mathematics from the University of Calcutta, India, and M.S. degree in Applied Mathematics from Vidyasagar University, India. His research interests include inventory/supply chain management, production planning and scheduling, and his research papers have appeared in Journal of Cleaner Production, Journal of Manufacturing System, International Journal of Production Economics, Applied Mathematics and Computation, International Transactions in Operational Research, Annals of Operations Research, Economic Modelling, Journal of Industrial and Management Optimization, International Journal of Machine Learning and Cybernetics, Operational Research: An Intentional Journal, Scientia Iranica E, and others.