A single-vendor, multiple-buyer coordinated supply chain model with unequal-sized batch shipments and cycle-dependent safety stocks

Abstract

This paper investigates a single-vendor, multiple-buyer coordinated supply chain under stochastic demand. Each buyer implements a continuous review policy, and the shortage quantity is fully back-ordered. The lead time for the first shipment includes setup, production, and transportation times, while the lead time for the remaining shipments includes only transportation time. The production time is a function of production lot and production rate, which are both decision variables, and the setup and transportation times are controllable as well. For each buyer, the safety stock in the first replenishment cycle is not necessarily identical to that in the remaining cycles. Two successive shipments from the vendor to a buyer may have different sizes, and their ratio is a decision variable. The problem is finding the production and inventory replenishment policy, production rate, and lead times that minimise the long-run expected total cost per time unit. We demonstrate properties satisfied by the cost function and develop an optimisation algorithm, whose performance is compared to a benchmark algorithm based on a commercial solver in a numerical experiment. The experiments also investigate the benefits stemming from the proposed model when compared to models reproducing situations that leverage some or any of the controlled factors.

KEYWORDS:

• Inventory
• Supply chain
• Lead time
• Production
• Stochastic
• Optimisation

Acknowledgments

The authors are grateful to the anonymous reviewers whose constructive comments on an earlier version of this manuscript helped to improve the paper substantially.

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 and its supplementary materials.

Additional information

Notes on contributors

Davide Castellano

Davide Castellano graduated in 2010 in Management Engineering at University of Pisa (Italy). In 2015, he obtained a PhD in Mechanical Engineering at the same university with specialisation in Operations Management and Supply Chain Management. In 2015, he was Research Associate at University of Pisa, while between 2016 and 2020 he was Research Assistant at University of Naples ‘Federico II’ (Italy), where he became Assistant Professor from 2020 to 2023. Since 2023, he is Associate Professor at University of Modena and Reggio Emilia (Italy). His research activity mainly concerns production management, logistics, and supply chain management. He is the author of more than 40 technical papers published in international journals or conference proceedings. He is Regional Editor of the International Journal of Logistics: Research and Applications and Area Editor of Operations Management Research. He held honorary positions at the University of Liverpool Management School.

Mosè Gallo

Mosè Gallo is an Associate Professor at Department of Chemical, Materials and Production Engineering of the University of Naples Federico II (Italy). He is a mechanical engineer and received a 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 industrial production systems. Specifically, he has tackled issues concerning production quality, maintenance, production planning, environmental sustainability and soft computing techniques applied to industrial production cases. He has authored several research papers and book chapters. He is in the editorial board of several international scientific journals and served also as reviewer for journals and various international conferences.

Christoph H. Glock

Christoph H. Glock is a Professor of Production and Supply Chain Management at Technical University of Darmstadt, Germany. His research interests include inventory management, supply chain management, warehousing, sustainable production, and human factors in logistics and inventory systems. His work has appeared in various international journals, such as IISE Transactions, Decision Sciences, OR Spectrum, the Journal of Business Logistics or the European Journal of Operational Research.