A collaborating inventory system in a supply chain under Brownian motion demand and imperfect quality

Abstract

This paper studies a coordinated supply with a single vendor and a single buyer. The vendor produces items in a large lot size but as the production continues the items are divided into smaller lots and shipped to the buyer. Each shipment has some defective items and the buyer screens the items to separate the defective while satisfying the Brownian motion demand. The lead time and the number of lots delivered in a production run are decision variables in addition to reorder point and the reorder quantity of the buyer. The objective is to determine the behaviour of these factors simultaneously so as to minimise the total joint costs incurred by the vendor and the buyer. An algorithm is developed to obtain the optimal parameters. Furthermore, numerical examples are presented to illustrate the usefulness of the proposed model and the effects of parameters, particularly the demand variability.

Keywords:

• integrated inventory model
• Brownian motion demand
• imperfect quality
• controllable lead time
• demand variability

Acknowledgements

The author thanks the editor, the associate editor, and the anonymous referees for their valuable comments and suggestions.

Additional information

Funding

This research was supported by the National Science Council, Taiwan, ROC [grant number NSC 100-2115-M-156-001].

Notes on contributors

Hsien-Jen Lin

Hsien-Jen Lin is a professor of applied mathematics at Aletheia University in Taiwan. He received his MS in applied mathematics from Michigan State University, USA, and his PhD in mathematics from National Central University in Taiwan. His current research interests are in the field of production/inventory control, mathematical finance, stochastic model, probability and statistics. His research has appeared in journals such as Applied Mathematical Modelling; Mathematical Problems in Engineering; Stochastic Analysis and Applications; Statistics and Probability Letters; Journal of the Korean Statistical Society (An Official Journal of the Korean Statistical Society); Journal of the Chinese Statistical Association; International Journal of Systems Science; International Journal of Information and Management Sciences; Yugoslav Journal of Operations Research; Far East Journal of Mathematical Sciences; International Journal of Pure and Applied Mathematics; Journal of Applied Science and Engineering; International Journal of Systems Science: Operations and Logistics; TOP: An Official Journal of the Spanish Society of Statistics and Operations Research.