A note on A two-level supply chain with consignment stock agreement and stock-dependent demand

This note points out that the cost functions within Zanoni and Jaber [Zanoni, S. and M. Y. Jaber. 2015. "A Two-level Supply Chain with Consignment Stock Agreement and Stock-dependent Demand." International Journal of Production Research 53: 3561-3572] might be incorrect due to misuse of demand representation. By incorporating Braglia and Zavanellas consignment stock model and relaxing the zero-inventory reordering constraint, Zanoni and Jaber made extensions of the integrated vendor-buyer supply chain with stock-dependent demand in Sajadieh, Thorstenson, and Akbari Jokars proposed model. However, Sajadieh, Thorstenson, and Akbari Jokars model has different scenarios than Braglia and Zavanellas model, and these inconsistencies cause false formulation in Zanoni and Jabers paper. In this note, we first formulate the justified cost functions and then present characteristics of the corrected model.