A note on “Coordinating a supply chain for deteriorating items with a revenue sharing and cooperative investment contract”

• We improve the proof in Zhang et al. without Taylor approximation.
• We generalize the model of Zhang et al. to a broader class of demand functions.
• We summarize critical structural properties regarding the equilibrium decisions.

In this short note, we first improve the proof in Zhang et al. [1] to show the strict concavity of the unit time total profit of the whole supply chain with respect to preservation technology investment without approximation. We then generalize the model of Zhang et al. [1] to a broader class of market demand functions. Additionally, theoretical results are provided to illustrate the features of the proposed model.