Note on: A necessary and sufficient conditions for the existence of the optimal solution of a single-vendor single-buyer integrated production-inventory model with process unreliability consideration

Chung (2008) discussed the necessary and sufficient conditions for the existence of the optimal solution of an integrated production-inventory model developed by Huang (2004), which allowed a vendor and a buyer to minimize their expected integrated total cost function with an imperfect production process. The objective of Chung (2008) was to improve the solution procedure presented in Huang (2004). In this study, we identify three errors, irrelevant conditions, and inappropriate examples used in Chung (2008). We provide a reformulation of the model and the correct necessary and sufficient conditions for optimality.