A two-echelon supply chain inventory model with shortage backlogging, inspection errors and uniform demand under imperfect quality items

Actually, some production and inspection processes do not work perfectly, thereby producing a certain number of defective items and inspection errors. Previous imperfect-quality integrated inventory studies have mostly focused on developing models that do not consider two-way imperfect inspection under stochastic demand. Thus, this paper proposes a cost-minimising integrated vendor-buyer production-inventory model that incorporates imperfect production quality, stochastic demand, and imperfect inspection processes. The imperfect inspection processes are Type I inspection error of classifying a non-defective item as defective and Type II inspection error of classifying a defective item as non-defective. Meanwhile, the demand is assumed uniformly distributed. The objective of this research is to determine the optimal order quantity and reorder point such that the expected integrated total annual cost is minimised. In order to solve the integrated model, an optimal solution procedure is developed. A numerical example is provided to illustrate the application of the model. Besides, a sensitivity analysis is also given to investigate the effects of six important parameters (the transportation cost, the buyer's holding cost, the vendor's holding cost, the percentage of defective items, Type I error, and Type II error) on the optimal solution.