An integrated single-vendor single-buyer inventory model with partial backorders solved using the complete squares method

The main purpose of this paper is fourfold. First we extend Yang et al.'s model by including a fixed backorder cost for the buyer and three types of inspection cost for the vendor. Second we derive, using the complete squares method, the optimal expressions of the extended model, and hence readily deduce the explicitly optimal solution to Yang et al.'s model. Third we solve a numerical example so as to illustrate the solution procedure. Finally, some concluding remarks are drawn.