Exact closed-form solutions for “optimal inventory model for items with imperfect quality and shortage backordering”

Wee et al. [Optimal inventory model for items with imperfect quality and shortage backordering. Omega 2007;35(1):7–11] recently contributed an optimal inventory model for items with imperfect quality and shortage backordering. This article revisits their study and applies the well-known renewal-reward theorem to obtain a new expected net profit per unit time. We derive the exact closed-form solutions to determine the optimal lot size, backordering quantity and maximum expected net profit per unit time, specifically without differential calculus. We also solve the same model algebraically from another direction, which has been mentioned, but the process has not been finished yet. The problem parameter effects upon the optimal solutions are examined analytically and numerically.