Convenient expressions for computing the exact annual cost of a continuous-review (Q, R) system with backordering

For a continuous-review order-quantity reorder point system, the ‘average on-hand inventory level’ (‘AOI’) is often computed by the approximate Hadley–Whitin expression, while the exact AOI is given by a double integral that appears daunting to both students and practitioners. This paper presents exact AOI expressions that are simple enough to be executed by the most basic business softwares. Numerical examples are provided to illustrate the ease of using these expressions as well as the necessity of using them in situations where the standard Hadley–Whitin approximation becomes too inaccurate.