Note on the backroom effect in retail operations

Eroglu et al. (2013) study a retailer with limited shelf capacity and a backroom. They study a continuous review (r, q) ordering policy with a known order quantity, q. Assuming that backorders can be satisfied from the backroom inventory (if available), they find the expression for the optimal reorder level, r. Our work builds on Eroglu et al. (2013). We correct an erroneous derivation of the expected overflow term, as well as derive an exact expression for the expected cost function, and hence optimal reorder level, instead of the approximate one used by Eroglu et al.