EOQ with backorders calculator
When planned shortages are allowed and backordered at cost b per unit per year, the extended Harris model gives Q* = sqrt(2DS/H) * sqrt((H+b)/b) and an optimal planned shortage B* = Q* * H/(H+b)[1]. The factor sqrt((H+b)/b) inflates Q* upward relative to Wilson because spreading some shortage across the cycle is cheaper than carrying every unit on the shelf.
When deliberate stockouts make sense
Three conditions: (1) the shortage cost b is genuinely lower than the holding cost H (rare in retail, common in industrial spares with patient customers); (2) the customer is contractually willing to wait without penalty; (3) the cost of capital tied up in inventory is the binding constraint. Outside those conditions, plan the model with B* = 0 (i.e. collapse to Wilson) and use safety stock to absorb demand variance instead.
Backorder allowance vs safety stock
Safety stock absorbs demand variance during lead time; backorder allowance accepts a deterministic stockout to lower average inventory. They solve different problems and can coexist: a (Q, r) policy with backorders runs Q* per the formula above and sets r = d*L + safety stock independently. See ROP calculator for the safety stock piece.