Economic Production Quantity (EPQ)
When stock is built up by a production line at rate p units per day while demand drains it at rate d, the EOQ model adjusts. Average inventory is (Q/2)(1 - d/p), not Q/2, and the optimal lot grows by 1 / sqrt(1 - d/p) over Wilson[1].
Why average inventory shrinks
Under Wilson, the lot Q arrives instantaneously; inventory drops from Q to 0 in a sawtooth and averages Q/2. Under EPQ, the lot builds up at rate (p - d) during the production phase, then consumes at rate d during the pure-consumption phase. The peak is Q(1 - d/p), reached when production ends. Average across the full cycle is half that.
Cycle decomposition
Production phase: duration Q/p, inventory rises from 0 to Q(1 - d/p). Pure-consumption phase: duration Q(1 - d/p)/d, inventory falls back to 0. Total cycle T = Q/d. The decomposition matters because the holding-cost piece of TC integrates over the full cycle but with a shorter peak than Wilson.
When p approaches d
The correction factor (1 - d/p) shrinks toward zero, Q* blows up to infinity, and the economically correct answer is "never shut the line." This is exactly the case where EPQ stops being a useful planning tool and the conversation moves to capacity investment.