Under Wilson’s assumptions (constant demand D, fixed order cost S, constant holding cost H, instantaneous resupply, no shortages), the annual variable cost of running a (Q, r) policy with batch size Q is the sum of two terms.

Ordering term (D/Q) * S. Annual demand D divided by batch size Q gives the number of orders per year. Each costs S. So the annual ordering cost is (D/Q) * S^[1].

Holding term (Q/2) * H. Under instantaneous resupply the on-hand inventory is a sawtooth: Q immediately after each delivery, declining linearly to 0, repeat. Average over the cycle is Q/2. Multiply by annual holding cost per unit H to get annual holding cost (Q/2) * H^[2].

What about purchase cost? If unit cost C is constant across all Q (no quantity discount), the total purchase cost is D * C - independent of Q. It drops out of optimisation. We omit it. The step 5 extension reintroduces D * C when C varies by tier.

The optimisation problem is now: minimise TC(Q) = (D/Q)S + (Q/2)H over Q > 0.