Inventory working-capital impact
Average on-hand inventory at Wilson Q* is Q*/2 + safety stock. Cash tied up = (Q*/2 + SS) * C. Cutting Q* by 30 percent (via lower S or higher i) cuts cycle stock by 30 percent; SS is unchanged because it’s independent. Balance-sheet inventory and the cash conversion cycle move proportionally[1].
The mean inventory level over a Wilson cycle, dollar-valued at unit cost.
Inventory turnover
Turnover = annual COGS / average inventory value = D * C / ((Q*/2 + SS) * C) = D / (Q*/2 + SS). Doubling Q* halves cycle-stock turnover. SMB target is typically 6 to 12 turns per year for stable goods, higher for perishables, lower for industrial spares[2].
Defending a higher Q* to a CFO
CFOs intuitively dislike inventory. Wilson Q* is defensible when you present the alternative: ordering smaller batches Q < Q* shifts cost from holding to ordering. If ordering cost S is real (PO admin labour, supplier setup), the total annual cost rises as Q drops below Q*. The math is not an excuse to carry inventory; it is an honest balance. The sensitivity strip shows how flat the curve is around Q*: if the CFO wants Q at 80 percent of Q*, total cost rises only 2 to 3 percent. Negotiable.
Where inventory cuts hit margin
Cutting Q below Q* increases stockout probability (more frequent reorders = more opportunities to miss). Compute the lost-sale economics before cutting Q on margin grounds. For most consumer goods, gross-margin recovery from one prevented stockout exceeds the carrying-cost saving from running Q at 50 percent of Q*.