Inventory Management and Control
Inventory management and control tests whether you can set order quantities, safety stock, and reorder points, and then control inventory with segmentation and counting. Expect EOQ, service levels, ABC analysis, cycle counting, and the difference between cycle service level and fill rate.
Core rules
- EOQ balances ordering cost and carrying cost: EOQ = sqrt(2DS / H), where D is annual demand, S is order cost, and H is annual holding cost per unit.
- Safety stock protects against demand and lead-time variability. For normally distributed demand with constant lead time, safety stock = z x sigma_d x sqrt(L).
- Reorder point = demand during lead time + safety stock. In a continuous-review system, place an order when inventory position reaches the ROP.
- Cycle service level is the probability of no stockout per replenishment cycle. Fill rate is the fraction of demand satisfied from stock. They are not interchangeable.
- ABC analysis ranks items by annual usage value, not unit cost. XYZ adds demand variability. Cycle counting replaces annual wall-to-wall counts with frequent, controlled counts.
Worked example
Annual demand D = 10,000 units, order cost S = $50, holding cost H = $4 per unit per year. EOQ = sqrt(2 x 10,000 x 50 / 4) = sqrt(250,000) = 500 units. Orders per year = 20; ordering cost = 20 x $50 = $1,000. Average cycle stock = 250; carrying cost = 250 x $4 = $1,000. Total relevant cost = $2,000. If the firm orders 1,000 units, ordering cost falls to $500 but carrying cost rises to $2,000, total $2,500. The EOQ is the cost minimum, not the largest discount quantity.
Traps that cost marks
- Applying EOQ where demand is lumpy, perishable, or quantity discounts change the cost curve.
- Using cycle service level to calculate fill rate, or vice versa.
- Ignoring lead-time variability when suppliers are unreliable.
- Treating holding cost as only interest; space, handling, obsolescence, and insurance also count.
- Ranking ABC by unit price rather than annual usage value.