库存：订货成本与持有成本的平衡点

Flour is 60% of a bun and 48,000 kg a year of cash

• Too little stops the line; too much is money mouldering in bins. Two costs pull against each other: ordering (50 pounds an order) and holding (1.20 a kg a year).
• The economic order quantity 经济订货批量 is where they balance.

The EOQ

• $EOQ = \sqrt{2DS/H} = \sqrt{2 \times 48{,}000 \times 50 / 1.20} = 2{,}000$ kg: 24 orders a year, one every 15.2 days.
• At the EOQ the costs tie: ordering $24 \times 50 = 1{,}200$, holding $1{,}000 \times 1.20 = 1{,}200$.

The reorder point

• Daily demand $48{,}000/365 = 131.5$ kg; the lead time 交货期 is 6 days, so $131.5 \times 6 = 789$ kg leaves the bin while the order is on the road.
• Demand sd 25 a day gives $\sigma_{LT} = 25\sqrt{6} = 61.2$; at 95% service $z = 1.645$, safety stock 安全库存 $= 101$ kg and the reorder point 再订货点 $= 789 + 101 = 890$ kg.

The discount that had to be checked

• 2% off 2.00 a kg for orders of 4,000 kg: purchase 94,080 + ordering 600 + holding 2,400 = 97,080 against 98,400 at the EOQ - saves 1,320 a year.
• The extra logistics cost is exactly 600, so the breakeven discount is $600/96{,}000 = 0.625\%$. The EOQ is the number every deviation must beat.

The shortage that was predictable

• Festival week runs 180 kg a day. The bin hits 890 and an order goes out - but $180 \times 6 = 1{,}080$ kg leaves before it lands: a 190 kg stockout.
• Safety stock was sized for sd 25 noise, not a calendar event 49 a day above the mean. Events need a scheduled pre-buy, not a bigger buffer.

Three inventory slips

Recap