Lot Size 5,000 vs EOQ at a Machined Bracket - With a Discount and an ECN Looming
A plant machines bracket BR-77 used in two product families. Annual demand is 12,000 units, average 231 per week, but it arrives lumpy: recent weeks ran 900, 100, 1,200, 0, 600, 350. The unit cost is $15, carrying cost is 22% per year, and a setup costs $180. The ERP lot-sizing rule is a fixed order quantity of 5,000, inherited from a legacy system nobody has reviewed. Symptoms: roughly 4,800 brackets on the floor and in racks, a space constraint in the machine shop, and two obsolescence write-offs in the last 18 months - both after engineering changes. The supplier has offered a 2% discount on orders of 3,000 or more, with a 2,000 minimum. Separately, an engineering change under review may remove BR-77 from one of its two parent products within 12 months, affecting roughly 30% of the volume.
1. Compare the current fixed order quantity of 5,000 with EOQ and with period order quantity, and show the cost reasoning.
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Holding cost per unit per year: 0.22 x $15 = $3.30.
EOQ = sqrt(2 x 12,000 x 180 / 3.30) = sqrt(4,320,000 / 3.30) = sqrt(1,309,091) = about 1,144 units, roughly 10.5 orders per year.
POQ = EOQ / average weekly demand = 1,144 / 231 = about 5 weeks per order (about 10.4 orders per year).
Cost comparison (setup + cycle stock holding, safety stock excluded since it is unaffected):
- FOQ 5,000: 12,000/5,000 = 2.4 orders x $180 = $432; average cycle stock 2,500 x $3.30 = $8,250; total about $8,682.
- EOQ 1,144: 10.5 x $180 = $1,890; average cycle stock 572 x $3.30 = $1,888; total about $3,778.
The FOQ is costing roughly $4,900 a year more than necessary, plus the space and obsolescence exposure that the cost formula does not capture. But EOQ assumes uniform demand, and BR-77 is anything but uniform; ordering 1,144 into a 100-unit week creates a bracket nobody needs for weeks.
POQ is the better structural fit because it converts the lot size into a time supply, so lots naturally shrink when demand is light and stretch when it is heavy. A 5-week supply is defensible here; many planners would run 3-4 weeks on a lumpy item and push the difference into safety stock.
2. Should the 2% discount at 3,000 units be accepted? Include the ECN risk in the judgement.
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Economics at 3,000 units: purchase saving = 2% x $15 x 12,000 = $3,600 per year. Orders fall to 12,000/3,000 = 4 per year, setup = $720, a saving of about $1,170 against EOQ. Holding cost rises: average cycle stock 1,500 vs 572, an extra 928 units; at the discounted carrying rate (0.22 x $14.70 = $3.23) that is about $3,000 more. Net: roughly $3,600 + $1,170 - $3,000 = about +$1,770 per year in favor of the discount, before risk.
So on pure cost arithmetic the discount wins, but only narrowly - roughly 1.5% of annual spend on the item - and the arithmetic ignores the thing that has already hurt this plant twice: obsolescence after an engineering change. A 3,000-unit lot is about 13 weeks of supply. If the pending ECN removes 30% of the volume, the item's annual demand drops to about 8,400 and a 3,000-unit lot becomes about 18 weeks of supply, with a real chance that a large share of it becomes obsolete when the parent changes.
Judgement: accept the discount only with conditions - (1) confirm the ECN decision and effective date before the next order; (2) if the change is likely within 12 months, cap lots at 2,000-2,500 and negotiate the discount threshold or take it on other, stable part numbers; (3) require supplier flexibility to defer or reduce a scheduled delivery inside the lead time. Do not let a $1,770 annual saving justify a five-figure write-off.
3. How should scrap and safety stock be handled when the lot-sizing rule changes?
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Changing the lot size changes the pipeline, so the two related parameters need to move at the same time or the changeover will look like a failure.
Scrap: if BR-77's machining operation has a yield loss (say 4%), the gross requirement must be inflated by the applicable scrap factor, not the order quantity. Scrap belongs at the level where it occurs - operation scrap in the routing, component scrap at the BOM if the loss is on components. Set this once, in one convention, and check it against actual usage. If scrap is 4% and demand is 12,000 good units, the planned quantity must be about 12,500, and the lot size decision should be made on the gross figure.
Safety stock: EOQ analysis deliberately excludes safety stock because the optimal order quantity does not depend on it. But lumpy demand means the plant will want buffer. Safety stock should be set from demand variability over the protection period (lead time plus review period), not from a round number, and it should be reviewed when the lot size changes - a 5-week POQ increases exposure between orders, which usually argues for a slightly higher safety stock than a 1,144 FOQ.
Watch the interaction: safety stock plus a large lot plus 4% scrap is how 4,800 brackets end up on the floor. Add a periodic check of on-hand against the lot-size-driven target, and treat any stock above target plus safety as a signal to reduce the lot, not to buy more racks.