Pooling Versus Service Time: A Four-DC Network Decision
A manufacturer serves four regions from four distribution centers. Weekly demand at each DC is independent and normally distributed with a mean of 1,000 units and a standard deviation of 200 units. Replenishment lead time is one week from the plant, and the company targets 95% cycle service level at each DC (z = 1.65). Carrying cost is 25% per year on a unit value of $60. A proposal would consolidate to one central DC; pooled demand would still average 4,000 units per week at the same 95% target. However, outbound freight would rise by $46,000 per year as average distance to customers increases, and 15% of volume currently shipped same-day or next-day would move to two-day transit. That time-sensitive segment is 12% of revenue, revenue is $6.2M, and gross margin is 30%.
1. Compute safety stock and its carrying cost before and after consolidation, and state the annual saving.
Read the worked answer
Safety stock = z x sigma x square root of lead time.
Four DCs (decentralized)
Per DC: 1.65 x 200 x square root of 1 = 330 units. Total: 4 x 330 = 1,320 units. Carrying cost: 1,320 x $60 x 0.25 = $19,800 per year.
One central DC
Pooled standard deviation = square root of (4 x 200 squared) = square root of 160,000 = 400 units. Safety stock = 1.65 x 400 = 660 units. Carrying cost: 660 x $60 x 0.25 = $9,900 per year.
Saving from pooling = $19,800 - $9,900 = $9,900 per year, on a 660-unit reduction in safety stock.
The square-root law is doing the work: demand quadruples but its standard deviation only doubles, because the four regions' independent errors offset each other. That independence assumption is the whole benefit, so test it before banking it. If regional demand is driven by national promotions and the correlation coefficient is 0.5, the pooled standard deviation becomes square root of (160,000 + 240,000) = 632, safety stock falls only to about 1,044, and the saving drops to roughly $4,140 per year.
2. Should the company consolidate? Quantify the freight and service effects and recommend an alternative if you would not consolidate.
Read the worked answer
No, not the whole network.
The pooling saving is $9,900. The freight penalty is $46,000. That is a net cost increase of $36,100 per year before any service consideration - the consolidation is a $36,100 loss on logistics alone, and the pooling benefit would have to more than quadruple to break even.
Service effect. The time-sensitive segment is 12% x $6.2M = $744,000 of revenue, contributing $223,200 of gross margin at 30%. If the move to two-day transit loses even 5% of that segment, that is $37,200 of revenue and about $11,160 of gross margin gone, taking the net position to roughly -$47,000 per year, plus growth risk in the segment most likely to grow.
Recommendation: selective pooling. Separate the network by service sensitivity rather than by geography.
- Keep forward stock in all four regions for the 12% time-sensitive segment and for fast-moving A items, so next-day capability is retained.
- Centralize the slow-moving tail (C items, low-velocity SKUs) where customers do not measure transit days. The absolute dollar benefit is smaller than the full-network $9,900, but so is the freight penalty, because these items move in consolidated bulk shipments.
- If a central facility is built, ship line-haul in bulk to the four forward locations and treat them as cross-docks for the fast movers, capturing part of the pooling benefit without extending customer lead time.
- Re-quote freight before any decision. A $46,000 estimate derived from average distance rather than actual lane rates is the single number that decides this case; test it against carrier quotes on the top ten lanes.