Reorder Point Failure on a High-Velocity SKU
A SKU sells an average of 400 units/week with a standard deviation of 120 units/week. Lead time from the supplier is 3 weeks, fairly stable (assume negligible lead-time variability). The current reorder point is 1,400 units and order quantity is 2,000 units. Service-level target is 95% (z ≈ 1.65). Over the last quarter, the SKU stocked out four times, each lasting 2–4 days, and the planner observed that demand during lead time occasionally exceeded 1,400. The supplier now offers a 2-week lead time if the shipper commits to a minimum order quantity of 3,000 units. The planner wants to keep the 2,000-unit order quantity and simply raise the reorder point.
1. Calculate the demand during lead time and the safety stock required for 95% service at the current 3-week lead time, and determine whether the current reorder point is adequate.
Read the worked answer
Demand during lead time (mean): 400 units/week × 3 weeks = 1,200 units.
Safety stock for 95% service: SS = z × σ_demand × √(lead time)
- σ over lead time = 120 × √3 ≈ 120 × 1.732 ≈ 207.8 units.
- SS = 1.65 × 207.8 ≈ 343 units.
Required reorder point: ROP = demand during lead time + SS = 1,200 + 343 = 1,543 units.
Assessment: the current ROP of 1,400 is 143 units below the required 1,543. That shortfall explains the stockouts: whenever demand during lead time runs above ~1,400 (which happens with meaningful frequency given σ ≈ 208), the SKU runs out before replenishment arrives. The planner's instinct to raise the ROP is directionally correct; the fix is to set it at ~1,543, not an arbitrary higher number.
2. Evaluate the supplier's 2-week lead-time offer with a 3,000-unit minimum order, and recommend whether to accept it.
Read the worked answer
At 2-week lead time:
- Demand during lead time = 400 × 2 = 800 units.
- σ over lead time = 120 × √2 ≈ 169.7 units.
- SS = 1.65 × 169.7 ≈ 280 units.
- ROP = 800 + 280 = 1,080 units.
Comparison:
- Safety stock falls from ~343 to ~280 (saves ~63 units of buffer).
- Pipeline inventory (cycle stock in transit) falls because lead time halves: average in-transit stock ≈ demand × lead time = 400 × 3 = 1,200 vs 400 × 2 = 800, a reduction of ~400 units of pipeline stock.
- But the minimum order rises from 2,000 to 3,000, adding ~1,000 units of cycle stock (average cycle stock = Q/2, so +500 units average) and increasing holding cost and obsolescence risk.
Judgment: the lead-time reduction lowers safety stock and pipeline inventory but the larger MOQ raises cycle stock. Net inventory depends on holding cost per unit and demand stability. If holding cost is material and demand is steady, the shorter lead time improves responsiveness and reduces stockout risk enough to justify the MOQ. Recommend accepting only if the 3,000-unit order does not exceed ~7.5 weeks of demand (3,000 / 400 = 7.5 weeks), which is a long coverage window and a real obsolescence concern. A conditional acceptance - negotiate a lower MOQ or a scheduled-release arrangement - is the balanced choice.
3. The planner proposes keeping the 2,000-unit order quantity and only raising the reorder point. Critique this and recommend a complete parameter set.
Read the worked answer
Critique: raising the ROP fixes the stockout symptom but ignores the interaction between order quantity and lead time. With Q = 2,000 and weekly demand of 400, the order cycle is 5 weeks. During the 3-week lead time, demand is only 1,200 on average, so a 2,000-unit order arrives with substantial remaining stock - meaning the ROP mainly needs to cover lead-time demand plus safety stock, which the calculation supports. However, the planner should verify the ROP against the actual review/reorder trigger: if ordering is triggered only when inventory hits the ROP, the ROP must account for the full lead-time demand, not partial.
Recommended parameters (3-week lead time, keep Q = 2,000):
- ROP = 1,543 units (1,200 mean + 343 SS).
- Q = 2,000 (5-week cycle; acceptable if holding cost is tolerable).
- Recompute SS if service target changes; at 99% (z ≈ 2.33), SS ≈ 484 and ROP ≈ 1,684.
If the 2-week offer is accepted: ROP = 1,080, Q = 3,000 (7.5-week cycle).
Additional control: because stockouts occurred four times in a quarter, audit actual lead-time variability - the assumption of negligible variability should be tested. If lead time varies, add lead-time variance to the safety-stock formula; otherwise the ROP will again under-protect.