Scenario 9.2
Shipments of Product X from a plant to a wholesaler are made in lots of 1500 units each. The wholesaler's average demand for X is 300 units per week. The lead time from the plant to the wholesaler is 3 weeks. The wholesaler pays for the shipments when they leave the plant.

Refer to Scenario 9.2. What is the total of the wholesaler's current cycle plus pipeline inventories?

Question

Scenario 9.2
Shipments of Product X from a plant to a wholesaler are made in lots of 1500 units each. The wholesaler's average demand for X is 300 units per week. The lead time from the plant to the wholesaler is 3 weeks. The wholesaler pays for the shipments when they leave the plant.

Refer to Scenario 9.2. What is the total of the wholesaler's current cycle plus pipeline inventories?

BlackTom AI · Accepted Answer

To tackle this question, I’ll break down the inventory components involved in a steady replenishment scenario.

Option 1: 1800 units. This would imply a total of 1800 units between cycle and pipeline inventories. If cycle stock were computed as Q/2, that would be 1500/2 = 750 units, and pipeline stock would need to be 1050 units to sum to 1800. However, pipeline stock is typically demand during lead time, which is L * demand rate = 3 weeks * 300 units/week = 900 units. That would give 750 + 900 = 1650, not 1800. So 1800 would be inconsistent with the standard breakdown here.

Option 2: 850 units. This value is near Q/2 (which is 750) but not equal, and it also doesn’t align with the pipeline stock calculation of 900 units. If we tried to force 850 as the sum, the implied pipeline or cycle components would be off from the known definitions (cycle stock = Q/2 = 750; pipeline = 900). Therefore 850 is not correct under the standard interpretation.

Option 3: 750 units. This exactly matches Q/2, which is the typical cycle stock when demand is steady and replenishments occur in fixed lots. However, this ignores the pipeline portion entirely. Pipeline stock should be the inventory in transit during the lead time, which here is 3 weeks of demand, i.e., 3 × 300 = 900 units. So 750 alone would omit the in-transit portion, making this option incomplete.

Option 4: 1650 units. This combines cycle stock of Q/2 = 1500/2 = 750 units with pipeline stock of 3 weeks of demand (3 × 300 = 900), giving 750 + 900 = 1650. This aligns with the standard decomposition of total inventory into cycle stock (average inventory tied up in the replenishment cycles) and pipeline stock (inventory in transit during lead time).

In summary, the correct approach uses:
- Cycle inventory (average in-cycle inventory) = Q/2 = 1500/2 = 750 units.
- Pipeline inventory (in-transit inventory during lead time) = L × demand rate = 3 × 300 = 900 units.
- Total of cycle plus pipeline inventories = 750 + 900 = 1650 units.

Therefore, Option 4 (1650 units) is the correct total for the wholesaler’s current cycle plus pipeline inventories. The other options misrepresent either the cycle portion, the pipeline portion, or both, by using incorrect sums or ignoring a key component of the inventory system.

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