Question:
Which ONE of the following is NOT an assumption of the economic order quantity (EOQ) model?
Which ONE of the following is NOT an assumption of the economic order quantity (EOQ) model?
Show Hint
Think about what the classic EOQ sawtooth inventory diagram looks like and whether it ever allows stock to run negative.
Updated On: Aug 5, 2026
- Demand is known and deterministic.
- Lead time is zero.
- Stockouts are permissible.
- Holding cost for the quantity in stock is linearly increasing with the order quantity.
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The Correct Option is C
Solution and Explanation
Step 1: Understanding the Question:
The basic economic order quantity (EOQ) model, also called the Wilson model, is built on a set of simplifying assumptions about demand, lead time, holding cost, and shortages.
We need to find the one statement among the four options that does NOT belong to this list of assumptions.
Step 2: Key Formula or Approach:
The classic EOQ formula is derived by minimizing the total annual cost, which is the sum of ordering cost and holding cost.
\[ TC(Q) = \frac{D}{Q}C_o + \frac{Q}{2}C_h \]
This formula, and the assumptions behind it, only holds true when demand is steady, replenishment happens instantly, holding cost grows in step with the order quantity, and shortages are never allowed to occur.
Step 3: Detailed Explanation:
Option (A), demand is known and deterministic: this is a core assumption, the EOQ model needs a constant, known demand rate to work, so this is a valid assumption and not the answer.
Option (B), lead time is zero: the basic model assumes replenishment is instantaneous, so an order arrives exactly when stock hits zero, this is treated as a valid assumption in the simplest form of the model, so it is not the answer.
Option (C), stockouts are permissible: the basic EOQ model is built specifically to avoid running out of stock, it assumes no shortages are allowed at any point in the cycle, so saying stockouts are permissible directly contradicts the model, this is NOT a valid assumption.
Option (D), holding cost rises linearly with order quantity: since average inventory is \( Q/2 \), holding cost is \( (Q/2)C_h \), which does increase linearly with \( Q \), so this is a valid assumption and not the answer.
Final Answer:
The statement that stockouts are permissible goes against the basic EOQ model, which is designed specifically to prevent any shortage.
\[ \boxed{\text{Stockouts are permissible - NOT an EOQ assumption}} \]
The basic economic order quantity (EOQ) model, also called the Wilson model, is built on a set of simplifying assumptions about demand, lead time, holding cost, and shortages.
We need to find the one statement among the four options that does NOT belong to this list of assumptions.
Step 2: Key Formula or Approach:
The classic EOQ formula is derived by minimizing the total annual cost, which is the sum of ordering cost and holding cost.
\[ TC(Q) = \frac{D}{Q}C_o + \frac{Q}{2}C_h \]
This formula, and the assumptions behind it, only holds true when demand is steady, replenishment happens instantly, holding cost grows in step with the order quantity, and shortages are never allowed to occur.
Step 3: Detailed Explanation:
Option (A), demand is known and deterministic: this is a core assumption, the EOQ model needs a constant, known demand rate to work, so this is a valid assumption and not the answer.
Option (B), lead time is zero: the basic model assumes replenishment is instantaneous, so an order arrives exactly when stock hits zero, this is treated as a valid assumption in the simplest form of the model, so it is not the answer.
Option (C), stockouts are permissible: the basic EOQ model is built specifically to avoid running out of stock, it assumes no shortages are allowed at any point in the cycle, so saying stockouts are permissible directly contradicts the model, this is NOT a valid assumption.
Option (D), holding cost rises linearly with order quantity: since average inventory is \( Q/2 \), holding cost is \( (Q/2)C_h \), which does increase linearly with \( Q \), so this is a valid assumption and not the answer.
Final Answer:
The statement that stockouts are permissible goes against the basic EOQ model, which is designed specifically to prevent any shortage.
\[ \boxed{\text{Stockouts are permissible - NOT an EOQ assumption}} \]
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