Question

In the classical economic order quantity (EOQ) model, let Q and C denote the optimal order quantity and the corresponding minimum total annual cost (the sum of the inventory holding and ordering costs). If the order quantity is estimated incorrectly as Q′ = 2Q, then the corresponding total annual cost C′ is
1. C′ = 1.25C
2. C′ = 1.5C
3. C′ = 1.75C
4. C′ = 2C

Answer 1

Correct Answer - Option 1 : C′ = 1.25C

Concept:

The total annual cost for the inventory system is given as:

 \(\mathbf{C~=~\frac{D}{Q}C_o~+~\frac{Q}{2}C_h}\)

where C is the total annual cost, D is the annual demand, Q is the order quantity, C_o is the ordering cost and C_h is the holding cost per unit per year.

In economic order quantity (EOQ), \(\mathbf{\frac{D}{Q}C_o~=~\frac{Q}{2}C_h}\)

Calculation:

Given:

In economic order quantity,  

\(\frac{D}{Q}C_o=\frac{Q}{2}C_h\) or C = \(\frac{Q}{2}C_h~+~\frac{Q}{2}C_h\)

⇒ C = QC_h

Now, the new order quantity is Q′ = 2Q, so the new total cost is

\(C^′~=~\frac{D}{Q^′ }C_o~+~\frac{Q^′}{2}C_h\) = \(C^′~=~\frac{D}{2Q }C_o~+~\frac{2Q}{2}C_h\)

⇒ \(\frac{1}{2}\left ( \frac{Q}{2}C_h \right)+QC_h\) = \( \frac{Q}{4}C_h~+~QC_h\) = \(\frac{5}{4}QC_h\)

∴ C′ = 1.25C