Question

The maximum level of inventory of an item is 100 and it is achieved with an infinite replenishment rate. The inventory becomes zero over one and half months due to consumption at a uniform rate. This cycle continues throughout the year. Ordering cost is Rs. 100 per order and inventory carrying cost is Rs. 10 per item per month. Annual cost (in Rs.) of the plan, neglecting material cost, is

• A. 800
• B. 6800
• C. 4800
• D. 2800

Answer 1

The correct option is B 6800

Total Annual cost = Annual carrying cost + Annual ordering cost.

$=\frac{Q}{2}\times C_h+\frac{D}{Q}{C}_0$

$\text{Now, annual carrying cost}=\frac{Q}{2}\times C_h$

Where

$\text{Q = Units per order = 100}$

$C_h=$ Inventory carrying cost is Rs. 10 per item per month

Hence,

$C_h=12\times 10\text{per item per year}$

$\text{= Rs 120 per item per year}$

$\therefore \text{Annual carrying cost}=\frac{100}{2}\times 120=6000$

Now cost of an order

$C_0=Rs.100$

No of orders per year,

$N=\frac{1}{T}=\frac{\text{12 months}}{\text{1.5 months}}=8$

$\text{Here, T = 1.5 months}$

$\text{Hence, annual ordering cost = 8 × 100 = 800}$

$\text{Hence, total annual cost = 6000 + 800 = Rs. 6800}$