Problem: A dealer supplies you the following information with regard to a product dealt in by him:
Annual demand: 10,000 units
Ordering cost: Rs. 10/- per order
Price: Rs. 20/- per unit
Inventory carrying cost: 20% of the value of inventory per year.
The dealer is considering the possibility of allowing some back-order (stock-out) to occur. He has estimated that the annual cost of back-ordering will be 25% of the value of inventory.
 What should be the optimal number of units (product) he should by in one lot?
 What quantity of the product should be allowed to be back-ordered, if any?
 What would the maximum inventory level?
 Would you recommend to allow back-ordering? If so, what would be the annual cost saving/ loss by adopting the policy of back-ordering
 Order quantity = (2AK/h)1/2
A - Annual demand, K - ordering cost, h - price
Order quantity = (2 x 10 000 x 10 / 20)1/2 = 100
 Back ordered quantity = Order quantity *(Ch/(Ch + Cb))
Ch - Inventory carrying cost
Cb - annual cost of back-ordering
Back ordered quantity = 100 x (0.2 / (0.2+0.25)) = 44
 Maximum Level = Re-order level + Re-order quantity – (Minimum usage × Minimum lead time)
 Back-ordering is not allowed