# Answer to Question #172660 in Mechanical Engineering for dean

Question #172660

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

1
2021-03-22T08:36:02-0400

 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

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