Question

A food store consumes an average of 3,000 units each month of a specific product. Customer demand is normally distributed with the standard deviation of the month of demand being 200 units. The store pays $10 for each unit to the supplier. The cost of ordering and receiving a shipment is $14 per order. The annual inventory carrying cost is 20% of the value of this product. The supplier lead time is 2 operating days. The shop operates 240 days per year or 20 days each month. Each order is received from a supplier in a single delivery. Fixed order quantity inventory system is used, and the supplier is paid when the order is delivered (cash on delivery). There are no quantity discounts. Please show your work with formulas and inputs used to obtain full credit for each answer.

1. What quantity should the store order with each order?

2. How many times per year will the shop order on avg?

3. How many operating days will elapse between 2 consecutive orders?

4. What is the store's minimum total annual cost of placing orders and carrying inventory (cycle stock)?

5. The company carries 60 units of safety stock. What is the annual cost to carry that safety stock?

Answer 1

The Economic Order Quantity (EOQ) can determine the optimal order quantity, considering ordering and carrying costs. This approach helps minimize the total inventory cost, which includes costs associated with ordering and holding inventory.

Step-by-step explanation:

To determine the optimal order quantity for the food store, we can use the Economic Order Quantity (EOQ) model. The EOQ minimizes the total inventory cost, which is the sum of the ordering costs and the carrying costs. The ordering cost is the cost of placing an order and receiving goods ($14 per order in this case), and the carrying cost is the cost of holding one unit of inventory for a year (20% of the unit cost).

Order Quantity (Q): The EOQ formula is given by the square root of (2DS/H), where D is the annual demand (3,000 units per month x 12 months), S is the ordering cost, and H is the annual holding cost per unit (which is 20% of the cost per unit, $10).

Number of Orders per Year (N): This is the annual demand (D) divided by the order quantity (Q).

Days between Orders (T): This can be calculated by dividing the number of operating days per year by the number of orders per year (N).

Minimum Total Annual Cost: This is computed by adding the annual ordering costs (order cost times number of orders) and the annual carrying costs (average inventory level times carrying cost per unit).

Carrying Cost of Safety Stock: The annual carrying cost for safety stock is the safety stock level multiplied by the carrying cost per unit.