Question 1

Inventory Control

a. A department store in the town of Napar sells cell a popular brand of cell phones to customers in the area. This cell phone is fairly durable and it has lots of features. The demand for this phone is normally distributed with a mean of 50 cell phones per day and a standard deviation of 10 phones. The store operates 350 days per year. Ordering cost is $300 per order and the holding cost is 5% of the cost of the phone. The store sells the phone for $800. The lead time is 4 days and the store would like to have a 95% cycle time which is equivalent to 2 standard deviations. Current on-hand inventory is 200 cell phones with no open orders or back orders

i. Calculate the EOQ? [3 marks]

ii. Calculate the number of order placed per year? [2 marks]

iii. Calculate the average time between orders? [2 marks]

iv. Calculate the ROP? [4 marks]

v. An inventory withdrawal of 200 units was just made. - Is it time to reorder? [2 marks]

vi. Calculate the total annual cost of using the EOQ. [2 marks]

b. The annual demand for an item is 10,000 units. The cost to process an order is $75 and the annual inventory holding cost is 20% of item cost.

i. What is the optimal order quantity, given the following price breaks for purchasing the item? [2 marks]

ii. What price should the firm pay per unit? [1 mark]

iii. What is the total cost at the optimal order size? [7 marks]

Price Breaks

Quantity	Price
1-9	$2.95 per unit
10 - 999	$2.50 per unit
1,000 - 4,999	$2.30 per unit
5,000 or more	$1.85 per unit