Question

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.

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]

Answer 1

Demand, d = 50 per day

Std dev of demand, s = 10 per day

Operating days per year, n = 350

Annual demand, D = n*d = 350*50 = 17,500

Ordering cost, S = $ 300 per order

Holding cost, H = Unit cost * Holding cost rate = 800*5% = $ 40   (considering holding cost rate is 5% per year)

Lead time, L = 4 days

z value = 2 (for 95% service level)

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i)

EOQ = sqrt(2DS/H)

= sqrt(2*17500*300/40)

= 512

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ii)

Number of orders placed per year = D/Q

= 17500/512

= 34 (rounded-off)

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iii)

Average time between orders = Q/d

= 512/50

= 10.24 days  

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iv)

ROP = d*L+z*s*sqrt(L)

= 50*4+2*10*sqrt(4)

= 240

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v)

Current inventory position = Current on hand inventory + open orders - backorders - withdrawals

= 200 + 0 - 0 - 200

= 0

Current inventory position is less than ROP.

Therefore, it is time to order.

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vi)

Total annual cost of using the EOQ = Holding cost + Ordering cost

= H*Q/2 + S*D/Q

= 40*512/2+300*17500/512

= $ 20,494