Surfsports Inc. manufactures jet-skis. The most expensive component of a jet-ski
ID: 448578 • Letter: S
Question
Surfsports Inc. manufactures jet-skis. The most expensive component of a jet-ski is the pump. The pump costs Surfsports $2800 per unit and constitutes 40% of the total cost of the jet-ski. Surfsports sells 3500 jet-skis each year. The demand for the product has been fairly constant over the years. Currently, Surfsports uses the EOQ model to determine how many pumps to purchase from its supplier. The ordering cost is $200 per order and the annual holding cost per unit is 20% of the variable cost of the product. The supplier’s lead time is 5 days. There are 350 operating days within a year.
NOTE: SHOW ALL YOUR WORK. USE 4 DECIMAL PLACES IN YOUR CALCULATIONS.
a) (2 points) Using the EOQ Model, what is the optimal order quantity for the pump?
b) (1 points) Using the EOQ Model, how many orders are placed per year?
c) (1 points) Using the EOQ Model, what is the total annual ordering cost?
d) (1 point) Using the EOQ Model, what is the total annual inventory holding cost?
e) (2 points) Using the EOQ Model, what is the reorder point for the product?
The remainder of the questions will be answered based on the following information:
In the next year of operations, Surfsports is expecting that a new Jet-ski brand by a rival company will be introduced to the market. The rival company will also use the same pump supplier. Due to the new market dynamics, Surfsports expect that demand for its Jet-skis will now be variable and estimates that demand for Jet-skis will follow a normal distribution with mean 2500 per year and standard deviation 300 per year. Due to short time span the pump supplier will not be able to increase its production capacity and hence can only deliver the pumps in 2 weeks. Surfsport would want to avoid stock outs 95% of the time
f) (2 points) What should be the reorder level for Surfsports?
g) (2 points) What is the number of items in the safety stock?
h) (2 points) What is the number of items in the pipeline inventory?
Explanation / Answer
a. optimal order quantity = (2*annual demand*order cost/holding cost)^0.5
annual demand = 3500. order cost = $200. holding cost = 20% of the variable cost = 20% of 2800 (pump cost is a variable cost for the end product) = $560.
Thus optimal quantity = (2*3500*200/560)^0.5 = 2500^0.5 = 50 units.
b. Number of orders = annual requirement/quantity per order = 3500/50 = 70 orders.
c. total annual ordering cost = cost per order*no. of orders = $200*70 = $14,000
d. annual inventory holding cost = optimal quantity/2*holding cost = 50/2*560 = $14,000
e. Re-order point = annual demand/number of days in a year*lead time = 3500/350*5 = 50 units.
f. reorder level = average daily demand*lead time + z*standard deviation * (lead time)^0.5
average daily demand = 2500/350 = 7.1428. z at 95% service level = 1.96 lead time = 2 weeks or 14 days.
thus re-order = 7.1428*14+1.96*300*(14)^0.5
= 100+2200 = 2,300
g. safety stock = z*standard deviation * (lead time)^0.5
z at 95% service level = 1.96 lead time = 2 weeks or 14 days
safety stock = 1.96*300*(14)^0.5 = 2,200
h. number of items in the inventory = safety stock +Q/2
Q = (2*2500*200/560)^0.5 = 42.2577
thus inventory = 42.2577/2+2,220 = 2221.22
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