Speedy Bicycle Company (SBC) is a wholesale distributor of a wide variety of bicycles and bicycle parts. The most
popular model is the Dragonfly, which sells for $170. All manufacturing is done at a plant in China, and shipment takes a
month (30 days) from the time an order is placed. The estimated order cost is $75, including customs clearance. SBC’s
cost per bicycle is 65% of retail price, and inventory carrying cost is 11% per year of SBC’s cost. If the company cannot
fulfill a retail order, the retailer will get the shipment from another distributor and SBC loses that business. SBC is
planning inventory for 2019 based on forecasted demand and wants to maintain a 93% service level to minimize lost
orders. The company has 300 working days per year.
2019 Forecasted Demand for the Dragonfly Bicycle Model:
J F M A M J J A S O N D
8 15 31 58 96 59 38 23 16 14 26 41
Develop an inventory plan for the Dragonfly model.
Order cost = $__________ per order
Cost per bicycle = $_____________
Annual holding cost per bicycle = $__________
Service level = _________% so z = __________
Lead time = __________ days
Annual demand for 2019 = __________ bicycles
Answer: (Show work and put answer in blank to receive credit. Work can be on back of page.)
1. What is the economic order quantity?
Q = __________ (round to nearest whole number)
2. If average demand during lead time is normally distributed with a standard deviation of 2.5 bicycles, what is the
reorder point with the desired service level?
Safety stock = __________ bicycles
ROP = __________ bicycles
3. What is the total annual inventory cost including safety stock?
4. If SBC is currently ordering 100 bicycles at a time, how much is the company overpaying in total inventory cost?
5. Each year during their anniversary celebration, SBC offers a collectable water bottle at the special price of $5. They
typically sell 100 bottles with a standard deviation of 12 bottles. The cost of each bottle is $1.50, and any unsold
inventory is donated to a local charity. What is the service level and optimal order quantity for the water bottles?
Service level = _____________________
Optimal order quantity = ________________________
Cost per bicycle = 0,65x170 = 110.5
Holding cost =0.11x110.5 =12.15
1. EOQ = [ 2xannual demand xordering cost / holding cot per unit per year]1/2
= [ 2x 425 x75/12.15]1/2 = 72.43 =72
2. ROP = lead time demand + safety stock
= 30x 425/300 + zx 2.5
= 42.5+ 1.48x2.5 =46.2 =46
3. Total inventory cost = [Q/2 + safety stock] x holding cost
= [ 36+3.7]x12.15 =482.35
4. Inventory cost with Q=200,
[ 200/2+3.7] x12.15 =1259.35
Difference = 1259-482 =777
5. shortage cost Cu = 5-1.5 =3.5
Overage cost Co = 1.5-0 =1.5
Critical ratio = Cu / Co+Cu = 3.5 /5 = 0.7
which is 70% service level
z = 0.52
Optimal order quantity can be determined by formula
z = x-mean /standard deviation
0.52 = x-100/12
which gives x = 106. Hence ordering 106 bottles will be appropriate.
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