Question

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.

Get organized:

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 = ________________________

Answer #1

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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