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Question & Answer: A Bike Company has a line of specialty mountain bikes which require 5,000 handlebars annually…..

A Bike Company has a line of specialty mountain bikes which require 5,000 handlebars annually The handlebars can be purchased from a supplier for $30 per unit, or they can be produced internally. The internal production cost is $20 per unit, and the production rate is 20,000 units per year. The cost to set up production is $5000. It costs $25 to issue a purchase order to buy handlebars from the supplier. Inventory holding cost is 25% per year a If the Bike Company decides to purchase the handlebars, what is the optimal order quantity? What is the annual cost? If the Bike Company decides to produce the handlebars, what is the optimal order quantity? What is the annual cost? b.
A Bike Company has a line of specialty mountain bikes which require 5,000 handlebars annually. The handlebars can be purchased from a supplier for $30 per unit, or they can be produced internally. The internal production cost is $20 per unit, and the production rate is 20,000 units per year. The cost to set up production is $5000. It costs $25 to issue a purchase order to buy handlebars from the supplier. Inventory holding cost is 25% per year. a. If the Bike Company decides to purchase the handlebars, what is the optimal order quantity? What is the annual cost? b. If the Bike Company decides to produce the handlebars, what is the optimal order quantity? What is the annual cost?

Expert Answer

a)

Given

Annual Demand D = 5000 handle bars

Cost C = $30

Ordering cost S = $25

Holding cost =25% = 0.25*30 = $7.5

Optimal order quantity Q

Q=sqrt{2DS/H}

Q=sqrt{(2*5000*25)/7.5}

Q= 182.57 units or 183 units

Total cost (Includung Purchase cost)= Annual purchase cost + Annual holding cost + Annual ordering cost

TC = DC + (Q/2)H +(D/Q)S

TC = (5000*30) + (183/2)7.5 + (5000/183)25 = 150000 + 686.25 + 683.06 = 151369.31

b)

Given

Assuming company works for 365 days

Given

Annual Demand D = 5000 handle bars

Daily demand d = 5000/365

Annual production = 20,000

Daily production p = (20000/365)

Cost C = $20

Set up cost S = 5000

Holding cost =25% = 0.25*20 = $5

Optimal production quantity Q

Q=sqrt{2DS/H}sqrt{p/(p-d)}

Q=sqrt{frac{2*5000*5000}{5}}sqrt{frac{(20000/365)}{(20000/365)-(5000/365)}}

Q = 3651.48 units or 3651 units

Annual cost = Annual holding cost + Annual Set up cost

Annual holding cost = Q((p-d)/p)(H/2)

Annual holding cost = 6845.625

Annual Set up cost = (D/Q)S =(5000/3651)*5000 = 6847.43

Total cost = 6845.62 + 6847.43 = 13693.05

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