Question

A company uses 36,000 tyres to produce car wheels every year. The company can make its own tyres simultaneously at a rate of 500 per day and the carrying cost is £2 per tyre per annum. If the company is open for 240 days of the year and each production run incurs a set-up cost of £40, what is:

• Economic production quantity
• Total annual set-up and carrying cost
• Cycle time for economic production quantity
• Run time

Be sure to demonstrate your work and provide a brief interpretation. (200 words maximum) - this is important

Answer 1

(a)

Annual Demand = D = 36000 tyres/year

Setup Cost = C_o = £40

Holding Cost = C_c = £2/year

Economic Production Quantity Q* = √(2DC_o/C_c) = √(2*36000*40/2) = 1200

(b)

Number of Production cycles = D/Q* = 36000/1200 = 30

Annual Setup cost = Number of production cycles * setup cost = (D/Q*) C_o = (30)*40 = £1200

Average Inventory = Q*/2 = 600

Annual Inventory Holding cost = average inventory * unit carrying cost = (Q*/2)*C_c = (600)*2 = £1200

(c) Number of Production cycles = D/Q* = 36000/1200 = 30

Cycle Time = Number of Days / Number of Production Cycles = 240/30 = 8 days

(d) Run time = 36000/500 = 72 days