Question

Carol Cagle has a repetitive manufacturing plant producing trailer hitches in Arlington, Texas. The plant has an average inventory turnover of only 12 times per year. He has therefore determined that he will reduce his component lot sizes. He has developed the following data for one component, the safety chain clip: Setup labor cost Annual holding cost Daily production Annual demand Desired lot size $30 per hour $14 per unit 1,008 units/8 hour day 43,680 (260 days each x daily demand of 168 units) 126 units (one hour of production) To obtain the desired lot size, the set-up time that should be achieved = minutes (round your response to two decimal places).

Answer 1

Annual demand(D) = 43680 units

Daily demand(d) = 168 units

Daily production(p) = 1008 units

Annual Holding cost(H) = $14 per unit

Desired lot size(Q) = 126 units

Set up cost(S) = [ Square of Q X H X (1-d/p) ] / 2D

= [ Square of 126 X 14 X (1-168/1008) ] / (2 X 43680)

= (15876 X 14 X 0.833) / 87360

= 185145.912/ 87360

= $2.12

Set up time = Set up cost / setup labor cost per hour

= $2.12/ $20

= 0.071 hour

= (0.071 X 60) minutes

= 4.26 minutes

So,To obtain the desired lot size ,the setup time that should be achieved = 4.26 minutes