Question

gle 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	​$2525 per hour
Annual holding cost	​$1212 per unit
Daily production	1 comma 0081,008 ​units/8 hour day
Annual demand	36 comma 00036,000 ​(250250 days eachtimes ×daily demand of 144144 ​units)
Desired lot size	126126 units​ (one hour of​ production)

To obtain the desired lot​ size, the​ set-up time that should be achieved​ =

5.445.44

minutes ​(round your response to two decimal​ places).

Answer 1

Solution:

Economic Production Quantity (Q) is calculated as,

Q = SQRT [(2 x D x S) / H x (1 - d/p)]

where,

D = Annual demand

S = Setup cost

H = Holding cost

d = Daily demand

p = Daily production

Modifying the above formula to solve for Setup cost (S), we get,

S = [(Q^2) x H x (1 - d/p)] / 2D

Putting the given values in the above formula, we get,

S = [(126^2) x $12 x (1 - 144/1008)] / (2 x 36,000)

S = $2.268

Setup cost = $2.268

Setup time is calculated as,

Setup time = (Setup cost / Setup labor cost) x 60 minutes (1 hour = 60 minutes)

Setup time = ($2.268 / $25) x 60 minutes

Setup time = 5.44 minutes