Carol Cagle has a repetitive manufacturing plant producing trailer hitches in Ar
ID: 334054 • Letter: C
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$20 per hour Annual holding cost $15 per unit Daily production 960 units/8 hour day Annual demand 39,600 (275 days each x daily demand of 144 units) Desired lot size 120 units (one hour of production) To obtain the desired lot size, the set-up time that should be achievedminutes (round your response to two decimal places).Explanation / Answer
Solution:
In Production Order Quantity (POQ) model, Optimal 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
From the above formula;
S = [(Q* ^ 2) x H x (1 - d/p)] / 2D
Putting the given values in the above formula, we get;
S = [(120 ^ 2) x $15 x (1 - 144/960)] / (2 x 39600)
S = (14400 x $15 x 0.85) / 79200
Setup cost, S = $2.32
Setup time is calculated as;
Setup time = (Setup cost / Setup labor cost) x 60 minutes
Setup time = ($2.32 / $20) x 60 minutes
Setup time = 6.96 minutes