a) What is the optimum production? quantity? b) What is the maximum number of wh
ID: 329891 • Letter: A
Question
a) What is the optimum production? quantity?
b) What is the maximum number of wheel bearings that will be in inventory at? Wheel-Rite?
c) How many production runs of wheel bearings will? Wheel-Rite have in a? year?
?d) What is the total setup plus holding cost for? Wheel-Rite?
Arthur Meiners is the production manager of Wheel-Rite, a small producer of metal parts. Wheel-Rite supplies Cal-Tex, a larger assembly company, with 10,000 wheel bearings each year. This order has been stable for some time. Setup cost for Wheel-Rite is $39, and holding cost is $0.80 per wheel bearing per year. Wheel-Rite can produce 550 wheel bearings per day. Cal-Tex is a just-in-time manufacturer and requires that 51 bearings be shipped to it each business day.Explanation / Answer
To be calculated:
(a) Optimal production quantity
(b) Maximum Inventory
(c) Number of production runs
(d) Total setup and holding cost
Given values:
Annual demand, D = 10,000
Setup cost, S = $39
Holding cost, H = $0.80
Daily production, p = 550
Daily demand, d = 51
Solution:
(a) Optimal or Economic production quantity (EPQ) is calculated as;
EPQ = SQRT (2 x D x S) / [H x (1 - d/p)]
where,
EPQ = Economic production quantity
D = Annual demand
S = Setup cost
H = Holding cost
d = daily demand
p = daily production
Putting the given values in the above formula, we get;
EPQ = SQRT (2 x D x S) / [H x (1 - d/p)]
EPQ = SQRT (2 x 10000 x 39) / [0.80 x (1 - 51/550)]
EPQ = SQRT (1074676.2193)
EPQ = 1036.67 or 1037 units (rounding off to nearest whole number)
Optimal production quantity = 1037 units
(b) Maximum Inventory is calculated as;
Maximum Inventory, Imax. = EPQ x (1 - d/p)
Maximum Inventory, Imax. = 1037 x (1 - 51/550)
Maximum Inventory, Imax. = 940.84 or 941 units (rounding off to nearest whole number)
Maximum Inventory, Imax. = 941 units
(c) Number of production runs is calculated as;
Number of production runs = D/EPQ
Number of production runs = 10000/1037
Number of production runs = 9.64
(d) Total setup and holding cost is calculated as;
Setup cost = (D/EPQ) x S
Setup cost = (10000/1037) x 39
Setup cost = $376.08
Holding cost = H x (EPQ/2) x (1 - d/p)
Holding cost = 0.80 x (1037/2) x (1 - 51/550)
Holding cost = 0.80 x 518.5 x 0.9073
Holding cost = $376.35
Total setup and holding cost = $376.08 + $376.35
Total setup and holding cost = $752.43
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