Question

# Sarah's Muffler Shop has one standard muffler that fits a large variety of cars. Sarah wishes...

Sarah's Muffler Shop has one standard muffler that fits a large variety of cars. Sarah wishes to establish a reorder point system to manage inventory of this standard muffler.

 Annual demand 4,500 mufflers Ordering cost \$65 per order Standard deviation of daily demand 6 mufflers per working day Service probability 90 % Item cost \$35 per muffler Lead time 3 working days Annual holding cost 20 % of item value Working days 300 per year
 Use the above information to determine the best order size and the reorder point: (Use Excel's NORMSINV() function to find the correct critical value for the given α-level. Do not round intermediate calculations. Round "z" value to 2 decimal places and final answer to the nearest whole number.)
 Best order size mufflers Reorder point mufflers

Solution:

(a) Best Order Size (Q):

Q = SQRT [(2 x D x Co) / H]

where,

D = Annual demand

Co = Ordering cost

H = Holding cost

Putting the given values in the above formula,

Q = SQRT [(2 x 4500 x \$65) / (0.20 x \$35)]

Q = 289.09 or 289 (Rounding off to the nearest whole number)

Best Order Size = 289 mufflers

(b) Reorder point (ROP):

Using NORMSINV function in MS Excel, value of Z can be determined.

Z = NORMSINV (Service Probability)

Z = NORMSINV (0.90)

Z = 1.28

ROP = (d x L) + [Z x Sigma-d x Sqrt(L)]

where,

d = Daily demand = Annual demand / Number of working days

d = 4500 / 300 = 15 mufflers

Sigma-d = Standard deviation of daily demand

Putting the given values in the above formula,

ROP = (15 x 3) + [1.28 x 6 x Sqrt(3)]

ROP = 45 + 13.30

ROP = 58.30 or 58 (Rounding off to the nearest whole number)

Reorder point = 58 mufflers

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