Question

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

Answer 1

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

L = Lead time

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