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 3,500 mufflers Ordering cost $50 per order
Standard deviation of daily demand 6 mufflers per working day Service probability 90 %
Item cost $30 per muffler Lead time 2 working days
Annual holding cost 25 % of item value Working days 300 per year
Use the above information to determine the best order size and the reorder point. (Round your answers to the nearest whole number.)
Best order size is 216
Best order size mufflers
Reorder point mufflers

Answer 1

Answer:

Best reorder size = 216

Reorder point = 35

Explanation:

Required:

Using the above information, find the best order size and the reorder point.

To find the best order size, EOQ, use the formula:

$EOQ = \sqrt{\frac{2DS}{H}}$

$= \sqrt{\frac{2*3500*50}{0.25*30}}$

$= \sqrt{\frac{350000}{7.5}}$

$= 216.02$

Best reorder size is 216 mufflers

To find the reorder point, use the formula:

R = d' L + z $\sigma_L$

Where d' = average daily demand

L = lead time in days

z = number of standard deviation from a specified probability

$\sigma_L$ = standard deviation of usage in lead time

Daily demand, d'= $\frac{3500}{300} = 12$

12 mufflers

Since lead time is 2 working days, standard deviation of lead time $\sigma_L = \sqrt{2} * 6 = 8.48$

Therefore,

R = d' L + z $\sigma_L$

= (12 * 2) + (1.28 * 8.48)

= 24 + 10.9

= 34.9

Approximately 35

Reorder point is = 35 mufflers