Question

Palin's Muffler Shop has one standard muffler that fits a large variety of cars. The shop wishes to establish a periodic review system to manage inventory of this standard muffler. Use the information in the following table to determine the optimal inventory target level (or order-up-to level).

Annual demand 2,870 mufflers Ordering cost $65per order
Standard deviation of daily demand 6 mufflers per working day Service probability 76%
Item cost $31.00 per muffler Lead time 2 working days
Annual holding cost 22% of item value Working days 205 per year
Review period 16working days
a. What is the optimal target level (order-up-to level)? (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.)
b. If the service probability requirement is 97 percent, the optimal target level will:
_____Increase
_____Decrease
_____Stay the same

Answer 1

A.) 270 units (b.) Increase

Step-by-step explanation:

Given the following :

Annual demand (A) = 2870

Working days = 205

Review period (P) = 16 working days

Lead time (L) = 2 working days

Standard deviation (σ) = 6 per working day

Service probability = 76%

Therefore, z = NORMSINV(0.76) = 0.71

Average demand (D) = 2870 / 205 = 14

Optimum target level, (S) is given by the relation:

D×(P+L) + z×σ×√(P+L)

14×(16+2) + 0.71×6×√(16+2)

(14×18) + 4.26 × √18

252 + 4.26*4.242

252 + 18.07

= 270.07 units = 270 units

B) If service probability increases to 97%, Z will automatically increase, hence a corresponding increase in the optimal target level.