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Chapter 4: Q 36OQ (page 550)

Palin鈥檚 Muffler Shop has one standard muffler that fits a large variety of cars. The shop wishes to establish a periodic review system to manage the 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

3,000 mufflers

Ordering cost

\(50 per order

The 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 the item value

Working days

300 per year

Review period

15 working days

a. What is the optimal target level (order-up-to level)?

b. If the service probability requirement is 95 percent, the optimal target level [your answer in part (a)] will (select one):

I. Increase.

II. Decrease.

III. Stay the same.

Short Answer

Expert verified

Answer

Optimizing the desired inventory level for each item and place necessitates a higher-level analysis and additional data.

Step by step solution

01

Step-by-Step Solution

Step 1: Optimal inventory target level

Still, to consistently meet goal service levels with low inventory and expediting, we must create and maintain appropriate target inventory levels for each item in each stocking site. As a result, we ask: Can you develop and maintain the ideal inventory position for each item in each location. Spreadsheets, of course, can handle intensive analysis and large amounts of input data, but their processing cost causes them to be sluggish.

02

(a) Calculation the optimal target level (order-up-to level)

Given:

D = Days operational =270days

A = Annual Demand 2970 units per year

d = Average Demand rate per time 11.00 per day

蟽 = Standard Deviation of daily demand 6 units

LT = Execution cycle, another term for all-out lead time 4 days

z for 89% target service level = NORMSINV(0.99) 1.23

蟽R+LT Standard deviation during reorder period and lead time (R+LT weeks) 156.00 units

R = Reorder period or Review Period 22.00 days

T1 = time increase utilized for figuring standard deviation of interest 1 days

Optimal target level = d脳(R+LT)+(z脳 (蟽(R+LT))

= 11脳 (156 + (1.23(6(156.00))

= 478 units

So, the Optimal target level is 478 units

03

(b) Calculation of increase, decrease or stay the same in Optimal Level target

On the off chance that the assistance likelihood prerequisite is 90%, the ideal objective level will 鈥淚ncrease鈥�

Given:

D = Days operational 270 days

A = Annual Demand 2970 units per year

d = Average Demand rate per time period=11.00 per day

蟽 = Standard Deviation of daily demand=6 units

LT = Execution cycle, another term for all-out lead time =4 days

z for 90% target service level =1.28

蟽R+LT Standard deviation during reorder period and lead time (R+LT weeks) 156.00 units

R = Reorder period or Review Period 22.00 days

T1 = time increase utilized for figuring standard deviation of interest= 1 days

Optimal target level = d*(R+LT)+(z*(蟽*(R+LT))) =486 units

Hence, the optimal target level increases.

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