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Reil
27 days ago
6

High Plains Inc. manufacturers furniture in North Dakota. High Plains receives its wood from a lumber yard in Calgary. The lead

time for orders is 3 weeks. One of their board costs $14 per unit and the holding cost for this board is $0.5 per week. They manage their inventory to achieve a 96 percent in-stock probability. Weekly demand is for 150 boards with a standard deviation of 200.a. How many boards do they have on on order on average? boardsb. How many boards do they have on hand on average? boardsc. For this board what is the total holding cost incurred per week? per weekd. What is the holding cost they incur per board? per board
Business
1 answer:
Free_Kalibri [3.1K]27 days ago
5 0

Answer:

a. The average number of boards ordered is 1,056 boards.

b. The average number of boards in stock is 560 boards.

c. Weekly holding costs total $140.

d. Holding cost allocated per board is $0.25.

Explanation:

The provided figures in the question indicate:

Service level = 96 %

Lead time = 3 weeks

Weekly demand = 150

Standard deviation = 200

This situation reflects variable demand with a consistent lead time.

a. Reorder point = Demand during lead time + Safety stock

= Average weekly demand * lead time + z*sqrt(lead time)*standard deviation of weekly demand

= 150*3 + NORMSINV(0.99)*sqrt(3)*200

= 450 + 1.7507*sqrt(3)*200

= 450 + 606.46 = 1,056.46

= 1,056 (rounded to the nearest whole number).

The average number of boards on order calculates to 1,056 boards.

b. In terms of normal distribution,

z=x-mean/std deviation

For a 96% confidence level, the z-value equals 2.05

2.05 = x-150/200

Therefore, x = 150 + 2.05 * 200 = 560

The average count of boards on hand is 560 boards.

c. Total weekly holding cost = Average inventory * holding cost per week = 560/2 * 0.5 = 280 * 0.5 = $140.

d. Holding costs for each board = Total holding cost / Number of boards = 140/560 = $0.25.

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