Question

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

Answer 1

Answer:

a. On average, the number of boards they have on order  = 1,056 boards.

b. On average, the number of boards they have =560 boards.

c. Total holding cost per week = $140.

d. Holding cost incurred per board = $ 0.25.

Explanation:

In the question, the details given are:

Service level =96 %

Lead time =3 weeks

Weekly demand =150

Standard deviation=200

This is a case of variable demand and constant 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 (nearest whole number).

On average, the number of boards they have on order  = 1,056 boards.

b. For a normal distribution,

z=x-mean/std deviation

z-value for a 96% confidence level = 2.05

2.05=x-150/200

x = 150+2.05*200=560

On average, the number of boards they have =560 boards.

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

d.Holding cost incurred per board =Total holding cost /Number of boards =140/560 = $ 0.25.

Answer 2

A. On average, the number of boards they have on order is = 1,056 boards.

B. On average, the number of boards they have is = 560 boards.

C. The Total holding cost per week is = $140.

D. Then the Holding cost incurred per board is = $0.25.

What is the Holding cost?

As per the given information In the question, the details are:

The Service level is =96 %

Lead time is = 3 weeks

Weekly demand is =150

The standard deviation is =200

This is a case of variable demand and also the constant lead time

A. When the Reorder point is = Demand during lead time + Safety stock

Then = the Average weekly demand*lead time+ z × sqrt(lead time) × standard deviation of weekly demand is =150 × 3+NORMSINV(0.99) × sqrt(3) × 200

After that =450+1.7507×sqrt(3)×200

Then =450+606.46=1,056.46

So that, =1,056 (nearest whole number).

On average, the number of boards they have on order is = 1,056 boards.

B. Now, For a normal distribution,

z is =x-mean/std deviation

After that z-value for a 96% confidence level is = 2.05

then 2.05=x-150/200

then x is = 150+2.05×200=560

On average, the number of boards they have is = 560 boards.

C. Then Total holding cost per week is =Average inventory ×holding cost per week is = 560/2 ×0.5=280×0.5 =$140

D. Then Holding cost incurred per board is =Total holding cost /Number of boards =140/560 = $ 0.25.

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