Chapter 11, Problem 3PA

a)

Summary Introduction

To determine: The per unit holding cost of a laptop with Country U production.

Explanation of Solution

Given information:

Safety factory (SF)                     = 2.25

Holding cost per laptop per week in Country U (H)     = $4

Holding cost per laptop per week in Country T (H)     = $3.50

Lead time in Country U (L)                 = 1 week

Lead time in Country T (L)                 = 8 weeks

Shipping cost (C)                     = $2

Weekly demand (D)                     = 1,000 laptops

Standard deviation (S)                 = 800

Calculation of on-order inventory:

$\begin{array}{c}\text{On-order inventory}=L\times D\\ =1\times 1,000\\ =1,000\text{ units}\end{array}$

Calculation of on-hand inventory:

$\begin{array}{c}\text{On-hand inventory}=\left(\sqrt{\left(L+1\right)}\right)\times \left(S\times SF\right)\\ =\left(\sqrt{\left(1+1\right)}\right)\times \left(800\times 2.25\right)\\ =1.414\times 1,800\\ =2,545.2\\ =2,546\text{ units}\end{array}$

Calculation of total average inventory:

$\begin{array}{c}\text{Total average inventory}=\text{On-order inventory}+\text{On-hand inventory}\\ =1,000+2,546\\ =3,546\text{ units}\end{array}$

Calculation of average weekly holding cost:

$\begin{array}{c}\text{Average weekly holding cost}=\text{H}\times \text{Total average inventory}\\ =4\times 3,546\\ =\$14,184\end{array}$

Calculation of average holding cost per unit:

$\begin{array}{c}\text{Average holding cost per unit}=\frac{\text{Average weekly holding cost}}{\text{D}}\\ =\frac{\$14,184}{1,000}\\ =\$14.184\end{array}$

The per unit holding cost of a laptop with Country U production is $14.184.

b)

Summary Introduction

To determine: The per unit holding cost of a laptop with Country T production.

Explanation of Solution

Given information:

Safety factory (SF)                     = 2.25

Holding cost per laptop per week in Country U (H)     = $4

Holding cost per laptop per week in Country T (H)     = $3.50

Lead time in Country U (L)                 = 1 week

Lead time in Country T (L)                 = 8 weeks

Shipping cost (C)                     = $2

Weekly demand (D)                     = 1,000 laptops

Standard deviation (S)                 = 800

Calculation of on-order inventory:

$\begin{array}{c}\text{On-order inventory}=L\times D\\ =8\times 1,000\\ =8,000\text{ units}\end{array}$

Calculation of on-hand inventory:

$\begin{array}{c}\text{On-hand inventory}=\left(\sqrt{\left(L+1\right)}\right)\times \left(S\times SF\right)\\ =\left(\sqrt{\left(8+1\right)}\right)\times \left(800\times 2.25\right)\\ =3\times 1,800\\ =5,400\text{ units}\end{array}$

Calculation of total average inventory:

$\begin{array}{c}\text{Total average inventory}=\text{On-order inventory}+\text{On-hand inventory}\\ =8,000+5,400\\ =13,400\text{ units}\end{array}$

Calculation of average weekly holding cost:

$\begin{array}{c}\text{Average weekly holding cost}=\text{H}\times \text{Total average inventory}\\ =3.50\times 13,400\\ =\$46,900\end{array}$

Calculation of average holding cost per unit:

$\begin{array}{c}\text{Average holding cost per unit}=\frac{\text{Average weekly holding cost}}{\text{D}}\\ =\frac{\$46,900}{1,000}\\ =\$46.90\end{array}$

The per unit holding cost of a laptop with Country T production is $46.90.

c)

Summary Introduction

To determine: The change in cost per laptop if the production switched to Country T.

Explanation of Solution

Given information:

Safety factory (SF)                     = 2.25

Holding cost per laptop per week in Country U (H)     = $4

Holding cost per laptop per week in Country T (H)     = $3.50

Lead time in Country U (L)                 = 1 week

Lead time in Country T (L)                 = 8 weeks

Shipping cost (C)                     = $2

Weekly demand (D)                     = 1,000 laptops

Standard deviation (S)                 = 800

Assembly time (T)                     = 40 minutes

Cost of labor in Country U (W)             = $40 per hour

Cost of labor in Country T (W)             = $10 per hour

When production is in Country U:

Calculation of labor cost per unit:

$\begin{array}{c}\text{Labor cost}=\text{W}\times \frac{\text{T}}{\text{Minutes per hour}}\\ =40\times \frac{40}{60}\\ =\$26.67\end{array}$

There is no transportation cost. The average holding cost per unit is $14.184.

Calculation of total cost:

$\begin{array}{c}\text{Total cost}=\$26.67+\$14.184\\ =\$40.854\end{array}$

When production is in Country T:

Calculation of labor cost per unit:

$\begin{array}{c}\text{Labor cost}=\text{W}\times \frac{\text{T}}{\text{Minutes per hour}}\\ =10\times \frac{40}{60}\\ =\$6.67\end{array}$

The shipping cost is $2. The average holding cost per unit is $46.90

Calculation of total cost:

$\begin{array}{c}\text{Total cost}=\$6.67+\$2+\$46.90\\ =\$55.57\end{array}$

Cost difference when the production moves from Country U to Country T:

$\begin{array}{c}\text{Cost difference}=55.57-40.854\\ =\$14.72\end{array}$

The cost increases by $14.72.