Chapter 11, Problem 10PA

a

Summary Introduction

Interpretation:Economic Order quantity is to be calculated.

Concept Introduction:

Economic Order Quantity (EOQ) model aims at minimizing the cost of a production unit of a business facility. It aims to define the optimal quantity so that there is a balance between order and carrying cost. This model gives an approximate result rather than guaranteeing it. Carrying cost is determined by management of business unit.

Answer to Problem 10PA

Economic Order quantity is 114 units.

Explanation of Solution

Given information:

Average demand, $\text{d}\text{=}\text{12}\text{.5}\text{calculators/week}$

Lead Time, $\text{LT}\text{=}\text{3}\text{weeks}$

Order cost, O $\text{s}\text{=}\text{20}\text{per}\text{order}$

Unit $\text{cost, I}\text{=}\text{\$8}\text{.00}\text{unit}$

Carrying charge rate = 0.25

Number of weeks, $\text{n}\text{=}\text{52}\text{weeks}$

Standard deviation of weekly demand, ${\text{σ}}_{\text{d}}\text{=}\text{3}\text{.75}\text{units}$

SKU service level, $\text{CSL}\text{=}\text{95\%}$

  $\text{Z-}\text{value}\text{(0}\text{.95)}\text{=}\text{1}\text{.64}$

Current on hand inventory, $\text{OH}\text{=}\text{35}\text{units}$

Schedule receipts, $\text{SR}\text{=}\text{20}\text{units}$

Back orders, $\text{BO}\text{=}\text{2}\text{units}$

Following is the formula to calculate economic order quantity.

  $\text{EOQ}\text{=}\sqrt{\frac{\text{2DS}}{\text{H}}}$

D = Annual demand

S = cost per order

H = Holding cost

Annual demand is calculated as follows:

  $\text{D}\text{=}\text{d×n}$

Where,

d= Average demand per week

n= number of weeks

  $\text{H}\text{=}\text{I×}\text{C}$

Holding cost is calculated as follows:

  $\text{H}\text{=}\text{I×}\text{C}$

Where,

I = Unit cost

C = carrying cost

Substituting values in formula:

  $\begin{array}{l}\text{H}\text{=}\text{0}\text{.25}\text{×}\text{8}\\ \text{=}\text{\$2/unit/year}\end{array}$

  $\begin{array}{l}\text{EOQ}\text{=}\sqrt{\frac{\text{2×650×20}}{\text{2}}}\\ \text{=}\text{114}\text{units}\end{array}$

b

Summary Introduction

Interpretation:Total annual order and inventory holding cost needs to be calculated.

Concept Introduction:

Economic Order Quantity (EOQ) model aims at minimizing the cost of a production unit of a business facility. It aims to define the optimal quantity so that there is a balance between order and carrying cost. This model gives an approximate result rather than guaranteeing it. Carrying cost is determined by management of business unit.

Answer to Problem 10PA

Annual order cost is 114.03 and inventory holding cost is $114

Explanation of Solution

Given information:

Average demand, $\text{d}\text{=}\text{12}\text{.5}\text{calculators/week}$

Lead Time, $\text{LT}\text{=}\text{3}\text{weeks}$

Order cost, O $\text{s}\text{=}\text{20}\text{per}\text{order}$

Unit $\text{cost, I}\text{=}\text{\$8}\text{.00}\text{unit}$

Carrying charge rate = 0.25

Number of weeks, $\text{n}\text{=}\text{52}\text{weeks}$

Standard deviation of weekly demand, ${\text{σ}}_{\text{d}}\text{=}\text{3}\text{.75}\text{units}$

SKU service level, $\text{CSL}\text{=}\text{95\%}$

  $\text{Z-}\text{value}\text{(0}\text{.95)}\text{=}\text{1}\text{.64}$

Current on hand inventory, $\text{OH}\text{=}\text{35}\text{units}$

Schedule receipts, $\text{SR}\text{=}\text{20}\text{units}$

Back orders, $\text{BO}\text{=}\text{2}\text{units}$

Following is the formula for calculating total cost.

Total cost = Annual ordering cost + Annual holding cost

  $\text{TC}\text{=}\left(\frac{\text{D}}{\text{Q}}\text{×}\text{S}\right)\text{+}\left(\frac{\text{Q}}{\text{2}}\text{×H}\right)$

D = Annual demand

Q= Order Size

S= Cost per order

H = Holding cost

  $\begin{array}{l}\text{TC}\text{=}\left(\frac{650}{114}\text{×}20\right)\text{+}\left(\frac{114}{\text{2}}\text{×2}\right)\\ =114.03+114\\ =228.03\\ =228\end{array}$

Annual order cost is 114.03 and inventory holding cost is $114

c

Summary Introduction

Interpretation:Reorder point without safety stock needs to be determined.

Concept Introduction:

Reorder point is point at which level of inventory has fallen upto that level. It measures the level of inventory which is kept as stock. As the firm reaches the reorder point, firm repurchase its inventory.

Answer to Problem 10PA

Reorder point without safety stock is 38 units

Explanation of Solution

Given information:

Average demand, $\text{d}\text{=}\text{12}\text{.5}\text{calculators/week}$

Lead Time, $\text{LT}\text{=}\text{3}\text{weeks}$

Order cost, O $\text{s}\text{=}\text{20}\text{per}\text{order}$

Unit $\text{cost, I}\text{=}\text{\$8}\text{.00}\text{unit}$

Carrying charge rate = 0.25

Number of weeks, $\text{n}\text{=}\text{52}\text{weeks}$

Standard deviation of weekly demand, ${\text{σ}}_{\text{d}}\text{=}\text{3}\text{.75}\text{units}$

SKU service level, $\text{CSL}\text{=}\text{95\%}$

  $\text{Z-}\text{value}\text{(0}\text{.95)}\text{=}\text{1}\text{.64}$

Current on hand inventory, $\text{OH}\text{=}\text{35}\text{units}$

Schedule receipts, $\text{SR}\text{=}\text{20}\text{units}$

Back orders, $\text{BO}\text{=}\text{2}\text{units}$

Following is the formula to calculate reorder point.

  $\text{ROP}\text{=}\text{d×}\text{LT}$

Where d= Average demand

LT = Lead Time

  $\begin{array}{l}\text{ROP}\text{=}\text{d×}\text{LT}\\ \text{=}\text{12}\text{.5×3}\\ \text{=}\text{37}\text{.5}\text{or}\text{38}\text{units}\end{array}$

Reorder point without safety stock is 38 units

d

Summary Introduction

Interpretation:Reorder point with safety stock needs to be calculated.

Concept Introduction:

Reorder point is point at which level of inventory has fallen upto that level. It measures the level of inventory which is kept as stock. As the firm reaches the reorder point, firm repurchase its inventory.

Answer to Problem 10PA

Reorder point with safety is 48 units.

Explanation of Solution

Given information:

Average demand, $\text{d}\text{=}\text{12}\text{.5}\text{calculators/week}$

Lead Time, $\text{LT}\text{=}\text{3}\text{weeks}$

Order cost, O $\text{s}\text{=}\text{20}\text{per}\text{order}$

Unit $\text{cost, I}\text{=}\text{\$8}\text{.00}\text{unit}$

Carrying charge rate = 0.25

Number of weeks, $\text{n}\text{=}\text{52}\text{weeks}$

Standard deviation of weekly demand, ${\text{σ}}_{\text{d}}\text{=}\text{3}\text{.75}\text{units}$

SKU service level, $\text{CSL}\text{=}\text{95\%}$

  $\text{Z-}\text{value}\text{(0}\text{.95)}\text{=}\text{1}\text{.64}$

Current on hand inventory, $\text{OH}\text{=}\text{35}\text{units}$

Schedule receipts, $\text{SR}\text{=}\text{20}\text{units}$

Back orders, $\text{BO}\text{=}\text{2}\text{units}$

Following is the formula to calculate reorder point.

  $\text{ROP}\text{=}\text{d×}\text{LT+z}\sqrt{\text{LT}}\text{σd}$

Where,

LT is lead time

d is average demand

z is 95% confidence interval value

  $\sigma$ is standard deviation

Substituting values in the formula:

  $\begin{array}{l}\text{ROP}\text{=}\text{d×}\text{LT+z}\sqrt{\text{LT}}\text{σd}\\ \text{=}\text{12}\text{.5×3+(1}\text{.64}\sqrt{\text{3}}\text{×}\text{3}\text{.75)}\\ \text{=}\text{37}\text{.5}\text{+10}\text{.64}\\ \text{=}\text{48}\text{.15}\\ \text{=}\text{48}\text{units}\end{array}$

Reorder point with safety is 48 units.

e

Summary Introduction

Interpretation:Whether fixed quantity of calculators to be purchased is to be determined along with its quantity.

Concept Introduction:

Economic Order Quantity (EOQ) model aims at minimizing the cost of a production unit of a business facility. It aims to define the optimal quantity so that there is a balance between order and carrying cost. This model gives an approximate result rather than guaranteeing it. Carrying cost is determined by management of business unit.

Explanation of Solution

Fixed quantity of calculators can be purchased up to 38 units. This is the minimum quantity which can be held as stock. Reorder point without safety stock measures this stock as it can readily be sold. To be on safer side, 38 units can be considered as inventory.