Chapter 4, Problem 31AP

(a)

Summary Introduction

Interpretation:

The total number of standing that should P’s have with its supplier and the ways these orders should be placed.

Concept Introduction:

The economic order quantity, often called EOQ refers to the order quantity that helps the organization in minimizing the ordering and holding cost of the organization’s business.

Explanation of Solution

Given data:

Monthly demand = 60 units

Annual demand

  $\begin{array}{l}=\text{ 12}\times \text{60}\\ \text{= 720 units }\end{array}$

Ordering cost = $20

The economic order quantity will be calculated by the following formula.

  $\begin{array}{l}\text{Economic order quantity (EOQ) = }\sqrt{\frac{\text{2×D×S}}{\text{H}}}\\ \text{EOQ = }\sqrt{\frac{\text{2×D×S}}{\text{H}}}\\ =\sqrt{\frac{2\times 720\times 20}{0.22\times 2.8}}\\ =\sqrt{\frac{28800}{0.616}}\\ =\sqrt{46753.25}\\ =\text{ 216}\text{.22 units }\end{array}$

Hence, the optimal order quantity that P should order with its suppliers is 216.22 units.

Cycle time will be calculated by the following formula.

  $\text{T=}\frac{\text{Q*}}{\text{λ}}$

  $\text{λ}$= Total demand per year

Q*= Economic order quantity

  $\begin{array}{l}\text{T=}\frac{\text{216}\text{.22}}{\text{720}}\\ \text{= 0}\text{.3 years }\end{array}$

Thus, the order should be placed after every 0.3 years or 3.6 months.

(b)

Summary Introduction

Interpretation:

If it takes 3 weeks to receive a shipment, then the total inventory in hand while placing the order.

Concept Introduction:

The re-order level refers to the inventory level at which an organization would place a new order or begin a new manufacturing run.

Explanation of Solution

The re-order level will be calculated by the following formula

  $\begin{array}{l}\text{Re-order level = λ×L}\\ \text{= 60}\times \frac{3}{4}\\ =\text{ 45 units }\end{array}$

Thus, on-hand inventory will be 45 units when the new order will be placed.

(c)

Summary Introduction

Interpretation:

The average annual holding and fixed costs associated with these filters assuming they adopted an optimal policy.

Concept Introduction:

The economic order quantity, often called EOQ refers to the order quantity that helps the organization in minimizing the ordering and holding cost of the organization’s business.

Explanation of Solution

The average annual holding cost will be calculated by the following formula.

  $\begin{array}{l}\text{Average annual cost = }\sqrt{\text{2KλH}}\\ =\sqrt{2\times 20\times 70\times 0.616}\\ =\sqrt{17740.8}\\ =\text{ \$133}\text{.194}\end{array}$

The average annual holding cost is $133.194

(d)

Summary Introduction

Interpretation:

The store of P’s in the city is small, the ways this might affect the solution recommended in part (a).

Concept Introduction:

Inventory management is the process of ordering, storing, and using the organization’s inventory.

Explanation of Solution

When the inventory is sourced from the suppliers, it is required to store at a suitable place for future use. If space will be less, then it will definitely impact the optimal quantity as there is less space to hold or store inventory. Thus, space impacts the optimal quantity to be ordered as it needed to be stored for the continuing requirement during the cycle time of production.