Chapter 13, Problem 12P

a)

Summary Introduction

To determine: The number of batches of heating element produced per year.

Introduction: Inventory is a stock or store of goods. Every company store lots of goods as inventory which will be used during replenishment periods. Management of inventory is so much essential to manage cost and also to reduce cost.

Answer to Problem 12P

The number of batches of heating element produced per year is 38 batches per year.

Explanation of Solution

Given information:

$\begin{array}{c}\text{u}=300\text{units/day}\\ \text{p}=800\text{units/day}\\ \text{Q}=\text{2,000}\text{units/batch}\end{array}$

Formula:

$\text{Number}\text{of}\text{batches}=\frac{\text{D}}{\text{Q}}$

Calculation of number of batches of heating element produced per year:

$\begin{array}{c}\text{Number}\text{of}\text{batches}=\frac{75,000}{2,000}\\ =38\text{batches/year}\end{array}$

The number of batches of heating element produced per year is calculated by dividing the demand with the economic order quantity which is 75,000 is divided by 2,000 which yields the resultant as 38 batches per year.

Hence, the number of batches of heating element produced per year is 38 batches per year.

b)

Summary Introduction

To determine: The inventory on hand.

Introduction: Inventory is a stock or store of goods. Every company store lots of goods as inventory which will be used during replenishment periods. Management of inventory is so much essential to manage cost and also to reduce cost.

Answer to Problem 12P

The inventory on hand is 1,000 units.

Explanation of Solution

Given information:

$\begin{array}{c}\text{u}=300\text{units/day}\\ \text{p}=800\text{units/day}\\ \text{Q}=\text{2,000}\text{units/batch}\end{array}$

Calculation of inventory on hand:

Batch begins with no inventory on hand.

$\begin{array}{c}\text{Number}\text{of}\text{units}\text{produced}\text{in}\text{two}\text{days}=800\times 2\\ =1600\text{units}\\ \text{Number}\text{of}\text{units}\text{produced}\text{in}\text{two}\text{days}=300\times 2\\ =600\text{units}\end{array}$

$\begin{array}{c}\text{Inventory}\text{after}\text{first}\text{two}\text{days}\text{of}\text{production}=1,600-600\\ =1,000\text{units}\end{array}$

$\begin{array}{c}\text{Total}\text{inventoryafter}\text{first}\text{two}\text{days}\text{of}\text{production}=\text{Beginning}\text{inventory}+\text{Inventory}\\ =0+1000\\ =1,000\text{units}\end{array}$

The inventory on hand after two days is calculated by adding the beginning inventory and inventory accumulated as a result of two days of production. Inventory after two days is calculated by finding the difference of number of units produced in two days (1,600) and number of units consumed in two days (600) which is 1,000 units.

Therefore, inventory after two days is obtained by adding 0 with 1,000 which gives 1,000units as the inventory after two days.

Hence, the inventory on hand is 1,000 units.

c)

Summary Introduction

To determine: The average inventory.

Introduction: Inventory is a stock or store of goods. Every company store lots of goods as inventory which will be used during replenishment periods. Management of inventory is so much essential to manage cost and also to reduce cost.

Answer to Problem 12P

The average inventory is 625 units.

Explanation of Solution

Given information:

$\begin{array}{c}\text{u}=300\text{units/day}\\ \text{p}=800\text{units/day}\\ \text{Q}=\text{2,000}\text{units/batch}\end{array}$

Formula:

$\text{Average}\text{inventory}=\frac{{\text{I}}_{\text{max}}}{2}$

Calculation of average inventory:

$\begin{array}{c}{\text{I}}_{\text{max}}=\frac{{\text{Q}}_{\text{p}}}{\text{p}}\left(\text{p}-\text{u}\right)\\ =\frac{2,000}{800}\left(800-300\right)\\ =\text{ 1},250\text{units}\end{array}$

$\begin{array}{c}\text{Average}\text{inventory}=\frac{1,250}{2}\\ =625\text{units}\end{array}$

The average inventory is calculated by dividing 1,250 by 2 which yields 625 units.

Hence, the average inventory is 625 units.

d)

Summary Introduction

To explain: Whether there is adequate time to do the job between the production batches.

Introduction: Inventory is a stock or store of goods. Every company store lots of goods as inventory which will be used during replenishment periods. Management of inventory is so much essential to manage cost and also to reduce cost.

Answer to Problem 12P

There will not be adequate time to run the other component.

Explanation of Solution

Given information:

$\begin{array}{c}\text{u}=300\text{units/day}\\ \text{p}=800\text{units/day}\\ \text{Q}=\text{2,000}\text{units/batch}\\ \text{Set}\text{up time for heating element }=\text{0}\text{.5 days}\end{array}$

Formula:

$\text{Cycle}\text{time}=\text{Run}\text{time}+\text{Consumption}\text{time}$

Calculation to check whether there is adequate time to do the job between the production batches:

$$ $$

The other component must be completed within the consumption time of the heating element. The end of the consumption time is the moment when the inventory falls to 0 units. When the other component takes more than the consumption time, there will be lag in the inventory level.

$\begin{array}{c}\text{Cycle}\text{time}=\frac{\text{Q}}{\text{u}}\\ =\frac{2,000}{300}\\ =7\text{days}\end{array}$

The cycle time is calculated by dividing 2,000 with 300 which yields the resultant as 7 days.

$\begin{array}{c}\text{Run}\text{time}=\frac{{\text{Q}}_{\text{p}}}{\text{p}}+\text{Setup}\text{time}\\ =\frac{2,000}{\text{800}}+0.5\\ =\text{3days}\end{array}$

The run time is calculated by dividing 2,000 by 800 and adding the resultant with setup time which yields 3 days.

$\begin{array}{c}\text{Cycle}\text{time}=\text{Run}\text{time}+\text{consumption}\text{time}\\ \text{Consumption}\text{time}=7-3\\ =4\text{days}\end{array}$

Consumption time is calculated by subtracting run time of 7 with the consumption time of 3 which yields the resultant as 4days which is not sufficient since other component requires 4 days.

Hence, there will not be adequate time to run the other component.