Chapter 11, Problem 7P

A company produces to a seasonal demand, with the forecast for the next 12 months as given below. The current labor force can produce 500 units per month. Each employee can produce 20 units per month and is paid $2,000 per month. The inventory-carrying cost is $50 per unit per year. Changes in the production level cost s100 per unit due to hiring or layoffs, line changeover costs, and so forth. Assume 200 units of initial inventory.

1. a. What is the cost of carrying inventory for the month of January for the level strategy?
2. b. What is the total cost of the level strategy including regular time, inventory carrying cost and changes in production level?
3. c. What is the total cost of the chase strategy?

Summary Introduction

To determine: The inventory carrying cost for the month of January for the level strategy.

Introduction:

The aggregate plan is the output of sales and operations planning. The major concern of aggregate planning is the production time and quantity for the intermediate future. There are three kinds of aggregate planning; they are level strategy, chase strategy, and mixed strategy.

Explanation of Solution

Given information:

The present labor force can produce 500 units per month, and the demand with the forecast for the next 12 months is given below:

Month	Demand
J	651
F	700
M	850
A	702
M	650
J	500
J	600
A	850
S	803
O	900
N	703
D	600

Each employee can produce 20 units per month and is paid $2,000 per month. Inventory carrying cost is given as $50 per unit per year. Changes in the production level is $100 per unit during line changeover costs, hiring, and layoffs. Initial inventory is given as 200 units.

Determine the inventory for 12 months:

Month	Demand	Production	Inventory
J	651	709.08	258.08
F	700	709.08	267.17
M	850	709.08	126.25
A	702	709.08	133.33
M	650	709.08	192.42
J	500	709.08	401.50
J	600	709.08	510.58
A	850	709.08	369.67
S	803	709.08	275.75
O	900	709.08	84.83
N	703	709.08	90.92
D	600	709.08	200.00
Total	8509	8509.00	2910.50

Computation of inventory for 12 months:

Determine the cost of carrying inventory for the month of January for the level strategy:

It is calculated by multiplying the inventory for the month of January (refer table), and the value is attained by dividing inventory carrying cost and number of months.

$\begin{array}{c}\text{Inventory carrying cost}=\text{Sum of inventory units}\times \frac{\text{Inventory carrying cost}}{\text{Number of months}}\\ =258.08\times \frac{50}{12}\\ =1,075.33\end{array}$

Hence, the inventory carrying cost is $1,075.33.

Summary Introduction

To determine: The total cost of level strategy.

Introduction:

The aggregate plan is the output of sales and operations planning. The major concern of aggregate planning is the production time and quantity for the intermediate future. There are three kinds of aggregate planning; they are level strategy, chase strategy, and mixed strategy.

Explanation of Solution

Given information:

The current labor force can produce 500 units per month, and the demand with the forecast for the next 12 months is given below:

Month	Demand
J	651
F	700
M	850
A	702
M	650
J	500
J	600
A	850
S	803
O	900
N	703
D	600

Each employee can produce 20 units per month and is paid $2,000 per month. Inventory carrying cost is given as $50 per unit per year. Deviations in the production level is $100 per unit during line changeover costs, hiring, and layoffs. Initial inventory is given as 200 units.

Determine the regular time cost:

It is calculated by multiplying production units, number of months, and changes in the production level cost.

$\begin{array}{c}\text{Regular time cost}=\text{Number of months}\times \text{Changes in the production line}\times \text{Production units}\\ =12\times 100\times 709.08\\ =850,896\end{array}$

Hence, the regular time cost is $850,896.

Determine the inventory carrying cost:

It is computed by multiplying the sum of inventory (refer table), and the value is attained by dividing inventory carrying cost and number of months.

$\begin{array}{c}\text{Inventory carrying cost}=\text{Sum of inventory units}\times \frac{\text{Inventory carrying cost}}{\text{Number of months}}\\ =2,910.50\times \frac{50}{12}\\ =12,127.08\end{array}$

Determine the change in production level:

It is calculated by multiplying the changes in the production line and the difference between regular production per month and the calculated production.

$\begin{array}{c}\text{Changing in production level}=\text{Cost of change in production line}\times \left(\begin{array}{l}\text{Production}-\\ \text{Regular production}\end{array}\right)\\ =100\times \left(709-500\right)\\ =100\times 209\\ =\$20,900\end{array}$

Determine the total cost of level strategy:

It is calculated by adding regular time cost, inventory carrying cost, and change in production level cost.

$\begin{array}{c}\text{Total cost of level strategy}=\left(\begin{array}{l}\text{Regular time cost}+\text{Inventory carrying cost}+\\ \text{Change in production level cost}\end{array}\right)\\ =\$850,896+\$12,127.08+\$20,900\\ =\$883,923.08\end{array}$

Hence, the total cost of level strategy is $883,923.08.

Summary Introduction

To determine: The total cost of chase strategy.

Introduction:

The aggregate plan is the output of sales and operations planning. The major concern of aggregate planning is the production time and quantity for the intermediate future. There are three kinds of aggregate planning; they are level strategy, chase strategy, and mixed strategy.

Explanation of Solution

Given information:

The current labor force can produce 500 units per month, and the demand with the forecast for the next 12 months is given below:

Month	Demand
J	651
F	700
M	850
A	702
M	650
J	500
J	600
A	850
S	803
O	900
N	703
D	600

Each employee can produce 20 units per month and is paid $2,000 per month. Inventory carrying cost is given as $50 per unit per year. Changes in the production level is $100 per unit during line changeover costs, hiring, and layoffs. Initial inventory is given as 200 units.

Determine the inventory for 12 months:

Month	Demand	Production	Inventory	Change in production level
J	651	651	200	151
F	700	700	200	49
M	850	850	200	150
A	702	702	200	148
M	650	650	200	52
J	500	500	200	150
J	600	600	200	100
A	850	850	200	250
S	803	803	200	47
O	900	900	200	97
N	703	703	200	197
D	600	600	200	103
Total	8509	8509	2400	1494

Computation of inventory for 12 months:

Determine the regular time cost:

It is computed by multiplying production units, number of months, and changes in the production level cost.

$\begin{array}{c}\text{Regular time cost}=\text{Changes in the production line}\times \text{Sum of production units}\\ =100\times 8,509\\ =\$850,900\end{array}$

Hence, the regular time cost is $850,900.

Determine the inventory carrying cost:

It is calculated by multiplying the sum of inventory (refer table), and the value is attained by dividing inventory carrying cost and number of months.

$\begin{array}{c}\text{Inventory carrying cost}=\text{Sum of inventory units}\times \frac{\text{Inventory carrying cost}}{\text{Number of months}}\\ =2,400\times \frac{50}{12}\\ =10,000\end{array}$

Determine the change in production level:

It is calculated by multiplying the sum of changes in the production level and cost of change in production line.

$\begin{array}{c}\text{Changing in production level=}\left(\begin{array}{l}\text{Cost of change in production line}\times \\ \text{Sum of change in production level}\end{array}\right)\\ =100\times 1,494\\ =\$149,400\end{array}$

Determine the total cost of chase strategy:

It is calculated by adding regular time cost, inventory carrying cost, and change in production level cost.

$\begin{array}{c}\text{Total cost of chase strategy}=\left(\begin{array}{l}\text{Regular time cost}+\text{Inventory carrying cost}+\\ \text{Change in production level cost}\end{array}\right)\\ =\$850,900+\$10,000+\$149,400\\ =\$1,010,300\end{array}$

Hence, the total cost of chase strategy is $1,010,300.