Principles Of Operations Management
Principles Of Operations Management
11th Edition
ISBN: 9780135173930
Author: RENDER, Barry, HEIZER, Jay, Munson, Chuck
Publisher: Pearson,
bartleby

Concept explainers

Question
Book Icon
Chapter 13, Problem 6P

a)

Summary Introduction

To evaluate: Plan D

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. Aggregate planning would encompass a time prospect of approximately 3 to 18 months.

a)

Expert Solution
Check Mark

Answer to Problem 6P

Plan D has been evaluated. The total cost of plan D is $128,000.

Explanation of Solution

Given information:

The production for all the months is 1,600 units. Overtime cost is $50 per unit. The maximum allowable inventor in the warehouse is 400 units or less. The demand requirement from period 0 to 8 is as follows:

Period Expected demand
0 0
1 1,400
2 1,600
3 1,800
4 1,800
5 2,200
6 2,200
7 1,800
8 1,800

Evaluate the cost of the plan:

Plan D
Period Demand Production Overtime (units) Ending inventory Stock-outs (units) Extra cost
0 200
1 1,400 1,600 - 400 $8,000
2 1,600 1,600 - 400 $8,000
3 1,800 1,600 - 200 $4,000
4 1,800 1,600 - - $0
5 2,200 1,600 320 - 280 $44,000
6 2,200 1,600 320 - 280 $44,000
7 1,800 1,600 200 - $10,000
8 1,800 1,600 200 - $10,000
Total 14,600 1,040 1,000 $128,000

Note: Production is given as 1,600 units. The ending inventory for December is given as 200 units. If the production is more than or equal to the demand, then there would be inventory. If the demand is more, then there would be stock out. Maximum overtime units allowed is 320 units (20% of production)

Calculate the ending inventory or stock-out for Period 1:

It is calculated by adding the production and ending inventory of the previous month and subtracting the result from the demand. The ending inventory for Period 1 is 400.

Ending inventory=(Production+Ending inventory of previous month)Demand=(1,600+200)1,400=1,8001,400=400

Calculate the ending inventory or stock-out for Period 2:

It is calculated by adding the production and ending inventory of the previous month and subtracting the result from the demand. The ending inventory for Period 2 is 400.

Ending inventory=(Production+Ending inventory)Demand=(1,600+400)1,600=2,0001,600=400

Calculate the ending inventory or stock-out for Period 3:

It is calculated by adding the production and ending inventory of the previous month and subtracting the result from the demand. The ending inventory for Period 3 is 200.

Ending inventory=(Production+Ending inventory)Demand=(1,600+400)1,800=2,0001,800=200

Calculate the ending inventory or stock-out for Period 4:

It is calculated by adding the production and ending inventory of the previous month and subtracting the result from the demand. The ending inventory for Period 4 is 0.

Ending inventory=(Production+Ending inventory)Demand=(1,600+200)1,800=1,8001,800=0

Calculate the ending inventory or stock-out for Period 5:

As the demand is more than the production, there would be a stock-out.

It is calculated by subtracting the production from the demand. The result should then be subtracted from the overtime units. Hence, the stock-out units for Period 5 is 280 units.

Stock-out=(DemandProduction)Overtime unit=(2,2001,600)320=600320=280 units

Calculate the ending inventory or stock-out for Period 6:

As the demand is more than the production, there would be a stock-out.

It is calculated by subtracting the production from the demand. The result should then be subtracted from the overtime units. Hence, the stock-out units for Period 6 is 280 units.

Stock-out=(DemandProduction)Overtime unit=(2,2001,600)320=600320=280 units

Calculate the ending inventory or stock-out for Period 7:

It is calculated by subtracting the production from the demand. The result should then be subtracted from the overtime units. Hence, the stock-out units for Period 7 is 0 units.

Stock-out=(DemandProduction)Overtime unit=(1,8001,600)200=200200=0 units

Note: Overtime units of 320 units would lead to a negative value. Hence, it was taken as 200 units.

Calculate the ending inventory or stock-out for Period 8:

It is calculated by subtracting the production from the demand. The result should then be subtracted from the overtime units. Hence, the stock-out units for Period 8 is 0 units.

Stock-out=(DemandProduction)Overtime unit=(1,8001,600)200=200200=0 units

Note: Overtime units of 320 units would lead to negative value. Hence, it was taken as 200 units.

Calculate the extra cost for Period 1:

It is calculated by multiplying the extra inventory units and inventory holding cost. The inventory holding cost is given as $20 per unit. Hence, the extra cost for period 1 is $8,000

Extra cost=Ending inventory×Inventory holding cost per unit=400×$20=$8,000

Calculate the extra cost for Period 2:

It is calculated by multiplying the extra inventory units and inventory holding cost. Inventory holding cost is given as $20 per unit. Hence, the extra cost for period 2 is $8,000

Extra cost=Ending inventory×Inventory holding cost per unit=400×$20=$8,000

Calculate the extra cost for Period 3:

It is calculated by multiplying the extra inventory units and inventory holding cost. Inventory holding cost is given as $20 per unit. Hence, the extra cost for period 3 is $4,000

Extra cost=Ending inventory×Inventory holding cost per unit=200×$20=$4,000

Calculate the extra cost for Period 4:

As there are no overtime units, ending inventory units, or stock-out units, there would not be any extra costs.

Calculate the extra cost for Period 5:

It is calculated by adding the product of overtime units and inventory holding overtime cost per unit, and the product of stock-out units and stock-out cost per unit. Stock-out cost is given as $100 per unit and overtime cost is given as $50 per unit. Hence, the extra cost for period 5 is $44,000

Extra cost=(Overtime unit×Overtime cost per unit)+(Stock-out units×Stock-out cost per unit)=(320×$50)+(280×$100)=$44,000

Calculate the extra cost for Period 6:

It is calculated by adding the product of overtime units and inventory holding overtime cost per unit, and the product of stock-out units and stock-out cost per unit. Stock-out cost is given as $100 per unit and overtime cost is given as $50 per unit. Hence, the extra cost for period 6 is $44,000

Extra cost=(Overtime unit×Overtime cost per unit)+(Stock-out units×Stock-out cost per unit)=(320×$50)+(280×$100)=$44,000

Calculate the extra cost for Period 7:

It is calculated by adding the product of overtime units and inventory holding overtime cost per unit, and the product of stock-out units and stock-out cost per unit. Stock-out cost is given as $100 per unit and overtime cost is given as $50 per unit. Hence, the extra cost for period 7 is $10,000

Extra cost=(Overtime unit×Overtime cost per unit)=(200×$50)=$10,000

Calculate the extra cost for Period 8:

It is calculated by adding the product of overtime units and inventory holding overtime cost per unit, and the product of stock-out units and stock-out cost per unit. Stock-out cost is given as $100 per unit and overtime cost is given as $50 per unit. Hence, the extra cost for period 8 is $10,000

Extra cost=(Overtime unit×Overtime cost per unit)=(200×$50)=$10,000

Calculate the total cost of Plan D:

It is calculated by adding the extra costs of all the periods.

Total cost=Extra costs of all periods=$8,000+$8,000+$4,000+$0+$44,000+$44,000+$10,000+$10,000=$128,000

Hence, the total cost for Plan D is $128,000.

b)

Summary Introduction

To determine: Plan E

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. Aggregate planning would encompass a time prospect of approximately 3 to 18 months.

b)

Expert Solution
Check Mark

Answer to Problem 6P

Plan E has been evaluated. The total cost of Plan E is $140,000.

Explanation of Solution

Given information:

Production for all the months is 1,600 units. Overtime cost is $50 per unit. Maximum allowable inventor in the warehouse is 400 units or less. Demand requirement from period 0 to 8 is as follows:

Period Expected demand
0 0
1 1,400
2 1,600
3 1,800
4 1,800
5 2,200
6 2,200
7 1,800
8 1,800

Evaluate the cost of the plan:

Plan E
Period Demand Production Subcontract (units) Ending inventory Extra cost
0 200
1 1,400 1,600 - 400 $8,000
2 1,600 1,600 - 400 $8,000
3 1,800 1,600 - 200 $4,000
4 1,800 1,600 - - $0
5 2,200 1,600 600 - $45,000
6 2,200 1,600 600 - $45,000
7 1,800 1,600 200 - $15,000
8 1,800 1,600 200 - $15,000
Total 14,600 1,600 1,000 $140,000

Note: Production is given as 1,600 units. The ending inventory for December is given as 200 units. If the production is more than or equal to the demand, then there would be inventory. If the demand is more, then there would be subcontract.

Calculate the ending inventory or subcontract for Period 1:

It is calculated by adding the production and ending inventory of previous month and subtracting the demand from the result. The ending inventory for Period 1 is 400.

Ending inventory=(Production+Ending inventory of previous month)Demand=(1,600+200)1,400=1,8001,400=400

Calculate the ending inventory or subcontract for Period 2:

It is calculated by adding the production and ending inventory of previous month and subtracting the demand from the result. The ending inventory for Period 2 is 400.

Ending inventory=(Production+Ending inventory)Demand=(1,600+400)1,600=2,0001,600=400

Calculate the ending inventory or subcontract for Period 3:

It is calculated by adding the production and ending inventory of previous month and subtracting the demand from the result. The ending inventory for Period 3 is 200.

Ending inventory=(Production+Ending inventory)Demand=(1,600+400)1,800=2,0001,800=200

Calculate the ending inventory or subcontract for Period 4:

It is calculated by adding the production and ending inventory of previous month and subtracting the demand from the result. The ending inventory for Period 4 is 0.

Ending inventory=(Production+Ending inventory)Demand=(1,600+200)1,800=1,8001,800=0

Calculate the ending inventory or subcontract for Period 5:

As the demand is more than the production, there would be a subcontract.

It is calculated by subtracting the production from the demand. Hence, the subcontract units for Period 5 is 600 units.

Stock-out=(DemandProduction)=(2,2001,600)=600 units

Calculate the ending inventory or subcontract for Period 6:

As the demand is more than the production, there would be a subcontract.

It is calculated by subtracting the production from the demand. Hence, the subcontract units for Period 6 is 600 units.

Stock-out=(DemandProduction)=(2,2001,600)=600 units

Calculate the ending inventory or subcontract for Period 7:

It is calculated by subtracting the production from the demand. The result should then be subtracted from the overtime units. Hence, the subcontract units for Period 7 is 200 units.

Stock-out=(DemandProduction)=(1,8001,600)=200 units

Calculate the ending inventory or subcontract for Period 8:

It is calculated by subtracting the production from the demand. The result should then be subtracted from the overtime units. Hence, the subcontract units for Period 8 is 0 units.

Stock-out=(DemandProduction)=(1,8001,600)=200 units

Calculate the extra cost for Period 1:

It is calculated by multiplying the extra inventory units and inventory holding cost. Inventory holding cost is given as $20 per unit. Hence, the extra cost for period 1 is $8,000

Extra cost=Ending inventory×Inventory holding cost per unit=400×$20=$8,000

Calculate the extra cost for Period 2:

It is calculated by multiplying the extra inventory units and inventory holding cost. Inventory holding cost is given as $20 per unit. Hence, the extra cost for period 2 is $8,000

Extra cost=Ending inventory×Inventory holding cost per unit=400×$20=$8,000

Calculate the extra cost for Period 3:

It is calculated by multiplying the extra inventory units and inventory holding cost. Inventory holding cost is given as $20 per unit. Hence, the extra cost for period 3 is $4,000

Extra cost=Ending inventory×Inventory holding cost per unit=200×$20=$4,000

Calculate the extra cost for Period 4:

As there are no overtime units, ending inventory units, and subcontract units, there would not be extra costs.

Calculate the extra cost for Period 5:

It is calculated by multiplying the subcontract units and subcontract cost per unit. Subcontract cost is given as $75 per unit. Hence, the extra cost for period 5 is $45,000

Extra cost=(Subcontract units×Subcontract cost per unit)=(600×$75)=$45,000

Calculate the extra cost for Period 6:

It is calculated by multiplying the subcontract units and subcontract cost per unit. Subcontract cost is given as $75 per unit. Hence, the extra cost for period 6 is $45,000

Extra cost=(Subcontract units×Subcontract cost per unit)=(600×$75)=$45,000

Calculate the extra cost for Period 7:

It is calculated by multiplying the subcontract units and subcontract cost per unit. Subcontract cost is given as $75 per unit. Hence, the extra cost for period 7 is $15,000

Extra cost=(Subcontract units×Subcontract cost per unit)=(200×$75)=$15,000

Calculate the extra cost for Period 8:

It is calculated by multiplying the subcontract units and subcontract cost per unit. Subcontract cost is given as $75 per unit. Hence, the extra cost for period 8 is $15,000

Extra cost=(Subcontract units×Subcontract cost per unit)=(200×$75)=$15,000

Calculate the total cost of Plan E:

It is calculated by adding the extra costs of all the periods.

Total cost=Extra costs of all periods=$8,000+$8,000+$4,000+$0+$45,000+$45,000+$15,000+$15,000=$140,000

Hence, the total cost for Plan E is $140,000.

Conclusion

The total cost for Plan D is preferable when compared with Plan E. However, Plan C, with the total cost of $86,000 is preferable over other plans.

Want to see more full solutions like this?

Subscribe now to access step-by-step solutions to millions of textbook problems written by subject matter experts!
Students have asked these similar questions
A 98.
The XYZ company has two plants producing "K Specials". It has the following expected data for the next month's operations. Variable (incremental) costs vary linearly from zero production to maximum capacity production. plant A plant B Max. Capacity, units 1,000 800 Total fixed cost 750,000 480,000 Variable (incremental) Costs Max. Capacity 900,000 800,000 Performance has not been good, so the company expects to receive domestic orders for only 1,200 units next month at a price of 1,400 per unit. How should the production be distributed between the plants for optimum economic operation? A. Plant A should produce 800 units and 400 units for Plant B. B. Plant A should produce 1,000 units and 200 units for Plant B. C. Plant A should produce 700 units and 500 units for Plant B. D. Plant A should produce 900 units and 300 units for Plant B.
Consuela Chua, Inc., is a disk drive manufacturer in need of an aggregate plan for July through December. The company has gathered the following data:                                                                                                                  What will each of the two fo llowing strategies cost?a) Vary the workforce so that production meets demand. Chuahad eight workers on board in June.b) Vary overtime only and use a constant workforce of eight.
Knowledge Booster
Background pattern image
Operations Management
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, operations-management and related others by exploring similar questions and additional content below.
Similar questions
SEE MORE QUESTIONS
Recommended textbooks for you
Text book image
Practical Management Science
Operations Management
ISBN:9781337406659
Author:WINSTON, Wayne L.
Publisher:Cengage,
Text book image
Operations Management
Operations Management
ISBN:9781259667473
Author:William J Stevenson
Publisher:McGraw-Hill Education
Text book image
Operations and Supply Chain Management (Mcgraw-hi...
Operations Management
ISBN:9781259666100
Author:F. Robert Jacobs, Richard B Chase
Publisher:McGraw-Hill Education
Text book image
Business in Action
Operations Management
ISBN:9780135198100
Author:BOVEE
Publisher:PEARSON CO
Text book image
Purchasing and Supply Chain Management
Operations Management
ISBN:9781285869681
Author:Robert M. Monczka, Robert B. Handfield, Larry C. Giunipero, James L. Patterson
Publisher:Cengage Learning
Text book image
Production and Operations Analysis, Seventh Editi...
Operations Management
ISBN:9781478623069
Author:Steven Nahmias, Tava Lennon Olsen
Publisher:Waveland Press, Inc.