Pearson eText Principles of Operations Management: Sustainability and Supply Chain Management -- Instant Access (Pearson+)
Pearson eText Principles of Operations Management: Sustainability and Supply Chain Management -- Instant Access (Pearson+)
11th Edition
ISBN: 9780135639221
Author: Jay Heizer, Barry Render
Publisher: PEARSON+
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Chapter 12, Problem 24P

a)

Summary Introduction

To determine: The optimal order quantity.

Introduction: Inventory management is the process of ordering, storing and using inventory of the company such raw material, components and finished goods. It governs the flow of goods from manufacturers to warehouse and to the point of sale. The key function is to maintain record of flow of new or returned products which enters or leaves the company.

a)

Expert Solution
Check Mark

Answer to Problem 24P

The optimal order quantity is 16,970.56.

Explanation of Solution

Given information:

Annualdemand=45,000piecesOrdercost=$200perorder

Pricefororderlessthan2000pieces=$7.80/piecePricefororderbetween2,001to5000pieces=$1.60/piecePricefororderbetween5,001to10,000pieces=$1.40/piecePriceforordermore than10,001pieces=1.25/piece

Formula:

EOQ,Q=2DSH

Where

D=DemandS=OrderingcostH=Holdingcost

Calculation of optimal order quantity:

Calculation of EOQ for orders less than 2000 pieces:

H1=0.05×7.80=0.39

Holding cost is 5% of the purchase price for orders less than 2000 pieces which is 0.05 multiplied by 7.80 which yields 0.39.

Q1=2DSH1=2×45,000×2000.39=6793.66pieces

EOQ for order less than 2000 pieces is calculated by multiplying 2, 45,000 and 200 and dividing the resultant with 0.39 and taking square root which gives 6,793.66 pieces.

Calculation of EOQ for orders between 2,001 to 5,000 pieces:

H2=0.05×1.60=0.08

Holding cost is 5% of the purchase price for orders between 2001 to 5000 pieces which is 0.05 multiplied by 1.60 which yields 0.08.

Q2=2DSH2=2×45,000×2000.08=15,000pieces

EOQ for order orders between 2,001 to 5,000 pieces is calculated by multiplying 2, 45,000 and 200 and dividing the resultant with 0.08 and taking square root which gives 15,000 pieces.

Calculation of EOQ for orders between 5,001 to 10,000 pieces:

H3=0.05×1.40=0.07

Holding cost is 5% of the purchase price for orders between 5,001 to 10,000 pieces which is 0.05 multiplied by 1.40 which yields 0.07.

Q3=2DSH3=2×45,000×2000.07=16,035.67pieces

EOQ for order orders between 5,001 to 10,000 pieces is calculated by multiplying 2, 45,000 and 200 and dividing the resultant with 0.07 and taking square root which gives 16,035.67 pieces.

Calculation of EOQ for orders more than 10,001 pieces:

H4=0.05×1.25=0.0625

Holding cost is 5% of the purchase price for orders more than 10,001 pieces which is 0.05 multiplied by 1.25 which yields 0.0625.

Q4=2DSH4=2×45,000×2000.0625=16,970.56pieces

EOQ for order orders more than 10,001 pieces is calculated by multiplying 2, 45,000 and 200 and dividing the resultant with 0.0625 and taking square root which gives 16,970.56 pieces.

Based on the above calculations, EOQ for orders more than 10,001 pieces gives optimal order quantity as the EOQ lies within the quantities ordered. Therefore the optimal order quantity is 16,970.56 pieces at $1.25.

Hence, the optimal order quantity is 16,970.56.

b)

Summary Introduction

To determine: The annual holding cost.

b)

Expert Solution
Check Mark

Answer to Problem 24P

The annual holding cost is $530.33.

Explanation of Solution

Given information:

Annualdemand=45,000piecesOrdercost=$200perorder

Pricefororderlessthan2000pieces=$7.80/piecePricefororderbetween2,001to5000pieces=$1.60/piecePricefororderbetween5,001to10,000pieces=$1.40/piecePriceforordermore than10,001pieces=1.25/piece

Formula:

Annualholdingcost=Q2×H

Calculation annual holding cost:

H=0.05×1.25=0.0625

Annualholdingcost=Q2×H=16,9712×0.0625=$530.33

Annual holding cost is calculated by multiplying half of the economic order quantity which is 16,971 divided by 2 and multiplying with 0.0625 which yields $530.33.

Hence, the annual holding cost is $530.33.

c)

Summary Introduction

To determine: The annual setup cost.

c)

Expert Solution
Check Mark

Answer to Problem 24P

The annual setup cost is $530.33.

Explanation of Solution

Given information:

Annualdemand=45,000piecesOrdercost=$200perorder

Pricefororderlessthan2000pieces=$7.80/piecePricefororderbetween2,001to5000pieces=$1.60/piecePricefororderbetween5,001to10,000pieces=$1.40/piecePriceforordermore than10,001pieces=1.25/piece

Formula:

Annualsetupcost=DQ×S

Calculation annual ordering cost:

=45,00016,971×200=$530.33

Annual ordering cost is calculated by dividing 45,000 with 16,971 and multiplying the resultant with 200 which yields $530.33.

Hence, the annual ordering cost is $530.33.

d)

Summary Introduction

To determine: The annual cost of silverware with optimal order quantity.

d)

Expert Solution
Check Mark

Answer to Problem 24P

The annual cost of silverware with optimal order quantity is $56,250.

Explanation of Solution

Given information:

Annualdemand=45,000piecesOrdercost=$200perorder

Pricefororderlessthan2000pieces=$7.80/piecePricefororderbetween2,001to5000pieces=$1.60/piecePricefororderbetween5,001to10,000pieces=$1.40/piecePriceforordermore than10,001pieces=1.25/piece

Formula:

Unitcost=P×D

Calculation of annual cost of silverware with optimal order quantity:

=$1.25×45,000=$56,250

Annual cost of silverware with optimal order quantity is calculated by multiplying 1.25 with 45,000 which gives $56,250.

Hence, the annual cost of silverware with optimal order quantity is $56,250.

e)

Summary Introduction

To determine: The total annual cost including ordering, holding and purchasing the silverware.

e)

Expert Solution
Check Mark

Answer to Problem 24P

The total annual cost including ordering, holding and purchasing the silverware is $57,310.66.

Explanation of Solution

Given information:

Annualdemand=45,000piecesOrdercost=$200perorder

Pricefororderlessthan2000pieces=$7.80/piecePricefororderbetween2,001to5000pieces=$1.60/piecePricefororderbetween5,001to10,000pieces=$1.40/piecePriceforordermore than10,001pieces=1.25/piece

Calculation of total annual cost:

Totalcost=530.33+530.33+56,250.00=$57,310.00

Total annual cost is calculated by adding holding cost, ordering cost and unit cost which is 530.33, 530.33 and 56,250 is summed up to give 57,310.66.

Hence, the total annual cost including ordering, holding and purchasing the silverware is $57,310.66.

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Chapter 12 Solutions

Pearson eText Principles of Operations Management: Sustainability and Supply Chain Management -- Instant Access (Pearson+)

Ch. 12 - Prob. 10DQCh. 12 - Prob. 11DQCh. 12 - Explain the following: All things being equal, the...Ch. 12 - Prob. 13DQCh. 12 - Prob. 14DQCh. 12 - Prob. 15DQCh. 12 - When demand is not constant, the reorder point is...Ch. 12 - Prob. 17DQCh. 12 - State a major advantage, and a major disadvantage,...Ch. 12 - L. Houts Plastics it a large manufacturer of...Ch. 12 - Prob. 2PCh. 12 - Jean-Mane Bourjollys restaurant has the following...Ch. 12 - Lindsay Electronics, a small manufacturer of...Ch. 12 - Prob. 5PCh. 12 - Prob. 6PCh. 12 - William Sevilles computer training school, in...Ch. 12 - Prob. 8PCh. 12 - Prob. 9PCh. 12 - Matthew Liotines Dream Store sells beds and...Ch. 12 - Southeastern Bell stocks a certain switch...Ch. 12 - Lead time for one of your fastest-moving products...Ch. 12 - Annual demand for the notebook binders at Duncans...Ch. 12 - Thomas Kratzer is the purchasing manager for the...Ch. 12 - Joe Henrys machine shop uses 2,500 brackets during...Ch. 12 - Prob. 16PCh. 12 - Prob. 17PCh. 12 - Prob. 18PCh. 12 - Prob. 19PCh. 12 - Prob. 20PCh. 12 - Cesar Rego Computers, a Mississippi chain of...Ch. 12 - Prob. 22PCh. 12 - Prob. 23PCh. 12 - Prob. 24PCh. 12 - Prob. 25PCh. 12 - M. P. VanOyen Manufacturing has gone out on bid...Ch. 12 - Chris Sandvig Irrigation, Inc., has summarized the...Ch. 12 - Prob. 28PCh. 12 - Prob. 29PCh. 12 - Prob. 30PCh. 12 - Prob. 31PCh. 12 - Prob. 32PCh. 12 - Prob. 33PCh. 12 - Prob. 34PCh. 12 - Prob. 35PCh. 12 - Prob. 36PCh. 12 - Prob. 37PCh. 12 - Prob. 38PCh. 12 - Prob. 39PCh. 12 - Prob. 40PCh. 12 - Barbara Flynn is in charge of maintaining hospital...Ch. 12 - Prob. 42PCh. 12 - Authentic Thai rattan chairs (shown in the photo)...Ch. 12 - Prob. 44PCh. 12 - Prob. 45PCh. 12 - Prob. 46PCh. 12 - Prob. 47PCh. 12 - Gainesville Cigar stocks Cuban agars that have...Ch. 12 - A gourmet coffee shop in downtown San Francisco is...Ch. 12 - Prob. 50PCh. 12 - Prob. 51PCh. 12 - Henrique Correas bakery prepares all its cakes...Ch. 12 - Prob. 53PCh. 12 - Prob. 1CSCh. 12 - Prob. 2CSCh. 12 - Prob. 3CSCh. 12 - Prob. 1.1VCCh. 12 - Prob. 1.2VCCh. 12 - Prob. 1.3VCCh. 12 - Prob. 1.4VCCh. 12 - Prob. 1.5VCCh. 12 - Prob. 1.6VCCh. 12 - Prob. 1.7VCCh. 12 - Prob. 2.1VCCh. 12 - Prob. 2.2VCCh. 12 - Prob. 2.3VCCh. 12 - Prob. 2.4VCCh. 12 - Inventory Control at Wheeled Coach Controlling...Ch. 12 - Prob. 3.2VCCh. 12 - Inventory Control at Wheeled Coach Controlling...
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