EBK PRINCIPLES OF OPERATIONS MANAGEMENT
EBK PRINCIPLES OF OPERATIONS MANAGEMENT
11th Edition
ISBN: 9780135175859
Author: Munson
Publisher: VST
Question
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Chapter 11.S, Problem 5P

a)

Summary Introduction

To determine: The probability that all three suppliers are disrupted using option 1.

Introduction: Supply chain management is one of the important elements of a business which impacts business product development. With expanding businesses in global conditions, supply chain activities can impact the cost effectiveness of these businesses.

a)

Expert Solution
Check Mark

Answer to Problem 5P

The probability that three suppliers are disrupted using option 1 is 0.025062.

Explanation of Solution

Given information:

Option 1

Probabilityofsuper-event,S=2.5%=0.025Probabilityofunique-event,U=4%=0.04Purchasing & Transportation cost=$1,000,000Disruption loss=$500,000

Option 2

Probabilityofsuper-event,S=0.4%=0.004Probabilityofunique-event,U=20%=0.20Purchasing & Transportation cost=$1,010,000Disruption loss=$500,000

Formula:

P(n)=S+(1-S)Un

Probability calculation when both suppliers are disrupted by option 1:

P(n)=S+(1-S)UnP(3)=0.025+(1-0.025)0.043=0.025+(0.975×0.000064)=0.025062 EBK PRINCIPLES OF OPERATIONS MANAGEMENT, Chapter 11.S, Problem 5P , additional homework tip  1

To find the probability of selection, one supplier substitutes the number of chosen suppliers, and the probability of super-event and unique-event in the above formula. Here, the number of suppliers chosen is ‘3’, S=0.025 and U=0.04, and is substituted in the above formula which gives probability as 0.025062.

Hence, the probability that two suppliers are disrupted using option 1 is 0.025062.

b)

Summary Introduction

To determine: The probability that all three suppliers are disrupted using option 2.

b)

Expert Solution
Check Mark

Answer to Problem 5P

The probability that three suppliers are disrupted using option 1 is 0.011968.

Explanation of Solution

Given information:

Option 1

Probabilityofsuper-event,S=2.5%=0.025Probabilityofunique-event,U=4%=0.04Purchasing & Transportation cost=$1,000,000Disruption loss=$500,000

Option 2

Probabilityofsuper-event,S=0.4%=0.004Probabilityofunique-event,U=20%=0.20Purchasing & Transportation cost=$1,010,000Disruption loss=$500,000

Formula:

P(n)=S+(1-S)Un

Probability calculation when both suppliers are disrupted by option 2:

P(n)=S+(1-S)UnP(3)=0.004+(1-0.004)0.203=0.004+(0.996×0.008)=0.011968 EBK PRINCIPLES OF OPERATIONS MANAGEMENT, Chapter 11.S, Problem 5P , additional homework tip  2

To find the probability of selection, one supplier substitutes the number of chosen suppliers, anf the probability of super-event and unique-event in the above formula. Here, the number of suppliers chosen is ‘3’, S=0.004 and U=0.20, and is substituted in the above formula which gives probability as 0.011968.

Hence, the probability that two suppliers are disrupted using option 1 is 0.011968.

c)

Summary Introduction

To determine: The total annual expected cost for option 1.

c)

Expert Solution
Check Mark

Answer to Problem 5P

The total expected cost for option 1 is $1,012,531.

Explanation of Solution

Given information:

Option 1

Probabilityofsuper-event,S=2.5%=0.025Probabilityofunique-event,U=4%=0.04Purchasing & Transportation cost=$1,000,000Disruption loss=$500,000

Option 2

Probabilityofsuper-event,S=0.4%=0.004Probabilityofunique-event,U=20%=0.20Purchasing & Transportation cost=$1,010,000Disruption loss=$500,000

Formula:

Total expected cost=Annualpurchasingcost+Expecteddisruptioncost

Calculation of total expected cost:

Total expected cost=Annualpurchasingcost+Expecteddisruptioncost=$1,000,000+($500,000×0.025062)=$1,012,531 (1)

The total expected cost is calculated by taking the summation of the annual purchasing cost and expected disruption cost. The product of $500,000 and 0.025062 is added with $1,000,000, which gives $1,012,531 as the total expected cost for option 1.

Hence, the total expected cost using option 1 is $1,012,531.

d)

Summary Introduction

To determine: The total annual expected cost for option 2.

d)

Expert Solution
Check Mark

Answer to Problem 5P

The total expected cost for option 2 is $1,015,984.

Explanation of Solution

Given information:

Option 1

Probabilityofsuper-event,S=2.5%=0.025Probabilityofunique-event,U=4%=0.04Purchasing & Transportation cost=$1,000,000Disruption loss=$500,000

Option 2

Probabilityofsuper-event,S=0.4%=0.004Probabilityofunique-event,U=20%=0.20Purchasing & Transportation cost=$1,010,000Disruption loss=$500,000

Formula:

Total expected cost=Annualpurchasingcost+Expecteddisruptioncost

Calculation of total expected cost:

Total expected cost=Annualpurchasingcost+Expecteddisruptioncost=$1,010,000+($500,000×0.11968)=$1,015,984 (2)

The total expected cost is calculated by taking the summation of the annual purchasing cost and expected disruption cost. The product of $500,000 and 0.11968 is added with $1,010,000 which gives $1,015,984 as the total expected cost for option 2.

Hence, the total expected cost using option 2 is $1,015,984.

e)

Summary Introduction

To determine: The best options.

e)

Expert Solution
Check Mark

Answer to Problem 5P

Option 1 is best.

Explanation of Solution

Given information:

Option 1

Probabilityofsuper-event,S=2.5%=0.025Probabilityofunique-event,U=4%=0.04Purchasing & Transportation cost=$1,000,000Disruption loss=$500,000

Option 2

Probabilityofsuper-event,S=0.4%=0.004Probabilityofunique-event,U=20%=0.20Purchasing & Transportation cost=$1,010,000Disruption loss=$500,000

On comparing equations (1) and (2), it can be inferred that option 1 has the least expected cost. Therefore, it is advisable for Company BJ to choose option 1.

Hence, Option 1 is best.

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