Production and Operations Analysis, Seventh Edition
Production and Operations Analysis, Seventh Edition
7th Edition
ISBN: 9781478623069
Author: Steven Nahmias, Tava Lennon Olsen
Publisher: Waveland Press, Inc.
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Chapter 5, Problem 44AP

a

Summary Introduction

Interpretation:Value of Q and R used to control the inventory of white dress shirts is to be determined.

Concept Introduction:

Normal distribution is the probability function with continuous series. It is bell shaped distribution function where mean, median and mode are same.

a

Expert Solution
Check Mark

Answer to Problem 44AP

Order quantity (Q) is 240 units and Reorder point (R) is also 240 units.

Explanation of Solution

Given information:

Cost of each shirt = $6

Selling cost of each shirt = $15

Monthly demand = 120

Standard deviation of monthly demand = 32

Reorder point = Two months of demand,

Order quantity = two months of demand

Q refers to the order quantity and R refers to the reorder point.

Order quantity is two months of demand i.e. 120 units × 2 = 240 units.

The proprietor orders when stock falls below the two-month’s supply stock. The two month’s supply stock means 120 units × 2 = 240 units.

Order quantity (Q) is 240 units and Reorder point (R) is also 240 units.

b

Summary Introduction

Interpretation:Fill rate achieved with current policy is to be determined.

Concept Introduction:

Normal distribution is the probability function with continuous series. It is bell shaped distribution function where mean, median and mode are same.

b

Expert Solution
Check Mark

Answer to Problem 44AP

The fill rate of 99.9% is being achieved in current policy.

Explanation of Solution

Given information:

Cost of each shirt = $6

Selling cost of each shirt = $15

Monthly demand = 120

Standard deviation of monthly demand = 32

Reorder point = Two months of demand,

Order quantity = two months of demand

Type 2 service:

  n(R)Q=1β

  n(R)=EOQ(1β)

  L(Z)=(1β)Q/σ

  R=σz+μ

  β=F(R)

  β = proportion

  μ = mean

  σ = standarddeviation

Lead time given = 3 weeks = 34month

Mean, μ=34×120=90

Standard deviation, σ=34×32=27.71

  n(R)=σL(z)

  z=Rμσ=2409027.71=5.41

  n(R)=(27.71)(<0.00001)

  n(R)=0.000099

Therefore, the fill rate of 99.9% is being achieved in current policy.

c

Summary Introduction

Interpretation:Optimal value of Q and R is to be determined based on the 99% fill rate criteria.

Concept Introduction:

Normal distribution is the probability function with continuous series. It is bell shaped distribution function where mean, median and mode are same.

c

Expert Solution
Check Mark

Answer to Problem 44AP

Optimal value of Q and R is (Q, R) = (455,107)

Explanation of Solution

Given information:

Cost of each shirt = $6

Selling cost of each shirt = $15

Monthly demand = 120

Standard deviation of monthly demand = 32

Reorder point = Two months of demand,

Order quantity = two months of demand

  Mean,μ=90

  Standarddeviation,σ=27.71

  Meanweeklydemand,λ=120×12=1440

  Holdingcost, h = $0.20×6 =1.2

  Setupcost,K=80

Iteration 1:

  Qο=2κλh

  Qο=2×80×14401.2

  =438.17

  n(Rο)=(1β)Q

  =(0.01)438.17

  =4.38

  L(zο)=n(Rο)σ=4.3827.71=0.1580

From L(zο) , calculate zο=0.64,F(zο)=0.261

Iteration 2:

  Q1=n(Rο)F(zο)+(Qο)2+(n(Rο)F(zο))2

  Q1=4.380.261+(438)2+(4.380.261)2

  Q1=455.10

  n(Rο)=(1β)Q

  =(0.01)455.10

  =4.55

  L(zο)=n(Rο)σ=4.5527.71=0.1642

From L(z1) , calculate z1=0.61,F(zο)=0.268

  R1=σz+μ=(27.71)(0.61)+90=107

Iteration 3:

  Q2=n(R1)F(z1)+(Q1)2+(n(R1)F(z1))2

  Q2=4.550.268+(455)2+(4.550.268)2

  Q2=455.10

Since the Q value is repeating, we terminate further iteration

Hence, (Q, R) = (455,107)

d

Summary Introduction

Interpretation:Difference in average annual holding and set up costs is to be determined.

Concept Introduction:

Normal distribution is the probability function with continuous series. It is bell shaped distribution function where mean, median and mode are same.

d

Expert Solution
Check Mark

Answer to Problem 44AP

Difference in average annual holding and set up costs is $257.

Explanation of Solution

Given information:

Cost of each shirt = $6

Selling cost of each shirt = $15

Monthly demand = 120

Standard deviation of monthly demand = 32

Reorder point = Two months of demand,

Order quantity = two months of demand

Considering (Q, R) from policy (b)

(Q, R) = (240,240)

  Annualholdingandset-upcosts=h[Q2+(R-μ)]+κλQ

  =1.2[2402+(24090)]+80×1440240

  =804

Therefore, the annual holding cost and set up cost are $804.

Considering (Q, R) from policy (c)

(Q, R) = (455,107)

  Annualholdingandset-upcosts=h[Q2+(R-μ)]+κλQ

  =1.2[4552+(10790)]+80×1440455=546.6

Therefore, the annual holding cost and set up cost are $547.

Saving on total = $804-$547 = $257

e

Summary Introduction

Interpretation:Time required paying for $25000 inventory control system is to be calculated.

Concept Introduction:

Normal distribution is the probability function with continuous series. It is bell shaped distribution function where mean, median and mode are same.

e

Expert Solution
Check Mark

Answer to Problem 44AP

Time required in paying $25,000 of inventory control is 4.86 yearsto the system.

Explanation of Solution

Given information:

Cost of each shirt = $6

Selling cost of each shirt = $15

Monthly demand = 120

Standard deviation of monthly demand = 32

Reorder point = Two months of demand,

Order quantity = two months of demand

Time required in paying $25,000 of inventory control is as shown below:

Assuming 20% of the annual interest rate to the estimate (Q, R)

Then the savings would be estimated as (20)($257) = $5,140

Here if the time value of money is ignored for the given inventory control of $25,000

Time required = 25,000/5140 = 4.86 years

Therefore, time required in paying $25,000 of inventory control is 4.86 yearsto the system.

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