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liane-varnes | 2015-10-12 | General
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Set 3: Advanced. Weekly . demand for DVD-Rs at a retailer is normally distributed with a . mean. of . 1,000. boxes and a . standard deviation . of . 150. . Currently, the store places orders via paper that is faxed to the supplier. Assume . ID: 158404

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Slide1

Re-Order Point Problems Set 3: Advanced

Slide2Weekly

demand for DVD-Rs at a retailer is normally distributed with a

mean of 1,000 boxes and a standard deviation of 150. Currently, the store places orders via paper that is faxed to the supplier. Assume 50 working weeks in a year. Lead time for replenishment of an order is 4 weeks. Fixed cost (ordering and transportation) per order is $100. Each box of DVD-Rs costs $1. Annual holding cost is 25% of average inventory value. The retailer currently orders 20,000 DVD-Rs when stock on hand reaches 4,200.

Problem 1: Problem 7.2 – Average Inventory With Isafety

R/week

= N(1000,150)L = 2 week Q = 20,000ROP = 4,200 50 weeks /yrAve. R /year = 50,000S =100C = 1H=0.25C = $0.25

a.1)

How long, on average, does a box of DVD-R spend in the store?

Icycle

=Q/2 = 20000/2

Isafety

= ROP – LTD

LTD = L×R = 4×1000 =

4000

Slide3Problem 1: Problem 7.2

– Average Inventory With

Isafety

Isafety = 4200 - 4000 = 200Average inventory = Icycle + IsafetyI = Average Inventory = 20000/2 + 200 = 10200RT = I = 1000T = 10200 T = 10.2 weeks

R/week

= N(1000,150)L = 2 week Q = 20,000ROP = 4,200 50 weeks /yrAve. R /year = 50,000S =100C = 1H=0.25C = $0.25

a.2) What is the annual ordering and holding cost. Number of orders R/QR/Q = 50,000/20,000 = 2.5Ordering cost = 100(2.5) = 250

Annual

holding cost

= 0.25

%

×1

×

10200 =2550

Total

inventory system cost

excluding purchasing = 250+2550

=

2800. OC ≠ CC for two reason,

(i) Not EOQ, (ii)

Isafety

Slide4b.1) Assuming

that the retailer wants the probability of stocking out in a cycle to be no more than 5%, recommend an optimal inventory policy: Q and R policy.

=6325

Problem 1: Problem 7.2

– Average Inventory With

Isafety

Z(95%) = 1.65

Z(95%) = 1.65

Isafety

= z

σ

LTD

=1.65(300

) =

495

ROP = 4000+195 = 4495

Optimal Q and R Policy: Order 6325 whenever inventory on hand is

4495

b.2) Under your recommended policy, how long, on average, would a box of DVD-Rs spend in the store

?

Slide5Average

inventory = Icycle+Isafety = Q/2 + IsafetyAverage inventory = I = 6325/2 + 495 = 3658 RT = I 1000T = 3658 T = 3.66 weeksc) Reduce lead time form 4 to 1. What is the impact on cost and flow time?

Problem 1: Problem 7.2 – Average Inventory With Isafety

Safety stock reduces from

495

to

247.5

247.5

units reductionThat is 0.25(247.5) = $62 savingAverage inventory = Icycle + Isafey = Q/2 + Isafety Average Inventory = I = (6,325/2) + 247.5 = 3,410.Average time in store I = RT3410 = 1000T T = 3.41 weeks

Slide6R/week in each warehouse follows Normal

distribution with mean of 10,000, and Standard deviation of 2,000. Compute mean and standard deviation of weekly demand in all the warehouse together – considered as a single central warehouse.Mean (central) = 4(10000) = 40,000 per week Variance (central) = SUM(variance at each warehouse)Variance (central) = 4(variance at each warehouse)Variance at each warehouse = (2000)2 = 4,000,000Variance (central) = 4(4,000,000) = 16,000,000

Problem 2: Problem 7.8 – Centralization

=

40000

Standard

deviation (central)

=

R

(central) = Normal(

40,000

,

4,000

)

Slide7The replenishment lead time (L) =

1 week.Standard deviation of demand during lead time in the centralized system

Problem 2: Problem 7.8 – Centralization

Safety stock at each store for 95% level of service Isafety (central) = 1.65 x 4,000 = 6,600.Average inventory in the centralized system

=26600

= 26600

I =

Icycle

+

Isafety

40000/2 +6600

Average Centralized Inventory

I = Q/2 +

Isafety

Average Decentralized Inventory = 53200

Average time spend in

inventory

(

Centralized):

RT =I

4000T = 26600

T

=

0.67

weeks

Slide8S(R/Q) = 1000(4)(500,000/40,000) = 50,000

H(

Isafety + Icycle) = 2.5(26,000) = 66,500Purchasing cost = CR = 10(500,000) = 5,000,000We do not consider RC because it does not depend on the inventory policy. But you can always add it.Inventory system cost for four warehouse in centralized system116,500Inventory system cost for four warehouses in decentralized system233,000

Problem 2: Problem 7.8

–

Centralization

Slide9Home

and Garden (HG) chain of superstores imports decorative planters from Italy. Weekly demand for planters averages 1,500 with a standard deviation of 800. Each planter costs $10. HG incurs a holding cost of 25% per year to carry inventory. HG has an opportunity to set up a superstore in the Phoenix region. Each order shipped from Italy incurs a fixed transportation and delivery cost of $10,000. Consider 52 weeks in the year

.

Problem 3: Problem 7.3- Lead Time vs Purchase Price

R/week

= N(1500,800)C = 10 h = 0.25 H =0.25(10) = 2.552 weeks /yrR = 78000/yrS =10000L = 4 weeksSL = 90%

a) Determine the optimal order quantity (EOQ).

=24980

b) If

the delivery lead

time

is 4 weeks and HG wants to provide a cycle service level of 90%, how much safety stock should it carry?

Slide10c) Reduce L from 4 to 1, Increase C by 0.2 per unit. Yes or no?

Safety stock decrease

from 2048 to 1024

1024 units reduction

Safety stock cost saving = 2.5(1024) = 2560

15600-2560 = 13040 increase in cost

Purchasing cost increase

0.2(78000

) = 15600

c.1) Rough computations.

Problem 3: Problem

7.3- Lead Time vs Purchase Price

Slide11R/week

= N(1500,800)

C = 10 + 0.2 H = .25(10+.2) = 2.5552 weeks /yrR = 78000S =10000L = 4 weeksSL = 90%

+

CR

+HI

s

For the original case of C = 10 and H =2.5

c.1) Detailed computations.

Change in

C

Change in H. Not only purchasing cost changesBut also cost of EOQ and Is ChangesReduce L from 4 to 1Purchasing cost increase = 0.2(78000) = 15600 Safety stock reduces from 2048@2.5 to 1024@2.55Safety stock cost saving = 2.5(2048)-2.55(1024) = 2509

Problem 3: Problem

7.3- Lead Time vs Purchase Price

Slide12R/week

= N(1500,800)

C = 10 + 0.2 H = .25(10+.2) = 2.5552 weeks /yrR = 78000S =10000L = 4 weeksSL = 90%

Total inventory cost (ordering + carrying) increase = 0.00995*62450 = 621

Total impact = +621+15600-2509 = 13712

Total inventory cost (ordering + carrying) will also increase

Problem 3: Problem

7.3- Lead Time vs Purchase Price

Slide13=20000

#

of warehouses = 4

R/week at each warehouse

N(10,000, 2,000)

50 weeks per year

C = 10

H=0.25(10) = 2.5 /yearS = 1000 L = 1 weekSL = 0.95

z(0.95) = 1.65, σLTD = 2,000

ROP = LTD + Is =

1×10,000 + 3,300 = 13,300.

I = 4(13300) = 53200

Average inventory at each warehouse :

+

Is

=10000+ 3300

=13300

Average Decentralized inventory in 4 warehouses =

Demand in in 4 warehouses =

4(10000) =40000/w

RT = I 40000T= 53200

Is = 1.65 x 2,000 = 3,300.

T = 1.33 weeks

Each time we order Q=20000 Icycle = Q/2 = 20000/2=10000

Average Inventory = Ic

Problem 3: Problem

7.3- Lead Time vs Purchase Price

Slide14OC = S(R/Q) = 1000[(50×10,000)]/Q = 25,000.

CC = H (

Icycle + Isafety) = H(Q/2+Isafety) = 2.5 (13300) =32,250. We do not consider RC because it does not depend on the inventory policy. But you can always add it.RC = 10 [(50×10,000)]= 5,000,0000Inventory system cost for one warehouse excluding purchasingTC = 25,000 + 32,000 = 58,200Inventory system cost for four warehouses = 4(58,250)Inventory system cost for four warehouses = 233,000 Inventory system cost for four warehouses including purchasing = 4(5,000,000) + 233,000 = 20,233,000

Problem 3: Problem

7.3- Lead Time vs Purchase Price

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