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Review of Exam 1

John H. Vande VateFall 2009

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Rules of the Game

• If you feel we (may have) made a mistake grading your exam – write an explanation on your exam and turn it in for re-grading. You’ll get it back before the final.

• Do not come and argue/debate about the grading!

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Exam 1 Key

• The capital required to run the system including the capital:• at Green Bay: ___$1.5 million ____________ • at the cross dock/DC in Indianapolis:__$12,859,649 or

$12,508,772 (if you don’t add outbound inventory for MP3s -- fine, even good to report this as $12.86 million or 12.51 million)______________

• at each store:_ $1,359,649 (fine, even good to report this as $1.36 million)_______________

• in-transit between– Green Bay and Indianapolis: _$750,000___________– Indianapolis and each store: _

2*$77,500_=$155,000____________• The total cost of operating the system including:

– Annual transportation costs: _ $1,115,625 (fine, even good to say $1.12 million)_______________and

– Annual inventory holding costs: ___ $41,643,640 (fine, even good to say $41.64 million)______________

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Question 1

A truck from Green Bay can hold 50,000/5 = 10,000 CPUs

Worth $300*10,000 = $3,000,000 So outbound inventory at Green Bay is $1.5

million And this contributes $1.5 million to inbound

inventory at IndianapolisA truck can hold 50000/0.25 = 200,000 MP3s Worth $20 million so this contributes $10 million

to inbound inventory at Indianapolis

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Question 1To get the outbound inventory at Indianapolis and the inventory at each

store, observe that one day’s sales at a store is125 Monitors weighing 10 lbs each25 CPUS weighing 5 lbs each and 200 MP3s weighing 0.25 lbs each So one day’s sales at a store weighs 1425 lbs and is worth $77,500A truck can hold 50000/1425 = 35.09 days of sales at a storeThat’s worth 35.09*77,500 = $2.72 millionSo outbound inventory at the cross dock will be $1.36 millionTotal Inventory at Indianapolis will be $11.5 million inbound + 1.36

million outbound = $12.86 million outbound (it’s reasonable to exclude the MP3s from the outbound inventory calculation in which case the inventory would be $12.51 million)

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Question 1At each store we will have 35.09/2 days

of sales in inventory or $1.36 millionIn transit between Green Bay and

Indianapolis we will have 1 days sales of CPUS or 100*25*$300 = $750,000 in pipeline inventory

In transit between Indianapolis and one store we will have 2 days sales or 2*77,500 = $155,000 in pipeline inventory

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What’s in truck to store?Annual transport costsTo Indianapolis will be $1.5/mile * 500 miles = $750 per tripAnd there will be around 100 stores*25 units/store/day * 250

days/10000 units per truck = 62.5 trips for a total cost of $46,875 per year

To each store will be $1.5/mile*1000 miles = $1500 per tripAnd since a truck holds 35.09 days of sales, we will visit each

store 250/35.09 = 7.13 times per year for a total of $10,688 per store per year

Total transport costs will be $1.12 million

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Question 1Total Inventory costs: Adding all the inventories we have about $166.57

million in working capital and at 25% that’s about $41.64 million in carrying cost per year.

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Question 2

• A. How should the company ship to a store 1,000 miles away? Use FTL, use TL rates to ship less than a full truck load or use LTL? _Use TL rates to ship less than a full truck load _______________

• B. How many TVs, how many computers and how many MP3 Players should the company send to each store in each shipment assuming the store is 1,000 miles away?

• TVs:________619 or so_______________ • Computers: ____155 or so_____________• MP3 Players: ___1,238 or so_____________

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Question 2 Let’s do the EPQ with TL rates first. It’s easy to translate

everything into days of sales: So A, the cost of a trip is $1500

D, annual demand at a store is 250 (days of sales) h, the holding percentage is 25% C, the value of a day of sales is $77,500 P, the annual production rate is 100*250 = 25,000EPQ is Sqrt(2*A*D/hC)*Sqrt(P/(P+D)) =

Sqrt(2*1500*250/19,375)*Sqrt(100/101) = 6.19 (so in practice, we would likely simply ship to each store once per week)

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Question 2

The cost of this easy to calculate from the store inventory:

We will have 3.1 days of sales in inventory at each store so that will require 3.1*77,500 $240,000 in inventory at each store or about $60,000 in carrying costs at each store.

The EPQ balances inventory and transport costs and, since the second term in the EPQ is essentially 1 (i.e., inventory at the dc is nearly irrelevant), we can get a good quick estimate of transport costs to each store as about $60,000 per year.

So the total cost of this solution is $120,000 per store.

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Question 2

• The LTL solutions. • Again it might be easiest to translate everything

into days. • 500 lbs is 5 CWT is 0.35 days of sales at a store.

Inventory will be very low. But transport costs will be $60/cwt*14.25CWT/store-day*250 days/year = $213,750/store per year already a loser.

• Similarly 1000 lbs is 10 CWT or .7 days of sales at a store. Inventory will be very low, but transport will be $39.9*14.25CWT/store-day*250 days/year = $142,144/store per year already a loser.

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Question 2

• Finally 20,000 lbs is 200 CWT or 14.04 days of sales. Inventory will be high, but transport will still be $24*14.25CWT/store-day*250 days/year = $85,500/store per year.

• But inventory costs will be 7.02*77,500*0.25 $135,965 per year per store so that’s not attractive.

• So, we didn’t even need to figure out the inventory impacts. Note that the one day delay would increase pipeline inventory, but at these rates, LTL isn’t even close to being competitive.

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Question 2So now all we need to do is

translate 6.19 days of sales into units of each product. That’s pretty straightforward

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Question 3

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Question 3

If CubeOutpool = Openpool = 1, then this constraint ensures there is enough demand in cubic feet at the pool to fill a trailer within MaxTime.

In other words, this will ensure at least DaysPerYear/MaxTime

trucks will be needed to carry the cubic volume of demand.

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Question 3

If CubeOutpool = 0 & Openpool = 1, then this constraint ensures there is enough demand in lbs at the pool to fill a trailer within MaxTime.

In other words, this will ensure at least DaysPerYear/MaxTime

trucks will be needed to carry the weight of demand.

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Question 4

• This is a poor analysis because it fails to consider inbound transportation costs to the inventory locations and, since the modes for inbound and outbound transportation are the same, the unit cost of transportation on this leg is just as large as the unit cost for outbound shipments.

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Question 4

• In addition, every unit shipped from an inventory location has to get shipped to that inventory location so the volume on this leg is equal to the sum of the volumes on the outbound legs. Those factors will pull the ideal inventory positions toward the ports.

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Question 4

• Finally, handling considerations will drive us to want to hold the inventories at the ports if possible: A major cost in moving items this large is the cost of loading and unloading the vehicle. If we can hold inventory at the port we can eliminate these costs.

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Results

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Summary

Average: 53Std. Dev: 19Grades? It’s all relativeRough Indication< 20 or so, we have a problem< 40 something C, say 45< 60 something B, say 65What to do?1. Study with a group2. Be sure to do several practice exams 3. Expectation that you are digging into the recommended

reading, reviewing and deciphering lecture notes, …

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Summary

Do a great job on the project!