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6203Exam #1Review

John H. Vande Vate

Spring, 2001

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Max the Minset Towns; /* The townships */

param X{Towns}; /* The X coordinate of each town’s location */

param Y{Towns}; /* The Y coordinate of each town’s location */

param MaxX;

param MinX;

param MaxY;

param MinY;

var Xloc >= MinX, <= MaxX; /* X coordinate of landfill */

var Yloc >= MinY, <= MaxY; /* Y coordinate of landfill */

var Xdist{Towns} >= 0; /* East-West distance to each town */

var Ydist{Towns} >= 0; /* North-South distance to each town */

var IsEast{Towns} binary; /* Whether landfill is east or not */

var IsNorth{Towns} binary; /* Whether landfill is north or not */

var MinDist >= 0; /* Distance to closest town */

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ConstraintsMax MinimumDistance: MinDist;

s.t. DefineMin{t in Towns}:

MinDist <= Xdist[t] + Ydist[t];

s.t. DefineXDistEast{t in Towns}:

Xdist[t] <= Xloc - X[t] +(1-IsEast[t])*(MaxX-MinX+X[t])

s.t. DefineXDistWest{t in Towns}:

Xdist[t] <= X[t] - Xloc +IsEast[t]*(2*MaxX-X[t])

s.t. DefineYDistNorth{t in Towns}:

Ydist[t] <= Yloc - Y[t] +(1-IsNorth[t])*(MaxY-MinY+Y[t])

s.t. DefineYDistSouth{t in Towns}:

Ydist[t] <= Y[t] - Yloc +IsNorth[t]*(2*MaxY-Y[t])

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Explanation

• IsEast[t] = 1 if Landfill is East of Town Xloc >= X[t]

• IsNorth[t] = 1 if Landfill is North of Town Yloc >= Y[t]

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So….

• We might add the constraints...

s.t. DefineEast{t in Towns}:

(MaxX - X[t])*IsEast[t] >= Xloc - X[t]

s.t. DefineNorth{t in Towns}:

(MaxY - Y[t])*IsNorth[t] >= Yloc - Y[t]

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Common Mistakes

var IsEast binary;

s.t. DefineXDistWest{t in Towns}:

Xdist[t] <= X[t] - Xloc +IsEast*(2*MaxX-X[t])

What’s wrong?

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Common Mistakesvar Xdist >= 0;

var Ydist >= 0;

max MinimumDistance: Xdist + Ydist;

s.t. DefineXDistWest{t in Towns}:

Xdist <= X[t] - Xloc +IsEast[t]*(2*MaxX-X[t]);

…

s.t. DefineYDistSouth{t in Towns}:

Ydist <= Y[t] - Yloc +IsNorth[t]*(2*MaxY-Y[t]);

What’s wrong?

88

Discussion

• Put aside personal “investment” in answers

• Clarify issues

• Do not argue, discuss

• Be brief. Think, then talk.

• Imagine this is a business meeting

99

BMWBMW ships Z3’s from Greer, S.C. to meet EMEA demand.

BMW delivers the vehicles by truck to the port of Savannah.

Each Friday the vehicles are loaded on a vessel

The vessel takes all the cars available at the time of departure.

Demand is relatively constant at 500/week and 25,000/year.

Each Z3 represents $35,000 in revenue when it is sold.

BMW uses an inventory carrying charge of 15% per year.

Can deliver vehicles up to 12 at a fixed cost of $1,200 per trip

How many vehicles should BMW ship to Savannah on each car hauler to balance the costs of transportation and inventory?

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Follow-up

How would your answer change (specifically) if BMW were to sell the vehicles to a trading company and realize revenue of $30,000 per car when the cars arrive in Savannah?

How many vehicles should BMW ship to Savannah on each car hauler to balance the costs of transportation and inventory?

1111

EOQ

• Annual Transportation Cost ($/year)– $/trip*(vehicles/year)/(vehicles/trip)

– 1200*25000/Q

• Annual Inventory Cost ($/year)– (%/year)*($/vehicle)*(Avg. vehicles in Inv.)

• Avg. vehicles in Inv. – At Greer:

– In Savannah:

– In Pipeline:

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Formula for EOQ• 1200*25000/Q + 0.15*30000*Q/2

• Q* = 2*1200*25000/4,500

= 2*12*25000/45

= 2*12*5000/9

= 4*3*10000/9

= 2003/3

= 200/3

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Common Misunderstanding:115 = 9*12 + 7!!!

Real Meaning: Send 12

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Other Common Mistakes

• 1200*500/Q + 0.15*30000*Q/2

$/Week $/Year

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Fancy Stuff from Project 1

• E.g. P/(P+D)

• Is this relevant here?

• We are not trying to assess total inventory at the plant...

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MōtivaPetroleum products refiner and marketer. Convent Refinery outside Baton Rouge, LA Colonial Pipeline Distribution Center Deliver the products to customers

Mansfield and Eagle both charge for full truck load delivery to commercial accounts – Minimize the maximum distance– Minimize the sum of the distances– Minimize the total gallon-miles (distance*volume)– Maximize the minimum distance

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Mōtiva

Suppose Mōtiva purchased a gas station from a Retail operator. You would expect the average inventory levels at the gas station to go Up? Down? Stay the same?

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MōtivaThe product has an average value of $30/bbl

The facility distributes 12,000 barrels per day

Cost of capital of approximately 15%/year

What’s the total value of a policy that changed the way product is delivered via the pipeline to reduce the inventory levels at the distribution center to 2 days supply.

The proposed policy has no effect on refining operations or on the cost of conveyance through the pipeline.

It will simply change the frequency and size of extractions from the pipeline.

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What’s it Worth?

• $180,000 = .5 days * 12,000 bbls/day * $30/bbl• $27,000 = .15 * 180,000• $81,000 = 3 years * .15 * 180,000/year• $0

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Raw Score Distribution

2020

Re-Grading• Ambiguous issues• Lots of thought and effort• Happy to Re-grade but ONLY if you submit a

WRITTEN request– Turn in your exam with a neatly prepared document that

• identifies point you feel I graded incorrectly• outlines your thinking on the issue• indicates the grade you believe you should have received on the

item

• Only one chance. My decision final.

• Any oral argument and you lose that chance.

2121

Opportunity• Global Network Design for a major US

Retailer based in Mid-West

• 4,800 stores in US, Canada, Guam, PR, Costa Rica,…

• Moving into Latin America

• Manufacturing in China, Indonesia, Mexico, Florida, Brazil…

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Questions

• Where to source products?

• Which ports to use?

• Where to locate DC’s?

• Where to locate “pools” (cross docks)?

• Objective: Achieve stated service levels at minimum cost

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Project Plan

• Clarify data requirements and develop prototype models by early April

• Full-scale model running by early May

• Report to Executive Committee early June

• On-going support through September

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Opportunity• 2 Students

• Complete project as scheduled

• GRA for Summer (Academic credit as well)

• Great experience

• Qualifications:– ISyE MS Students– Computer Savvy– Good English – Willing to meet deadlines– >= 80 on Mid-Term

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E-mail me your Resume

• No Viruses!

• Relevant Experience

• GPA, etc.

• Career Goals

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Project #2 Comments• Real Estate will decide final locations• Don’t need a single monolithic model• AMPL has looping commands• Xpress and MPL can be called from VB or Excel, or

Access…• Due Date:

– March 27th – April 10 for Video students