ANA Steel CorporationMANAGING LOGISTICS VIA INTEGER LINEAR PROGRAMMINGBYALEX MIDENCENIKOLE CUNNINGHAMASHLEY MAGEE

MENTOR: RAIDA ABUIZAM, PH.D.

Learning Objectives

Use network diagrams to represent the problem graphically. The graphic presentation will be used in developing the spreadsheet model.

Take care of fixed costs by using binary variables (0,1). Because fixed costs are not a linear function, the use of binary variables will convert a non-linear model into a linear model.

Develop a spreadsheet model to minimize total cost without having to formulate the problem algebraically.

Case Overview

ANA Steel Corporation is a growing plate steel manufacturing company. The company wants to expand to four production and warehouse locations throughout the United States due to customer demand.

The CEO of ANA Steel Corp. would like to know the most cost efficient way to get the product from the plants to the customers. The possible plant locations are in Alabama, Indiana, Ohio and Missouri.

Case Overview Continued

Table 1: Plant Information

State Fixed Cost/ Year

Production Capacity tons/

YearAlabama $96,000,000 3,000,000Indiana $80,000,000 2,500,000Ohio $33,600,000 1,050,000Missouri $24,000,000 700,000

Case Overview Continued

ANA Steel Corporation determined that there are four potential warehouse locations to be used as distribution channels. When deciding warehouse locations, we researched fixed costs along with their storage capacities as shown in Table 2. The four prospective warehouse locations are Texas, Georgia, Illinois, and California. Table 2: Warehouse Information

State Fixed Cost/ Year Storage Capacity (tons/yr)

Texas $563,250 1,345,000Georgia $450,600 1,336,000Illinois $450,600 2,236,000

California $585,780 2,246,800

Case Overview Continued

ANA had found the estimated yearly demand for their product and listed their outcomes in Table 3. Table 3: Customer Demand

State Yearly Demand (tons)Texas 92,800

California 518,400Georgia 817,600Illinois 351,200

South Carolina 584,000Pennsylvania 584,000

Michigan 525,000Tennessee 116,800

Iowa 525,600Arkansas 525,600

Case Overview Continued

ANA projected transportation costs from each plant to warehouse and from each warehouse to customer. Their findings are recorded in tables 4 and 5, respectively. Table 4: Transportation costs per ton from plants to warehouses

Texas Georgia Illinois CaliforniaAlabama $1,651 $231 $832 $2,671Indiana $2,019 $1,136 $2,442 $1,969

Ohio $1,093 $875 $2,672 $2,119Missouri $1,235 $2,025 $990 $781

Case Overview Continued

Table 5: Transportation cost per ton from warehouse to customers

Texas California

Georgia

Illinois South Carolina

Pennsylvania

Michigan Tennessee

Iowa Arkansas

Texas $251 $2,427 $1,576

$1,503

$1,757 $2,453 $2,143 $1,353 $1,473 $848

Georgia $1,505 $3,452 $225 $1,031

$306 $1,209 $1,370 $332 $1,359 $744

Illinois $1,533 $3,145 $1,383

$307 $1,373 $1,206 $699 $859 $315 $804

California

$2,198 $605 $3,652

$2,886

$3,720 $3,788 $3,333 $3,244 $2,556 $2,751

Statement of Problem

Which plants to keep open and which warehouses to ship plate steel from in order to meet customer demand in the most cost efficient manner.

Network Diagram

IN

OH

MO

TX

AR

IA

TN

MI

PA

SC

IL

GA

CA

TX

GA

IL

CA

AL

Plants Warehouses

Customers

Requirement SolutionSpreadsheet Model

Development

Record all of the inputs into the spreadsheet:WarehousesTexas Georgia Illinois California Plants Capacity Fixed cost

Plants Alabama $1,651 $231 $832 $2,671 3,000,000 $96,000,000Indiana $2,019 $1,136 $2,442 $1,969 2,500,000 $80,000,000Ohio $1,093 $875 $2,672 $2,119 1,050,000 $33,600,000Missouri $1,235 $2,025 $990 $781 700,000 $24,000,000

7,250,000

WarehousesTexas Georgia Illinois California Demand

Texas $251 $1,505 $1,533 $2,198 92,800 California $2,427 $3,452 $3,145 $605 518,400 Georgia $1,576 $225 $1,383 $3,652 817,600 Illinois $1,503 $1,031 $307 $2,886 351,200

Customers South Carolina $1,757 $306 $1,373 $3,720 584,000 Pennsylvania $2,453 $1,209 $1,206 $3,788 584,000 Michigan $2,143 $1,370 $699 $3,333 525,600 Tennessee $1,353 $332 $859 $3,244 116,800 Iowa $1,473 $1,359 $315 $2,556 116,800 Arkansas $848 $744 $804 $2,751 525,600

4,232,800Texas Georgia Illinois California

Fixed Cost $563,250 $450,600 $450,600 $585,780

WHSE Capacity 1,345,000 1,336,000 2,236,000 2,246,800 7,163,800

Spreadsheet Model Development

The model should display each of the following: The quantity in tons that should be shipped from warehouses to customers. Fixed costs in US dollars of the operating plants and warehouses chosen to

be kept open Shipping costs from plants to warehouses and subsequently from

warehouses to customers Quantity in tons received by each open warehouse should equal the

quantity shipped out of each warehouse. No excess quantities should be kept at any warehouse

The quantity in tons that should be shipped from plants to warehouses Total amount shipped to customers from open warehouses should equal

customers’ demand

Solution

ANA linear programming model.xlsx

Texas Georgia Illinois California Plants Capacity Fixed cost Use Plant?Alabama $1,651 $231 $832 $2,671 3,000,000 $96,000,000 1Indiana $2,019 $1,136 $2,442 $1,969 2,500,000 $80,000,000 0Ohio $1,093 $875 $2,672 $2,119 1,050,000 $33,600,000 1Missouri $1,235 $2,025 $990 $781 700,000 $24,000,000 1

7,250,000Texas Georgia Illinois California Out of PLNTS Plant Capacity

Alabama - 1,336,000 1,664,000 - 3,000,000 <= 3,000,000Indiana - - - - 0 <= 0Ohio 532,800 - - - 532,800 <= 1,050,000Missouri - - 181,600 518,400 700,000 <= 700,000Into WHSE 532,800 1,336,000 1,845,600 518,400

<= <= <= <=WHSE Capacity 1,345,000 1,336,000 2,236,000 2,246,800

Texas Georgia Illinois CaliforniaTexas $251 $1,505 $1,533 $2,198California $2,427 $3,452 $3,145 $605Georgia $1,576 $225 $1,383 $3,652Illinois $1,503 $1,031 $307 $2,886South Carolina $1,757 $306 $1,373 $3,720Pennsylvania $2,453 $1,209 $1,206 $3,788Michigan $2,143 $1,370 $699 $3,333Tennessee $1,353 $332 $859 $3,244

Iowa $1,473 $1,359 $315 $2,556Arkansas $848 $744 $804 $2,751

Texas Georgia Illinois CaliforniaFixed Cost $563,250 $450,600 $450,600 $585,780

WHSE Capacity 1,345,000 1,336,000 2,236,000 2,246,800 7,163,800

Use WHSE? 1 1 1 1Out to CUST Demand

Texas 92,800 - - - 92,800 >= 92,800 California - - - 518,400 518,400 >= 518,400 Georgia - 817,600 - - 817,600 >= 817,600 Illinois - - 351,200 - 351,200 >= 351,200 South Carolina - 518,400 65,600 - 584,000 >= 584,000 Pennsylvania - - 584,000 - 584,000 >= 584,000 Michigan - - 525,600 - 525,600 >= 525,600 Tennessee - - 116,800 - 116,800 >= 116,800 Iowa - - 116,800 - 116,800 >= 116,800 Arkansas 440,000 - 85,600 - 525,600 >= 525,600 Going from WHSE to CUST 532,800 1,336,000 1,845,600 518,400 4,232,800

= = = =Coming into WHSE 532,800 1,336,000 1,845,600 518,400

CostsFixed costs PLNTS 153,600,000.00$ Fixed costs WHSE 2,050,230.00$ Transport PLNTS to WHSE 2,858,211,600.00$ Transport WHSE to CUST 2,527,951,840.00$

Total Cost 5,541,813,670.00$

Warehouses

Plan

ts

Warehouses

Cust

omer

s

Solution ContinuedSolution Network Diagram

This model solved for:

AL

IN

OH

MO

TX

GA

IL

CA

TX

CA

GA

IL

SC

PA

MI

TN

IA

AR

Plants Warehouses

Customers

1,336,000

1,664,000

532,800

181,600

518,400

92,800

440,000

817,600

518,400

351,200

65,600

584,000

525,600

116,800

116,800

85,600

518,400

Interpretation of Solver Solution

In generating a solution for minimal costs, Solver determined that only three of the four plants needs to be open for manufacturing. The binary variables (0,1) informed us NOT to open the Indiana plant and to proceed using each of the four warehouses. Also, instead of each warehouse distributing to each customer, it is actually more economical for each warehouse to ship product to a select amount of customers. This led to the Illinois warehouse distributing to the most customers.

ThankYou

Resources

http://www.freightcenter.com/freight/rail-freight.aspx http://www.alibaba.com/showroom/steel-plate-price-per-ton.html http://worldfreightrates.com/freight# http://www.flatbedsource.com/truckload-market-price-index/ http://minerals.usgs.gov/minerals/pubs/commodity/iron_&_steel/mcs-2015-feste.pdf https://www.steel.org/~/media/Files/AISI/Reports/AISI_Profile_14_FINAL.pdf http://www.statista.com/statistics/268683/us-steel-demand-since-2008/