Quiz Number 2Group 1 – North of Newark

Thamer AbuDiakReynald Benoit

Jose LopezRosele LynnDave Neal

Deyanira Pena

Professor Kenneth D. LawerenceNew Jersey Inst. Of Tech

MIS 680

Problems Assigned Ragsdale/ Dielman

Problems Done By: Thamer AbuDiak

5-7/4-11 Reynald Benoit

5-13, 6-18 / 4-1 Jose Lopez

6-6/4-5,5-1 Rosele Lynn

5-10,6-15 Dave Neal

5-16, 6-9 Deyanira Pena

5-19 and 6-12

Ragsdale 5-7 by Thamer

1

2 4

3 5

$63,985

$67,824$60,363

First contract cost

Two computer leases are available for Comp-Trail:Two computer leases are available for Comp-Trail:Company 1:Company 1:

$62,000 initial cost$62,000 initial costPrice of equipment increases by 6% every yearPrice of equipment increases by 6% every yearTrade in credit:Trade in credit:

60% after 1 year.60% after 1 year.15% after 2 years.15% after 2 years.

$2,000 Labor cost whenever equipment needs to be replaced.$2,000 Labor cost whenever equipment needs to be replaced.Company 2:Company 2:

$62,000 initial cost$62,000 initial costPrice of equipment increases by 2% every yearPrice of equipment increases by 2% every yearTrade in credit:Trade in credit:

10% after 2 years.10% after 2 years.30% after 1 year.30% after 1 year.

$2,000 Labor cost whenever equipment needs to be replaced$2,000 Labor cost whenever equipment needs to be replaced

Ragsdale 5-7 by Thamer Set up

Decision Variable X12: cost of equipment if purchased the 1st year and replaced the 2nd year. X13: cost of equipment if purchased the 1st year and replaced the 3rd year. X23: cost of equipment if purchased the 2nd year and replaced the 3rd year. X24: cost of equipment if purchased the 2nd year and replaced the 4th year. X34: cost of equipment if purchased the 3rd year and replaced the 4th year. X35: cost of equipment if purchased the 3rd year and replaced the 5th year. X45: cost of equipment if purchased the 4th year and replaced the 5th year. C1-7: Constants.

Objective Function Min: C1*(X12+2000)+ C2*(X13+2000) + C3*(X23+2000) + C4*(X24+2000) +C5*(X34+2000) + C6*(X35+2000)

+ C7*(X45+2000) Constraints

C1-C7 = 0,1. - X12 – X13 = -1 } Flow constraint for node 1. X12 – X23 – X24 = 0 } Flow constraint for node 2. X12 + X13 – X34 – X35 = 0 } Flow constraint for node 3. X24 + X34 + X45 = 0 } Flow constraint for node 4. X35 + X45 = +1 } Flow constraint for node

5.

Cost of the first contract

Cost of the second contract

Ragsdale 5-7 by ThamerInitial Solution Second contract

is $5,799 cheaper than the first one

Cost of the first contract after revision

Cost of the second contract after revision

Ragsdale 5-7 by ThamerRevised Solution

Second contract is $9,799 cheaper than the first one

Solver

Ragsdale 5-7 by Thamer Conclusion

The additional $2,000 in labor cost increases the price of the first lease by $8,000 and the second lease by $4,000. The decision of what year to change computers

remains the same. Lease 2 remains cheaper than Lease 1.

The second contract remains more optimal financially.

Ragsdale 5-13 by Reynald

Statesboro1

Brooklet2

Claxton 3

Millen4

Hinesville5

Claxton6

Millen7

Savanah8

Perry9

Valdosta10

-700

-500

-24

-23

.5

-25.5

-25

-.5

-10

-11

Max 700Min 350

Max 600Min 300

50

44

45

48

42

43

400

300

450

Ragsdale 5-13 by Reynald Set up

Decision Variable Xij: tons of products flowing from node i to j

Objective Function Min: -24X13 - 23X14 - .5X15 - 25.5X23 - 25X24 +.5X25 - 10X36 - 11X47 + 50X68 + 44X69 +

45X610 + 48X78 + 42X79 + 43X710

Constraints X13 + X14 + X15 <= 700 X23 - X24 + X25 <= 500 X13 + X23 - X68 - X69 - X610 >= 0 X14 + X24 - X78 - X79 - X710 >= 0 350 <= X13 + X23 <= 700 300 <= X14 + X24 <= 600 X68 + X78 = 400 X69 + X79 = 300 X610 + X710= 450

Ragsdale 5-13 by Reynald Excel

Ragsdale 5-13 by Reynald Conclusion

The cotton grower should ship 250 from Statesboro to Claxton 450 from Statesboro to Millen 450 from Brooklet to Claxton 250 from Claxton to Savannah 450 from Claxton to Valdosta 150 from Millen to Savannah 300 from Millen to Perry Total Profit = 12,775

Ragsdale 5-16 by Dave Neal

A company has 3 warehouses that supply 4 stores with a given product.

Each warehouse has 30 units of the product (Total Supply = 90 units).

Stores 1,2,3,4 require 20,25,30,35 units respectively (Total Demand = 110 units).

PROBLEM: Determine least expensive shipping plan to fill store demand.

Ragsdale 5-16 by Dave Neal

Ragsdale 5-16 by Dave Neal Initial Problem Set-Up

Type of Problem: Transportation Objective Function: Minimize Shipping Cost

MIN: 5 X11 + 4 X12 + 6 X13 + 5 X14 + 3 X21 + 6 X22 + 4 X23 + 4 X24 +

4 X31 + 3 X32 + 3 X33 + 2 X34 Constraints:

-X11 - X12 - X13 - X14 = -30 -X21 - X22 - X23 - X24 = -30 -X31 - X32 - X33 - X34 = -30 +X11 + X21 + X31 <= +20 +X12 + X22 + X32 <= +25 +X13 + X23+ X33 <= +30 +X14 + X24+ X34 <= +35 Xij >= 0

NOTE: SUPPLY < DEMAND: 90 < 110 For minimum cost network flow problems where total supply<total demand,

apply this balance-of-flow rule at each node: Inflow-Outflow<=Supply or Demand.

Ragsdale 5-16 by Dave Neal Initial Excel Settings

Ragsdale 5-16 by Dave Neal Results

Ragsdale 5-16 by Dave Neal Revised Excel Settings

No shipments between warehouse 1, store 2 and warehouse 2, store 3.

Added 2 constraints to solve the modified problem. X12, X23 = 0

Ragsdale 5-16 by Dave Neal Revised Results

Ragsdale Chap 5-19 by Deyanira Pena

Net flow

Toulon3

Doha1

Port6

Suez 5

Damietta7

Rotterdam2

Palermo4

+15

+15

+6

+9

--30

$.16

$.35

$.20

$.15

$1.35$.19 $.25

$.23

$.20 $1.40

$1.20

$.27

Ragsdale Chap 5-19 by Deyanira Pena Lp Model

 Xij = the number of barrels shipped from node i to node j   X12 = the number of barrels shipped from node 1(Doha) to node 2 (Rotterdam) X13 the number of barrels shipped from node 1(Doha) to node 3 (Toulon) X14 the number of barrels shipped from node 1(Doha) to node 4 (Palermo) X15 the number of barrels shipped from node 1(Doha) to node 5(Suez) X56 the number of barrels shipped from node 5(Suez) to node 6 (Port) X57 the number of barrels shipped from node 5(Suez) to node 7(Damietta) X62 the number of barrels shipped from node 6(Port) to node 2 (Rotterdam)

Ragsdale Chap 5-19 by Deyanira Pena Lp Model Cont.

X63 the number of barrels shipped from node 6 (Port) to node 3 (Toulon) X64 the number of barrels shipped from node 6(Port) to node 4 (Palermo) X72 the number of barrels shipped from node 7(Damietta) to node 2 (Rotterdam) X73 the number of barrels shipped from node 7(Damietta) to node 3 (Toulon) X74 the number of barrels shipped from node 7(Damietta) to node 4 (Palermo)

Min: + 1.20X12 + 1.40X13 + 1.35X14 + .20X56 + .27X62 + .23X63 + .19X64 + .35X15 + .16X57 + .25X72+ .20X73 + .15X74  

Ragsdale Chap 5-19 by Deyanira Pena Lp Model Cont.

Constraints

 

Subject To

 

-         X12 - X13 -X14 >= -3000000

+ X12 + X13 + X14 >= 2500000

- X15 + X56 + X62 >= 6000000

- X15 + X56 + X63 >= 1500000

- X15 + X56 + X62 >= 9000000

- X15 – X57 + X72 + X73 + X74 >= 15000000

Ragsdale Chap 5-19 by Deyanira Pena Spreadsheet

Conch Oil Company

Ship From To Unit Cost Nodes Net Flow Supply/Demand in millions

1 Doha 2 Rotterdam 1.20$ 1 Doha 0 -150000001 Doha 3 Toulon 1.40$ 2 Rotterdam 0 60000001 Doha 4 Palermo 1.35$ 3 Toulon 0 150000001 Doha 5 Suez 0.35$ 4 Palermo 0 90000005 Suez 6 Port 0.20$ 5 Suez 0 -150000005 Suez 7 Damietta 0.16$ 6 Port 0 06 Port 2 Rotterdam 0.27$ 7 Damietta 0 06 Port 3 Toulon 0.23$ 6 Port 4 Palermo 0.19$ 7 Damietta 2 Rotterdam 0.25$ 7 Damietta 3 Toulon 0.20$ 7 Damietta 4 Palermo 0.15$

Total Transportation Cost

Ragsdale Chap 5-19 by Deyanira Pena Optimal Solution

Conch Oil Company

Ship From To Unit Cost Nodes Net Flow Supply/Demand in millions

2500000 1 Doha 2 Rotterdam 1.20$ 1 Doha -15000000 -150000002500000 1 Doha 3 Toulon 1.40$ 2 Rotterdam 6000000 60000002500000 1 Doha 4 Palermo 1.35$ 3 Toulon 15000000 150000007500000 1 Doha 5 Suez 0.35$ 4 Palermo 9000000 9000000

0 5 Suez 6 Port 0.20$ 5 Suez -15000000 -1500000022500000 5 Suez 7 Damietta 0.16$ 6 Port 0 0

0 6 Port 2 Rotterdam 0.27$ 7 Damietta 0 00 6 Port 3 Toulon 0.23$ 0 6 Port 4 Palermo 0.19$

3500000 7 Damietta 2 Rotterdam 0.25$ 12500000 7 Damietta 3 Toulon 0.20$ 6500000 7 Damietta 4 Palermo 0.15$

20,450,000.00$ Total Transportation Cost

Ragsdale 6-9 by Dave Neal

Health Care Systems of Florida planning to build emergency-care clinics.

Management divided area into 7 regions. All 7 regions must be served by at least 1 of the 5

possible facility sites. PROBLEM: Determine which sites to select that will

result in the least cost while providing convenient service to all locations.

Ragsdale 6-9 by Dave Neal Initial Problem Set-Up

Type of Problem: Integer Linear Programming Model / Capital Budgeting Problem Objective Function: Minimize cost while providing convenient service to all locations.

MIN: 450X1 + 650X2 + 550X3 + 500X4 + 525X5 Constraints: X1 + X3 >= 1 X1 + X2 + X4 + X5 >= 1 X2 +X4 > = 1 X3 +X5 > = 1 X1 +X2 > = 1 X3 +X5 > = 1 X4 +X5 > = 1 Xi must be BINARY, i = 1,2,3,4,5 Xi = 1, if building site i is selected Xi = 0, otherwise

Ragsdale 6-9 by Dave Neal Initial Excel Settings

Ragsdale 6-9 by Dave Neal

Ragsdale Chap 6-12 by Deyanira Pena

Xi= { 1,if investment I is selected i= 1,2,…,5 0,otherwise

Max :30X1 + 30X2 +30X3+ 30X4+ 30X5 Subject to:35X1 + 16X2 +125X3+ 25X4+40X5 + 5X6 30 } year 1 investment value

37X1 + 17X2 +130X3+ 27X4+43X5 + 7X6 30 } year 2 investment value

39X1 + 18X2 +136X3+ 29X4+46X5 + 8X6 30 } year 3 investment value

42X1+19X2 +139X3+ 30X4+50X5 +10X6 30 } year 4 investment value

45X1 +20X2 +144X3+ 33X4+52X5 + 11X6 30 } year 5 investment value

Ragsdale Chap 6-12 by Deyanira PenaSpreadsheet Model

Select?Investment (0=no, 1=yes) NPV Year 1 Year 2 Year 3 Year 4 Year 5

Car 1 0 30$ 35$ 37$ 39$ 42$ 45$ Piano 2 0 30$ 16$ 17$ 18$ 19$ 20$ Necklace 3 0 30$ 125$ 130$ 136$ 139$ 144$ Desk 4 0 30$ 25$ 27$ 29$ 30$ 33$ Golf Clubs 5 0 30$ 40$ 43$ 46$ 50$ 52$ Humidor 6 0 30$ 5$ 7$ 8$ 10$ 11$

Capital Asserts Worth 0 0 0 0 0Capital required 30$ 30$ 30$ 30$ 30$

Total Net Present Value -$

Teenage Investments

Ragsdale Chap 6-12 by Deyanira Penaoptimal solution

Select?Investment (0=no, 1=yes) NPV Year 1 Year 2 Year 3 Year 4 Year 5

Car 1 1 30$ 35$ 37$ 39$ 42$ 45$ Piano 2 1 30$ 16$ 17$ 18$ 19$ 20$ Necklace 3 1 30$ 125$ 130$ 136$ 139$ 144$ Desk 4 1 30$ 25$ 27$ 29$ 30$ 33$ Golf Clubs 5 1 30$ 40$ 43$ 46$ 50$ 52$ Humidor 6 1 30$ 5$ 7$ 8$ 10$ 11$

Capital Asserts Worth 246 261 276 290 305Capital required 30$ 30$ 30$ 30$ 30$

Total Net Present Value 180.00$

Teenage Investments

Ragsdale 6-15 by Rosele Lynn

Problem: Where should a manufacturer build its new plants if it wants to be closer to its main supply

customers X,Y,Z?

Decision variables: Of the 5 alternative plants, which plants should the manufacturer build?

P1= plant 1, 1 is selected, 0 if it is not selected

P2=plant 2, 1 is selected, 0 if it is not selected

P3=plant 3, 1 is selected, 0 if it is not selected

P4=plant 4, 1 is selected, 0 if it is not selected

P5=plant 5, 1 is selected, 0 if it is not selected

Ragsdale 6-15 by Rosele Lynn

Objective Function: Which plant should be built in order to satisfy customer demand at a minimum cost?

MIN: 35 P1X + 30 P1Y + 45 P1Z + 45 P2X + 40 P2Y + 50 P2Z + 70 P3X + 65 P3Y + 50 P3Z + 20 P4X + 45 P4Y + 25 P4Z + 65 P5X + 45 P5Y + 45 P5Z + 1000*(1,325 Y1 + 1,100 Y2 + 1,500 Y3 + 1,200 Y4 + 1,400 Y5)

Constraints:

Decision to build is Binary, Yi = binary

Production Capacity for Plants 1,2,3,4,5 are as follows:

P1X + P1Y + P1Z < 40,000 Y1P2X + P2Y + P2Z <30,000 Y2P3X + P3Y + P3Z < 50,000 Y3P4X + P4Y + P4Z <20,000 Y4P5X + P5Y + P5Z <40,000 Y5

Expected Demand: 40,000 from Customer X, 25,000 from Customer Y, 35,000 from Customer ZP1X + P2X + P3X + P4X + P5X > 40,000P1Y + P2Y + P3Y + P4Y + P5Y >25,000P1Z + P2Z + P3Z + P4Z + P5Z >35,000

Ragsdale 6-15 by Rosele Lynn

Ragsdale 6-15 by Rosele Lynn Solver Parameters

The optimal solution is to build plant 1, 4, and 5. Here all constraints are satisfied and the binary is 1 (yes, to build).

Ragsdale 6-15 by Rosele Lynn

Plant Location Problem

Ragsdale 6-18 by Reynald Decision Variables

X1 = the barrels to buy from TX X2 = the barrels to buy from OK X3 = the barrels to buy from PA X4 = the barrels to buy from AL Y1,Y2,Y3,Y4 = 1 if X >0 and 0 otherwise

Objective Function 22X1 + 21X2 + 22X3 + 24X4 + 1500Y1 + 1700Y2 + 1500Y3 + 1400Y4

Constraints Numbers to be produced 2X11 + 1.8X21 + 2.3X31 + 2.1X41 >= 750 2.8X12 + 2.3X22 + 2.2X32 + 2.6X42 >= 800 1.70X13 + 1.75X23 + 1.6X33 + 1.9X43 >= 1000 2.4X14 + 1.90X24 + 2.6X34 + 2.4X44 >= 300

Ragsdale 6-18 by Reynald

Constraints (cont’) Minimum required X1 – 500Y1 >= 0 X2 – 500Y2 >= 0 X3 – 500Y3 >= 0 X4 – 500Y4 >= 0 Maximum X1 – 1500Y1 <= 0 X2 – 2000Y2 <=0 X3 – 1500Y3 <= 0 X4 – 1800Y4 <=0

Ragsdale 6-18 by Reynald Excel

Ragsdale 6-18 by Reynald Solver

Ragsdale 6-18 by Reynald Conclusion

The company should purchase 1316 barrels from Alabama.

The total cost will be $31,671

Dielman 4-1 by ReynaldVar Coe Std Dev T stat P val

Inter 51.72 21.70 2.38 0.026

Paper 0.95 0.12 7.90 0.000

Mach 2.47 0.47 5.31 0.000

Over 0.05 0.53 0.09 0.92

Labor -0.05 0.04 -1.26 0.223

Standard Error = 11.0756; R-Sq = 99.9%; R-Sq(avg) = 99.9%

source DF Sum Sq Mean SQ F stat P val

Regression 4 2271423 567856 4629.17 0.000

Error 22 2699 123

Total 26 2274122

Analysis of Variance

Dielman 4-1 by Reynald Cont.

A) What is the equation? COST = 51.72 + 0.95Paper + 2.47Machine

+0.05Overhead – 0.05Labor B) Conduct an F test.

Decision Rule: Reject Ho if F> F(0.05; 4, 22) = 2.82 Test Stat: F = 4629.17 Reject Ho. At least one of the coefficients is not equal to zero

C) Find 95% confidence interval estimate 2.47, 2.47 +- ( 2.074 )( 0.47 )

D) Conduct two-tailed test procedure Critical Value: t(0.025, 22) = 2.074 Test Statistic: t = -0.42 Decision: Do not reject Ho. The true marginal cost is 1.

E) What percentage have been explained? 99.9% F) What is the adjusted R squared? 99.9% G) What action might be taken.

This information can be use to reduce cost. It shows the influence of one variable

The estimated Regression equation is: FUELCON = 916 - 218 DRIVERS - 0.00078 HWYMILES - 3.69

GASTAX - 0.00549 INCOME. Using a 5% level of significance.

Gas tax and drivers are the most significant factors in this regression model.

From the regression: S = 56.2806 R-Sq = 44.4% R-Sq(adj) = 39.6% PRESS = 190252 R-Sq(pred) = 27.40%

Income and Highway Miles appear to be unnecessary in the regression. Their factor is very insignificant in the equation and the model.

No Variables where omitted from the regression.

Dielman 4.11 by Thamer

Cont.Dielman 4.11 by Thamer

Regression