Quiz Number 2 Group 1 – North of Newark Thamer AbuDiak Reynald Benoit Jose Lopez Rosele Lynn Dave...
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Transcript of Quiz Number 2 Group 1 – North of Newark Thamer AbuDiak Reynald Benoit Jose Lopez Rosele Lynn Dave...
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