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Quiz Number 2

Quiz Number 2

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Quiz Number 2

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  1. Quiz Number 2 Group 1 – North of Newark Thamer AbuDiak Reynald Benoit Jose Lopez Rosele Lynn Dave Neal Deyanira Pena Professor Kenneth D. Lawerence New Jersey Inst. Of Tech MIS 680

  2. 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

  3. Ragsdale 5-7 by Thamer • Two computer leases are available for Comp-Trail: • Company 1: • $62,000 initial cost • Price of equipment increases by 6% every year • Trade in credit: • 60% after 1 year. • 15% after 2 years. • $2,000 Labor cost whenever equipment needs to be replaced. • Company 2: • $62,000 initial cost • Price of equipment increases by 2% every year • Trade in credit: • 10% after 2 years. • 30% after 1 year. • $2,000 Labor cost whenever equipment needs to be replaced • First contract cost

  4. 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.

  5. Ragsdale 5-7 by Thamer Initial Solution Second contract is $5,799 cheaper than the first one Cost of the first contract Cost of the second contract

  6. Ragsdale 5-7 by Thamer Revised Solution Second contract is $9,799 cheaper than the first one Cost of the first contract after revision Solver Cost of the second contract after revision

  7. 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.

  8. Ragsdale 5-13 by Reynald

  9. 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

  10. Ragsdale 5-13 by ReynaldExcel

  11. 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

  12. 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.

  13. Ragsdale 5-16 by Dave Neal

  14. 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.

  15. Ragsdale 5-16 by Dave Neal Initial Excel Settings

  16. Ragsdale 5-16 by Dave Neal Results

  17. 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

  18. Ragsdale 5-16 by Dave Neal Revised Results

  19. Ragsdale Chap 5-19 by Deyanira Pena Net flow Port 6 Toulon 3 $.23 +15 $.20 $1.40 $.20 Doha 1 - -30 $.27 Rotterdam 2 Suez 5 $.35 +15 $1.20 +6 $.16 $1.35 $.25 $.19 Damietta 7 Palermo 4 $.15 +9

  20. 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)

  21. 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

  22. 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

  23. Ragsdale Chap 5-19 by Deyanira Pena Spreadsheet

  24. Ragsdale Chap 5-19 by Deyanira Pena Optimal Solution

  25. 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.

  26. 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

  27. Ragsdale 6-9 by Dave Neal Initial Excel Settings

  28. Ragsdale 6-9 by Dave Neal

  29. 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

  30. Ragsdale Chap 6-12 by Deyanira PenaSpreadsheet Model

  31. Ragsdale Chap 6-12 by Deyanira Penaoptimal solution

  32. Ragsdale 6-15 by Rosele Lynn 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 Problem: Where should a manufacturer build its new plants if it wants to be closer to its main supply customers X,Y,Z?

  33. 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 Y1 • P2X + P2Y + P2Z <30,000 Y2 • P3X + P3Y + P3Z < 50,000 Y3 • P4X + P4Y + P4Z <20,000 Y4 • P5X + P5Y + P5Z <40,000 Y5 • Expected Demand: 40,000 from Customer X, 25,000 from Customer Y, 35,000 from Customer Z • P1X + P2X + P3X + P4X + P5X > 40,000 • P1Y + P2Y + P3Y + P4Y + P5Y >25,000 • P1Z + P2Z + P3Z + P4Z + P5Z >35,000 Ragsdale 6-15 by Rosele Lynn

  34. Ragsdale 6-15 by Rosele Lynn

  35. Ragsdale 6-15 by Rosele Lynn Solver Parameters

  36. Ragsdale 6-15 by Rosele Lynn Plant Location Problem The optimal solution is to build plant 1, 4, and 5. Here all constraints are satisfied and the binary is 1 (yes, to build).

  37. 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

  38. 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

  39. Ragsdale 6-18 by Reynald Excel

  40. Ragsdale 6-18 by Reynald Solver

  41. Ragsdale 6-18 by Reynald Conclusion • The company should purchase 1316 barrels from Alabama. • The total cost will be $31,671

  42. Dielman 4-1 by Reynald Standard Error = 11.0756; R-Sq = 99.9%; R-Sq(avg) = 99.9% Analysis of Variance

  43. 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

  44. Dielman 4.11 by Thamer • 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.

  45. Regression Cont.Dielman 4.11 by Thamer