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# AGBU ANLY & FORECASTING AGEC 622

Texas A&M

GPA 3.72

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This 17 page Study Guide was uploaded by Clifford Mertz on Wednesday October 21, 2015. The Study Guide belongs to AGEC 622 at Texas A&M University taught by Staff in Fall. Since its upload, it has received 64 views. For similar materials see /class/225922/agec-622-texas-a-m-university in Agricultural & Resource Econ at Texas A&M University.

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Date Created: 10/21/15

AGEC 622 Review Notes for Test 02102004 I Formulation of LP Problem V Pick a possible problem that a business might have to solve and formulate a LP model to solve it with following terms 0 Objective Function 0 Decision variables 0 Constraints V What kinds of information does the firm get from such a formulation and what type of data might they need I Assumptions of LP 0 Objective Function Appropriateness 0 Decision variable Appropriateness o Constraint Appropriateness o Proportionality o Additivity o Divisibility o Certainty l Violation ofthe LP Assumptions 0 State a case where each of the LP assumptions might be violatde in a specific LP problem Transportation Feeding Portfolio Integer Programming etc I Predictive setting vs Prescriptive setting I Read and Interpret LP results V Key questions 1 Where are the results 2 What are the values 3 What is the interpretation of each item in a business decision making 0 Objective function value Final value under target cell on answer report The max or min value a rm can get given the parameters and resource constraints 0 Decision Variable nal value column under adjustable cells on answer report The decision variable values that max or min its objective function valueihow much of each variable to employ 0 Shadow price Lagrange multiplier column on sensitivity report The change in the objective function value when one unit of resource is changed Economic meaning is marginal value of the resource 0 Reduced Cost Reduced gradient column on sensitivity report Reduced cost is the reduction in objective function value when one unit of a decision variable that is not in the solution is forced into solution 0 Non zero Zero variables Explain in terms of Decision variable Reduced cost 0 Binding Nonbinding constraints Explain in terms of Shadow price Slack I Basic LP Problems 1 Transportation 2 Diet Feed Mix Blending 3 Joint Product 4 Dissassembly l Portfolio Selection Including risk in LP problem 0 When do we need to incorporate risk in LP problem We face a situation in which parameters are not certain or risky Violate the assumption of certainty But we assume that we have historical probability distribution of parameters and that this is relevant to future decisions 0 Why do we need to incorporate risk in LP problem Generate a plan which is robust in face of the uncertainty yielding a good solution across the set of possible events not the best solution necessarily in any possible events o EV Model example 7 tradeoff of expected value and variance 0 What does RAP alteration yield l Integer Programming 0 When do we need Integer programming Decision variables are integer or binary Violate the assumption of divisz39 bility Lumpy Investments and fixed costs Logical Conditions 0 How can we handle the indivisibility problems in Excel Put constraints on decision variable integer or binary AGEC 622 Review Notes for Test 02102004 I Formulation of LP Problem V Pick a possible problem that a business might have to solve and formulate a LP model to solve it with following terms 0 Objective Function 0 Decision variables 0 Constraints V What kinds of information does the firm get from such a formulation and what type of data might they need I Assumptions of LP 0 Objective Function Appropriateness 0 Decision variable Appropriateness o Constraint Appropriateness o Proportionality o Additivity o Divisibility o Certainty l Violation ofthe LP Assumptions 0 State a case where each of the LP assumptions might be violatde in a specific LP problem Transportation Feeding Portfolio Integer Programming etc I Predictive setting vs Prescriptive setting I Read and Interpret LP results V Key questions 1 Where are the results 2 What are the values 3 What is the interpretation of each item in a business decision making 0 Objective function value Final value under target cell on answer report The max or min value a rm can get given the parameters and resource constraints 0 Decision Variable nal value column under adjustable cells on answer report The decision variable values that max or min its objective function valueihow much of each variable to employ 0 Shadow price Lagrange multiplier column on sensitivity report The change in the objective function value when one unit of resource is changed Economic meaning is marginal value of the resource 0 Reduced Cost Reduced gradient column on sensitivity report Reduced cost is the reduction in objective function value when one unit of a decision variable that is not in the solution is forced into solution 0 Non zero Zero variables Explain in terms of Decision variable Reduced cost 0 Binding Nonbinding constraints Explain in terms of Shadow price Slack I Basic LP Problems 1 Transportation 2 Diet Feed Mix Blending 3 Joint Product 4 Dissassembly l Portfolio Selection Including risk in LP problem 0 When do we need to incorporate risk in LP problem We face a situation in which parameters are not certain or risky Violate the assumption of certainty But we assume that we have historical probability distribution of parameters and that this is relevant to future decisions 0 Why do we need to incorporate risk in LP problem Generate a plan which is robust in face of the uncertainty yielding a good solution across the set of possible events not the best solution necessarily in any possible events o EV Model example 7 tradeoff of expected value and variance 0 What does RAP alteration yield l Integer Programming 0 When do we need Integer programming Decision variables are integer or binary Violate the assumption of divisz39 bility Lumpy Investments and fixed costs Logical Conditions 0 How can we handle the indivisibility problems in Excel Put constraints on decision variable integer or binary 1 N E 4 5 10 points Suppose you have the model x Agricultural Economics 622 Spring 2005 Midterm Exam on Math programming Topic 25 points Darius39s dairy is trying to gure out how to move milk to customers Darius operates two dairies Brenham and Stephenville and serves customers in 3 cities Houston Dallas and Austin In Brenham they have 200000 gallons available per day that costs 60 cents to produce while in Stephenville they have 500000 gallons available per day that costs 55 cents per gallon Their existing contracts are for 225000 in Austin 175000 in Houston and 250000 in Dallas In addition a potential client in College Station has offered to buy up to 50000 gallons at 1 per gallon Costs per gallon for milk movement from Brenham are 10 cents to Houston and Austin 7 cents to College Station and 13 cents to Dallas Costs per gallon for milk movement from Stephenville are 18 cents to Houston 12 cents to Austin 13 cents to College Station and 8 cents to Dallas Set up an LP model of this situation 15 points In the context of problem number 1 above state a small case where each of the assumptions of LP might be violated using no more than 23 sentences for each assumption 15 points Given the model Max c1 x1 c2x2 2 x1 4 x2 S 55 4 x1 x2 S 45 x1 x2 2 0 Suppose that over time c1 and c2 have been uncertain where the mean of c1 is 10 and the mean of c2 is 11 while the standard error of c1 is 4 the standard error of c2 is 5 and their correlation is 05 Set a model that considers the risk and returns and tell how you numerically solve it for different risk return possibilities note the covariance between c1 and c2 is the correlation times the product of the standard deviations 15 points Give an example of where you would use the LP in problem 1 in each of a a predictive setting and b a prescriptive setting Limit the answer for each to no more than 4 sentences Max 3 1 2 x2 10 Y 4 x2 50Y S 0 4 x1 x2 S 45 x1 x2 2 0 Y is 0 or 1 Explain the coefficients and function of the variable Y in this problem along with the constraint relating x2 and Y 6 20 points Given the following problem where the 0 rst two variables tell number of hogs to skin or scald in head the next 4 tell how to cut up disassemble the hogs in head the next 5 variables give products sold in number of skins or lbs for other products the last variable gives waste disposed of in lbs the rst equation is profits in the second equation is hogs available in number of head the next 5 equations balance products in number of skins and lbs for others the next to last equation gives waste to be disposed of in lbs the last equation limits labor in hours and the Excel solution below it a indicate where you nd the amount of each variable in the solution and provide a one sentence interpretation one would place on one nonzero and one zero variable b indicate where you nd the value of the shadow price for each constraint and provide a one sentence interpretation one would place on one of those shadow prices c indicate where you nd the value of the reduced costs for each variable not produced and provide a one sentence interpretation one would place on one of those reduced costs which is non zero d Tell what the objective function value is and give a one sentence interpretation one would place on that Skin Scald pilieiin pigegm pg pill Skins Harns Bacon sauesag FrailJet Weast Pro t 50 48 8 19 185 1 04 001 361 1 1 1 1 1 1 5 0 Skins 1 1 S 0 Ham 40 40 1 S 0 Bacon 20 30 1 S 0 Sausage 50 70 90 130 1 S 0 By product 30 50 50 40 30 1 S 0 Waste 40 40 40 40 1 0 Labor 6 4 25 3 2 22 7 5000 Plus all variables greater than or equal to zero The solution follows EXCEL answer sheet Target Cell Max Cell Name Original Value Final Value O18 50 132000 Adjustable Cells Cell Name Original Value Final Value B2 Skin 1 0 C2 Scald 0 1250 D2 Hog pattern 1 0 0 E2 Hog pattern 2 0 0 F2 Hog pattern 3 0 0 G2 Hog pattern 4 0 1250 H2 Skins 0 0 2 Hams 0 0 J 2 Bacon 0 0 K 2 Sausage 0 162500 L 2 By Product 0 75000 M2 Waste 0 50000 EXCEL sensitivity sheet Ad39ustable Cells Final Reduced Cell Name Value Cost B2 Skin 0 588 C2 Scald 1250 0 D2 Hog pattern 1 0 2500 E2 Hog pattern 2 0 6048 F2 Hog pattern 3 0 3858 G2 Hog pattern 4 1250 0 H2 Skins 0 0 2 Hams 0 0 J2 Bacon 0 0 K2 Sausage 162500 0 L2 By Product 75000 0 M2 Waste 50000 0 Constraints Final Shadow Cell Name Value Price O20 H0 5 for 51311 hter 0 1416 O21 Skins 0 8 O22 Ham 0 19 O23 Bacon 0 185 O24 Sausage 0 1 O25 BYPmd39JCt 0 04 O26 Waste 0 001 O27 Law 5000 264 Note this is 15 by 15 and does not imply the problem is that size Test Answers and Grading Key 1 LP model 25 points Darius39s dairy is trying to gure out how to move milk to customers Darius operates two dairies Brenham and Stephenville and serves customers in 3 cities Houston Dallas and Austin In Brenham they have 200000 gallons available per day that costs 60 cents to produce while in Stephenville they have 500000 gallons available per day that costs 55 cents per gallon Their existing contracts are for 225000 in Austin 175000 in Houston and 250000 in Dallas In addition a potential client in College Station has offered to buy up to 50000 gallons at 1 per gallon Costs per gallon for milk movement from Brenham are 10 cents to Houston and Austin 7 cents to College Station and 13 cents to Dallas Costs per gallon for milk movement from Stephenville are 18 cents to Houston 12 cents to Austin 13 cents to College Station and 8 cents to Dallas 0 Point allocation I Transport variables to existing cities 6 points I Objective function transport costs 3 points I Objective function production costs 2 points I Supply constraints 2 points I Demand constraints 3 points I Transport variables to college station 1 points I College station demand constraint 1 points I College station maX demand constraint 1 points I College station demand variable 2 points I nonnegativity 3 points Here we have explicit variables for production cost and demand Variant 1 g 5 2 2 2 2 5 5 39E g 2 2 2 2 E g g g g 395 a a q a a m 395 395 q 395 395 m 3913 m 5 mg g a g s g 2 g 2 cu 2 cu s a a a H 3 nu H 5 H o H cc 3 o 3 3 3 o 3 s 3 o 02 o m m E III lt2 III E m Q DC 0 to lt2 0 E m D m 0 Q 0 Objective 60 55 10 10 13 7 12 18 8 13 100 Brenham prod 1 E 200000 supply Stephenville 1 E 500000 prod supply Brenham supply 1 1 1 1 1 S 0 Stephenville 1 1 1 1 1 S 0 supply Austin Demand 1 1 2 225000 Houston 1 1 2 175000 Demand Dallas demand 1 1 2 250000 College Station 1 1 1 2 0 Max college 1 S 50000 station All variables are non negative Variant 2 Here we add production cost to transport cost and have a variable for demand 5 2 2 2 2 5 5 2 2 2 2 E E E E E E a a q a a m E E q E E m 3913 m 3 a 3 9 3 2 3 lt1o n lt12 q lt12 9 lt12 2 lt12 G51 5 G51 3 O N 3 O N E lt E E E Q E 8 2 lt 2 E 2 Q 2 8 E 8 Objective 70 70 73 67 67 73 63 68 100 Brenham prod 1 1 1 1 E 200000 supply StephenVille 1 1 1 1 E 500000 prod supply Brenham supply S 0 StephenVille S 0 supply Austin Demand 1 1 2 225000 Houston 1 1 2 175000 Demand Dallas demand 1 1 2 250000 College Station 1 1 1 2 0 Max college 1 S 50000 station Variant 3 Here we add production cost to transport cost and subtract cs price demand 5 2 2 2 2 5 2 2 2 2 E E E E E E a a q a a m E E s E E m 3 a 3 9 3 2 3 lt1o n lt12 q lt12 9 lt12 2 lt12 G51 3 O N 3 O N E lt E E E Q E 8 2 lt 2 E 2 Q 2 8 Objective 70 70 73 33 67 73 63 32 Brenham prod 1 1 1 1 E 200000 supply StephenVille 1 1 1 1 E 500000 prod supply Brenham supply S 0 StephenVille S 0 supply Austin Demand 1 1 2 225000 Houston 1 1 2 175000 Demand Dallas demand 1 1 2 250000 College Station 1 1 2 0 Max college 1 1 S 50000 station 2 Violation of LP assumptions 15 points 0 7 assumptions 2 points per each 0 1 point for showing up 1 Objective Function Appropriateness Obj Fn in the above case might not be the sole criteria for choosing the decision variables The rm might take the supply risk into account 2 Decision Variable Appropriateness We might have omitted major choice variables like buy milk from elsewhere 3 Constraint Appropriateness There might be any omitted restrictions such as transport capacity 4 Proportionality transport cost per unit shipped might be increasing or decreasing as the firm produces more 5 Additivity There might be interactions between shipping routes lower or adding to costs 6 Divisibility The rm might not be permitted to sell 4X4s or 2X4s in amounts smaller than one bundle 7 Certainty The supply might vary 15 points 3 Suppose that over time c1 and c2 have been uncertain where the mean ofcl is 10 and the mean of c2 is 11 while the standard error of c1 is 4 the standard error of c2 is 5 and their correlation is 05 Set a model that considers the risk and returns and tell how you numerically solve it for different risk return possibilities note the covariance between c1 and c2 is the correlation times the product of the standard deviations MaX 10 X1 11X2 iRAP k X SX 2 X1 4 X2 S 55 4 X1 X2 S 45 X1 X2 2 0 16 10 2 2 S X SX16X125X2210X1X2 K10 25 Vary RAP from 0 to larger values to get different risk return possibilities Obj eXpected values 2 points RAP and X SX 5 points Empirical Var covar matriX 2 points Use of RAF 6 points uh Integer programming 10 points gtxlt Predictive and Prescriptive 15 points 0 7 points for a and 8 points for b a Predictive Consequence of adding customers or milk supply or changing transport costs b Prescriptive What is the optimal transport pattern and should we take on college station MaX 3 X 2 X2 10 Y 4 X2 50Y S 0 4 X1 X2 S 45 X1 X2 2 0 Y is 0 or 1 EXplain the coefficients and function of the variable Y in this problem along with the constraint relating X2 and Y Y must be nonzero for X2 to be nonzero and is a zero one variable 5 points 10 y is Xed cost 3 points 50 y is maXimum capacity for number of 4 X2 s 2 points Interpretation of the Excel Solution 0 5 points for each question 2 points for values and 3 points for interpretation a Decision variables Final Value column under Adjustable Cells in EXCEL answer sheet 0 Scald 1250 hogs 0 Cut with pattern 4 0 Sell 162500 lbs sausage 75000 lbs ofby product 0 the last variable gives lbs disposed of which is 50000 0 do not skin any hogs or cut any with patterns 13 or sell any skins hams or bacon b Shadow price Shadow price column under Constraints in EXCEL sensitivity sheet 0 the second equation is hogs available and one more worth 1416 0 one more skin worth 8 0 one more lb ham worth 19 0 one more lb bacon worth 185 0 one more lb sausage worth 1 0 one more lb by product worth 04 o the neXt to last equation gives waste to be disposed of and one lb costs 001 o the last equation limits labor and one hr worth 264 c Reduced cost Reduced cost column under Adjustable Cells in EXCEL sensitivity sheet 0 Skinning would cost 5850 per hog 0 Using cutting pattern 1 would cost 25 per hog d Using cutting pattern 2 would cost 6048 per hog Using cutting pattern 3 would cost 3858 per hog o All other variables have zero reduced cost and are produced to point where marginal pro t contribution is zero Objective function value s in EXCEL answer sheet Final value under Target Cell Objective Function Value 132000 The value is the maximum pro t given the resources and parameters

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