Exam 7: Goal Programming and Multiple Objective Optimization

Multi-objective linear programming MOLP)provide

MINIMAX solutions to multi-objective linear programming MOLP)problems are

A company wants to purchase large and small delivery trucks.The company wants to purchase about 10 large and 15 small trucks.Each large truck costs $30,000 and has a 10 ton capacity.Each small truck costs $20,000 and has a 7 ton capacity.The company wants to have about 200 tons of capacity and spend about $600,000. Based on the following formulation and associated integer solution,what values should go in cells B2:E16 of the spreadsheet?

Suppose that environmental and human variables are assigned the weight of zero.Then the "triple bottom line" approach reduces to:

A dietician wants to formulate a low cost,high calorie food product for a customer.The following information is available about the 2 ingredients which can be combined to make the food.The customer wants 1000 pounds of the food product and it should contain 250 pounds of Food 1 and 300 pounds of Food 2.The final cost of the blend should be about $1.15 and contain about 2500 calories per pound.The percent of fat,protein,carbohydrate in each food is summarized below with the target values for the goals.The dietician would prefer the food product be low in fat while also high in protein and carbohydrates. Food 1 Food 2 TARGET Cost \ / pound) \ 1.00 \ 1.25 \ 1.15 Fat 15\% 25\% 300 pounds Protein 35\% 40\% 370 pounds Carbohydrate 50\% 35\% 400 pounds Calories/pound 3000 2000 2500 Pounds of food 1 250 Pounds of food 2 300 Formulate the GP for this problem

A company wants to purchase large and small delivery trucks.The company wants to purchase about 10 large and 15 small trucks.Each large truck costs $30,000 and has a 10 ton capacity.Each small truck costs $20,000 and has a 7 ton capacity.The company wants to have about 200 tons of capacity and spend about $600,000. Formulate a goal programming model of this problem.

A soft constraint

Exhibit 7.2 The following questions are based on the problem below. An investor has $150,000 to invest in investments A and B.Investment A requires a $10,000 minimum investment,pays a return of 12% and has a risk factor of .50.Investment B requires a $15,000 minimum investment,pays a return of 10% and has a risk factor of .20.The investor wants to maximize the return while minimizing the risk of the portfolio.The following multi-objective linear programming MOLP)has been solved in Excel. A B C D 1 Problem data A B 2 Expected return 12\% 10\% 3 Risk rating 0.50 0.20 4 5 Variables Total 6 Amount invested 0 0 0 7 Minimum required \ 10,000 \ 15,000 \ 150,000 8 9 Objectives: 10 Average return 0 11 Average risk 0 -Refer to Exhibit 7.2.What Analytic Solver Platform constraint involves cells $B$6:$C$6?

An investor wants to invest $50,000 in two mutual funds,A and B.The rates of return,risks and minimum investment requirements for each fund are: Minimum Fund Rate of return Risk investment 12\% 0.5 \ 20,000 9\% 0.3 \ 10.000 Note that a low Risk rating means a less risky investment.The investor wants to maximize the expected rate of return while minimizing his risk.Any money beyond the minimum investment requirements can be invested in either fund.The investor has found that the maximum possible expected rate of return is 11.4% and the minimum possible risk is 0.32. Formulate a goal programming model with a MINIMAX objective function.

One major advantage of goal programming GP)is that the technique:

Exhibit 7.3 The following questions are based on the problem below. An investor has $150,000 to invest in investments A and B.Investment A requires a $10,000 minimum investment,pays a return of 12% and has a risk factor of .50.Investment B requires a $15,000 minimum investment,pays a return of 10% and has a risk factor of .20.The investor wants to maximize the return while minimizing the risk of the portfolio.The following minimax formulation of the problem has been solved in Excel. A B C D E 1 Problem data A B 2 Expected return 12\% 10\% 3 Risk rating 0.50 0.20 4 5 Variables A B Total 6 Amount invested 0 0 0 7 Minimum required \ 10,000 \ 15,000 \ 150,000 8 9 Weighted 10 Goals Actual Target Weights \% Deviation 11 Average return 0 11.8\% 1 0 12 Average risk 0 0.22 1 0 13 14 Objective: 0 -Refer to Exhibit 7.3.Which value should the investor change,and in what direction,if he wants to reduce the risk of the portfolio?

A constraint which represents a target value for a problem is called a

Exhibit 7.1 The following questions are based on the problem below. A company wants to advertise on TV and radio.The company wants to produce about 6 TV ads and 12 radio ads.Each TV ad costs $20,000 and is viewed by 10 million people.Radio ads cost $10,000 and are heard by 7 million people.The company wants to reach about 140 million people,and spend about $200,000 for all the ads.The problem has been set up in the following Excel spreadsheet. A B C D E 1 Problem Data TV Radio 2 Cost 20 10 3 Coverage 10 7 4 5 Goal Constraints TV Radio Cost Coverage 6 Actual Amount 0 0 7 +Under 0 0 0 0 8 - Over 0 0 0 0 9 F Goal 0 0 0 0 10 Target Value 6 12 200 140 11 12 Percentage Deviation: 13 Under 1 1 1 1 14 Over 0 0 0 0 15 16 Weights 17 Under 18 Over 19 20 Objective 0 -Refer to Exhibit 7.1.What formula goes in cell D6?

Goal programming problems

Goal programming GP)is:

Exhibit 7.1 The following questions are based on the problem below. A company wants to advertise on TV and radio.The company wants to produce about 6 TV ads and 12 radio ads.Each TV ad costs $20,000 and is viewed by 10 million people.Radio ads cost $10,000 and are heard by 7 million people.The company wants to reach about 140 million people,and spend about $200,000 for all the ads.The problem has been set up in the following Excel spreadsheet. A B C D E 1 Problem Data TV Radio 2 Cost 20 10 3 Coverage 10 7 4 5 Goal Constraints TV Radio Cost Coverage 6 Actual Amount 0 0 7 +Under 0 0 0 0 8 - Over 0 0 0 0 9 F Goal 0 0 0 0 10 Target Value 6 12 200 140 11 12 Percentage Deviation: 13 Under 1 1 1 1 14 Over 0 0 0 0 15 16 Weights 17 Under 18 Over 19 20 Objective 0 -Refer to Exhibit 7.1.Which of the following is a constraint specified to Analytic Solver Platform for this model?

A company makes 2 products A and B from 2 resources.The products have the following resource requirements and produce the accompanying profits.The available quantity of resources is also shown in the table. Product 1 2 Available resources Labor hr/unit) 3 2 150 Material ounces/unit) 1 2 200 Profit \/ unit) 7 6 Management has developed the following set of goals Goal 1: Produce approximately 40 units of product 1. Goal 2: Produce approximately 70 units of product 2.Goal 3: Achieve a profit over $400. Goal 4: Consume less than 150 hours of labor Goal 5: Consume less than 200 ounces of material Based on this GP formulation of the problem and the associated optimal integer solution what values should go in cells B2:F16 of the following Excel spreadsheet?

Exhibit 7.1 The following questions are based on the problem below. A company wants to advertise on TV and radio.The company wants to produce about 6 TV ads and 12 radio ads.Each TV ad costs $20,000 and is viewed by 10 million people.Radio ads cost $10,000 and are heard by 7 million people.The company wants to reach about 140 million people,and spend about $200,000 for all the ads.The problem has been set up in the following Excel spreadsheet. A B C D E 1 Problem Data TV Radio 2 Cost 20 10 3 Coverage 10 7 4 5 Goal Constraints TV Radio Cost Coverage 6 Actual Amount 0 0 7 +Under 0 0 0 0 8 - Over 0 0 0 0 9 F Goal 0 0 0 0 10 Target Value 6 12 200 140 11 12 Percentage Deviation: 13 Under 1 1 1 1 14 Over 0 0 0 0 15 16 Weights 17 Under 18 Over 19 20 Objective 0 -Refer to Exhibit 7.1.If the company is very concerned about going over the $200,000 budget,which cell value should change and how should it change?

Exhibit 7.4 The following questions are based on the problem below. Robert Gardner runs a small,local-only delivery service.His fleet consists of three smaller panel trucks.He recently accepted a contract to deliver 12 shipping boxes of goods for delivery to 12 different customers.The box weights are: 210,160,320,90,110,70,410,260,170,240,80 and 180 for boxes 1 through 12,respectively.Since each truck differs each truck has different load capacities as given below: Truck Weight Capacity Box Capacity Cost per pound 1 800 pounds 5 \ 0.34 2 900 pounds 6 \ 0.42 3 700 pounds 4 \ 0.25 Robert would like each truck equally loaded,both in terms of number of boxes and in terms of total weight,while minimizing his shipping costs.Assume a cost of $50 per item for trucks carrying extra boxes and $0.10 per pound cost for trucks carrying less weight. The following integer goal programming formulation applies to his problem. Y₁ = weight loaded in truck 1;Y₂ = weight loaded in truck 2;Y₃ = weight loaded intruck3;X_i,j = 0 if truck i not loaded with box j;1 if truck i loaded with box j. Given the following spreadsheet solution of this integer goal programming formulation,answer the following questions. -Refer to Exhibit 7.4.What formulas should go in cell E26 of the spreadsheet?

A hard constraint