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Exhibit 7.4 The Following Questions Are Based on the Problem Below

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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: 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:   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. Y<sub>1</sub> = weight loaded in truck 1; Y<sub>2</sub> = weight loaded in truck 2; Y<sub>3</sub> = weight loaded in truck 3; X<sub>i,j</sub> = 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. The solution indicates Truck 3 is under the target weight by 67 pounds. What if anything can be done to this model to provide a solution in which Truck 3 is closer to the target weight? 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 in truck 3;
Xi,j = 0 if truck i not loaded with box j; 1 if truck i loaded with box j. 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:   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. Y<sub>1</sub> = weight loaded in truck 1; Y<sub>2</sub> = weight loaded in truck 2; Y<sub>3</sub> = weight loaded in truck 3; X<sub>i,j</sub> = 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. The solution indicates Truck 3 is under the target weight by 67 pounds. What if anything can be done to this model to provide a solution in which Truck 3 is closer to the target weight? Given the following spreadsheet solution of this integer goal programming formulation, answer the following questions. 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:   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. Y<sub>1</sub> = weight loaded in truck 1; Y<sub>2</sub> = weight loaded in truck 2; Y<sub>3</sub> = weight loaded in truck 3; X<sub>i,j</sub> = 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. The solution indicates Truck 3 is under the target weight by 67 pounds. What if anything can be done to this model to provide a solution in which Truck 3 is closer to the target weight?
-Refer to Exhibit 7.4. The solution indicates Truck 3 is under the target weight by 67 pounds. What if anything can be done to this model to provide a solution in which Truck 3 is closer to the target weight?

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