Exam 7: Goal Programming and Multiple Objective Optimization

Question

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. $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: \begin{array}{llll}\text { Truck} & \text { Weight Capacity } & \text { Box Capacity } & \text { Cost per pound }\\ \hline 1 & 800 \text { pounds } & 5 & \$ 0.34 \\ 2 & 900 \text { pounds } & 6 & \$ 0.42 \\ 3 & 700 \text { pounds } & 4 & \$ 0.25 \end{array} 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 $0.10 per pound cost for trucks carrying less weight. The following integer goal programming formulation applies to his problem. Y1 = weight loaded in truck 1;Y2 = weight loaded in truck 2;Y3 = weight loaded intruck3;Xi,j = 0 if truck i not loaded with box j;1 if truck i loaded with box j. Given the following spreadsheet solution of this integer goal programming formulation,answer the following questions. -Refer to Exhibit 7.4.Given the solution indicated in the spreadsheet,which trucks,if any,are under an equal weight amount,and which trucks are over an equal weight amount?$ -Refer to Exhibit 7.4.Given the solution indicated in the spreadsheet,which trucks,if any,are under an equal weight amount,and which trucks are over an equal weight amount?

The MINIMAX objective

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

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