Consider the following graph where the nodes J = {3,5,6,7,8} in dashed boxes are possible facility...

 

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Consider the following graph where the nodes J = {3,5,6,7,8} in dashed boxes are possible facility locations, the nodes I = {1,2,4,9,10} are customers, and the edge weights correspond to direct distances between nodes i and j. We can calculate the total distance dj which corresponds to the length of the shortest path between nodes i and j. Suppose the allowable maximum distance between a customer and the facility it utilizes is D. What is the smallest maximum distance D needed to ensure that every customer's demand can be satisfied by one facility? Formulate an integer program for this problem to determine the value of D and where the locate the single facility. Clearly identify your decision variables, parameters/sets, Model 2, and a description of your model. 1 1 4 3 1 3 3 2 9 4 5 3 5 2 4 1 5 10 1 1 2 3 8 3 5 Consider the following graph where the nodes J = {3,5,6,7,8} in dashed boxes are possible facility locations, the nodes I = {1,2,4,9,10} are customers, and the edge weights correspond to direct distances between nodes i and j. We can calculate the total distance dj which corresponds to the length of the shortest path between nodes i and j. Suppose the allowable maximum distance between a customer and the facility it utilizes is D. What is the smallest maximum distance D needed to ensure that every customer's demand can be satisfied by one facility? Formulate an integer program for this problem to determine the value of D and where the locate the single facility. Clearly identify your decision variables, parameters/sets, Model 2, and a description of your model. 1 1 4 3 1 3 3 2 9 4 5 3 5 2 4 1 5 10 1 1 2 3 8 3 5

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