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Lec 10 - IEOR 151| Notes 10.4 Zahin Ali Young Kim...

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Unformatted text preview: IEOR 151| Notes 10.4 Zahin Ali, Young Kim, Geetanjali Johary, Divya Sharma ADMINISTRATIVE ISSUES: 10.6: Team presentations (1‐3), project proposal 10.20 Team presentations (4‐6) 10.25: Midterm Review 10.27: Midterm CENTER PROBLEM Objective: to minimize the longest travel distance from any customer to the closest facility Parameters: Decision Variables: Formulation: Example Given a network tree with distances for each node. The goal is to locate one facility and minimize the maximum distance from any node of the network to the facility. IEOR 151| Notes 10.4 Zahin Ali, Young Kim, Geetanjali Johary, Divya Sharma 1‐Center, P=1 Steps to determine the optimal location: 1. Start at any node, for example: C 2. Find the maximum distance in the network tree from C to a node, In this case: C to G with a distance of 21. This is known as e1. 3. Start the tree with e1 and find the longest path from e1. In this case: longest path is to node H, distance of 41. 4. Find the middle point between starting at e1 and e2. Minimum distance: 2‐Center, P =2 Begin at the absolute center and divide the network down the middle. The problem is then reduced to two 1‐Center problems. IEOR 151| Notes 10.4 Zahin Ali, Young Kim, Geetanjali Johary, Divya Sharma SET‐COVERING PROBLEM Objective: To maximize the population covered within a desired distance. Formulation Example: Maximum Coverage Problem Parameters: Decision Variables: ...
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