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Unformatted text preview: Logistical and Transportation Planning Methods 1.203J/6.281J/13.665J/15.073J/16.76J/ESD.216J Massachusetts Institute of Technology Cambridge, Massachusetts Quiz #2 December 12, 2005 OPEN BOOK TWO HOURS 5 PAGES, 3 PROBLEMS PLEASE SHOW ALL YOUR WORK! INSPIRATIONAL QUOTE: If you come to a fork in the road, take it. Yogi Berra, once a baseball catcher for the New York Yankees 1 Problem 1 (36 points) In the tree network shown below, demands are generated uniformly along the edges of the network in a Poisson manner at the rate of per unit of time. (Think of the edges as city streets, with houses located along the streets.) (a) (9 points) Find a solution to the 3-absolute-center problem on this network, i.e., locate three facilities in a way that minimizes the maximum distance between any demand and its nearest facility. What is the maximum distance associated with your solution? (Any answer that finds the correct maximum distance will receive full credit.) (b) (9 points) Find a solution to the 4-absolute-center problem on this network. What is the maximum distance associated with your solution? (Any answer that finds the correct maximum distance will receive full credit.) Suppose now that we wish to locate a station for a single ambulance on this network in a way that minimizes expected response time to calls from the network. Assume that the station is located at some point X on the network. Response time then consists of the sum of (1) the round-trip travel time between X and the demand and (2) any waiting time until the ambulance is dispatched from point X. Specifically, assume that the speed of the ambulance during its travel to and from each demand is equal to 1 and that the time it spends on the scene of the demand is exactly 1 unit. Service to demands is provided in a first-come, first-served way. first-come, first-served way....
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