On Monday, January 17, 1994, an earthquake of magnitude 6.6 on the Richter scale hit Los Angeles killing over 30 people and causing major damage to buildings, roads, and other parts of the urban...

On Monday, January 17, 1994, an earthquake of magnitude 6.6 on the Richter scale hit Los Angeles killing over 30 people and causing major damage to buildings, roads, and other parts of the urban infrastructure. In partial response to this, President Clinton ordered a 60-vehicle mobile emergency response unit to be dispatched from Denver to Los Angeles. Included in the response unit were telecommunications and electric generation facilities.

(a) Of critical concern in such a situation is the distance between the responding units and the emergency. Also, we are concerned that the units themselves not be damaged in the emergency. Use the SITATION software and the 88-node data set (CITY1900.GRT available online) to find the minimum number of facility bases needed to ensure that all demand nodes are covered within a distance of 500 miles. Assume that a facility base at a particular city cannot cover emergencies in that city since there is some reasonable likelihood that the vehicles in the affected city will be disabled. Thus, cities in which a facility base is located must be covered by a facility in some other city.

How many facilities are needed? Where are facilities located? Which cities cover the cities in which facilities are located?

(b) Print a map showing the locations of the facilities and the assignments of cities to facilities.

(c) How many more facilities are needed for the solution to the problem as posed in part (a) than would be needed if we allowed facilities based in city i to cover city i itself?