A trauma center keeps ambulances at locations throughout the east side of a city

Question

A trauma center keeps ambulances at locations throughout the east side of a city in an attempt to minimize the response time in the event of an emergency. The times, in minutes, from the ambulance locations to the population centers are given in the table at the top of the next column.

9

Find the optimal assignment of ambulances to population centers that will minimize the total emergency response time.

Population Centers Ambulance Locations East Northeast Southeast Central Site 1 12 8 9 13 Site 2 10 9 11 10 Site 11 12 14 11 Site 4 13 11 12

9

Explanation / Answer

LOCATIONS EAST NORTH-
EAST SOUTH-
EAST CENTRAL
Site 1 12 8 9 13
Site 2 10 9 11 10
Site 3 11 12 14 11
Site 4 13 11 12 9

Ambulance Locations Population Centers Flow balance equations
East North-East South-East Central Flow out Location Flow in Flow out Net flow Sign RHS
Site 1 0.0 0.0 1.0 0.0 1.0 Site 1 0.0 1 -1 = -1
Site 2 0.0 1.0 0.0 0.0 1.0 Site 2 0.0 1 -1 = -1
Site 3 1.0 0.0 0.0 0.0 1.0 Site 3 0.0 1 -1 = -1
Site 4 0.0 0.0 0.0 1.0 1.0 Site 4 0 1 -1 = -1
Flow in 1.0 1.0 1.0 1.0 Site 1 1 1 = 1
Site 2 1 1 = 1
Ambulance Locations Population Centers Site 3 1 1 = 1
East North-East South-East Central Site 4 1 1 = 1
Site 1 12.0 8.0 9.0 13.0
Site 2 10.0 9.0 11.0 10.0
Site 3 11.0 12.0 14.0 11.0
Site 4 13.0 11.0 12.0 9.0

Total Emergency Response Time 38

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