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MAXIMAL FLOW PROBLEM 369

system needs to be developed to better coordinate According to the proposed operating procedure,
the use of the ambulance services at the two hospi- incoming emergency calls would be identified by zone
tals so that together they can provide the fastest number, and an ambulance from the hospital closest
possible emergency service for the city. to that zone would be assigned the service call. How-
A proposal being considered is for all ambulance ever, if all ambulances from the closest hospital were
service calls to be handled through a central dis- occupied with other emergencies, the service call
patcher, who would assign a call to the hospital capa- would be assigned to the other hospital. Regardless
ble of providing the fastest service. In studying this of which hospital responded to the service call, the
proposal, a project team consisting of employees individual or individuals requiring the emergency serv-
from both hospitals met and decided that the best ice would be taken to the closest hospital.
approach would be to divide the city into 20 service To make the coordinated service as efficient as
zones. In the proposed configuration, Western Medi- possible, the ambulance drivers must know in
cal would be located in zone 1 and Binghamton advance the quickest route to take to each zone, which
General in zone 20. A map showing the placement hospital the individual or individuals in that zone
of the 20 zones and the travel time (in minutes) should be taken to, and the quickest route to that
between adjacent zones is provided in Figure 8.20. hospital.

Figure 8.20 Network for Proposed Ambulance Service
6 8
9 15
6 5
7
5 4 16
4
5 14 6
8 7
20 6
5 5 4
4
4 8 6 13 17
8 7
7
7 5 7
10 5 5 19
1 6
6 12
6 18
4 7
7 9
3 8 6 9
2 3
5
5
10 11
Managerial Report 3 A chart for the Binghamton General ambulance
drivers that provides the minimum time routes
Prepare a report for the two hospital administrators
from Binghamton General to every zone in
describing your analysis of the problem. Include in your
the city, including Western Medical. Include
report recommendations regarding the following items:
a chart that tells Binghamton General
1 A chart for the dispatcher that identifies the primary drivers which hospital the individuals should
hospital ambulance service for every zone in the city. be taken to and the route that should be
followed.
2 A chart for the Western Medical ambulance
drivers that provides the minimum time routes 4 Include recommendations regarding how the
from Western Medical to every zone in the city, system could be modified to take into account
including Binghamton General. Include a chart varying traffic conditions that occur throughout
that tells Western Medical drivers which hospital the day and changes in driving conditions
the individuals should be taken to and the route resulting from temporary road construction
that should be followed. projects.

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