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362 CHAPTER 8 NETWORK MODELS

Summary

In this chapter we have introduced network models and shown how they can help with managerial
decision making.

l Network models are concerned with the flow of an item through paths or routes.
l We introduced three types of network model: the shortest-route, the minimal spanning tree and the
maximal flow.
l All three types of model have their own specialist solution algorithm which prove useful when the
models become large and complex.

WORKED EXAMPLE

he transportation manager in the regional health The first iteration then looks at three routes:
T service in Saudi Arabia is reviewing how she
CSD–A 50 minutes
manages the transportation of emergency medical
CSD–B 60 minutes
supplies to small community health clinics in differ-
CSD–C 70 minutes
ent parts of the region. There are a total of six clinics
that occasionally need emergency medical supplies The CSD–A routes has the shortest time so becomes
and it is essential that the supplies arrive in the permanent in the network. For the next iteration we
shortest possible time. The manager is trying to plan now consider the routes from all permanent nodes:
ahead and identify in advance the best routes to use
CSD–B 60 minutes
to supply each clinic. The road network is shown in
CSD–C 70 minutes
the figure. The numbers on the arcs represent typical
A–D 110 minutes
travel time in minutes. In addition, the Highways
A–B 80 minutes
Department is planning to open a new road next
year between Clinic C and Clinic E with a travel time The CSD–B route has the shortest time so becomes
of 15 minutes. permanent. Again, we consider the routes from all
What advice can we give the manager? permanent nodes:
CSD–C 70 minutes
Solution
B–C 80 minutes
We have a shortest route problem where we are A–D 110 minutes
seeking the shortest route between the central sup- B–D 80 minutes
ply depot (CSD) and each clinic. B–E 90 minutes

Clinic A 60
50 Clinic D
30 40
20
60
Central
supply Clinic B Clinic E
depot
30
20

70
Clinic C

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