NETWORK OPTIMIZATION MODELS:PROTOTYPE EXAMPLE

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PROTOTYPE EXAMPLE

SEERVADA PARK has recently been set aside for a limited amount of sightseeing and backpack hiking. Cars are not allowed into the park, but there is a narrow, winding road system for trams and for jeeps driven by the park rangers. This road system is shown (without the curves) in Fig. 10.1, where location O is the entrance into the park; other letters designate the locations of ranger stations (and other limited facilities). The numbers give the distances of these winding roads in miles.

The park contains a scenic wonder at station T. A small number of trams are used to transport sightseers from the park entrance to station T and back.

The park management currently faces three problems. One is to determine which route from the park entrance to station T has the smallest total distance for the operation of the trams. (This is an example of the shortest-path problem to be discussed in Sec. 10.3.)

INTRODUCTION TO OPERATIONS RESEARCH-0000

A second problem is that telephone lines must be installed under the roads to establish telephone communication among all the stations (including the park entrance). Be- cause the installation is both expensive and disruptive to the natural environment, lines will be installed under just enough roads to provide some connection between every pair of stations. The question is where the lines should be laid to accomplish this with a minimum total number of miles of line installed. (This is an example of the minimum spanning tree problem to be discussed in Sec. 10.4.)

The third problem is that more people want to take the tram ride from the park entrance to station T than can be accommodated during the peak season. To avoid un- duly disturbing the ecology and wildlife of the region, a strict ration has been placed on the number of tram trips that can be made on each of the roads per day. (These lim- its differ for the different roads, as we shall describe in detail in Sec. 10.5.) Therefore, during the peak season, various routes might be followed regardless of distance to in- crease the number of tram trips that can be made each day. The question pertains to how to route the various trips to maximize the number of trips that can be made per day without violating the limits on any individual road. (This is an example of the maximum flow problem to be discussed in Sec. 10.5.)

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