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Unformatted text preview: ENGRI 1101 Engineering Applications of OR Fall 2008 Homework 1 Homework 1 Solutions 1. All that was required was to draw, close to scale and with labeled axes, the inputs to the problem, i.e., the line segment from each package, with arrows indicating the direction from pickup to dropoff. An example is shown below: Figure 1: Schematic picture of the input 2. The first thing to realize in order to convert this package delivery problem into a TSP is that there are 5 cities, and associated with these 5 cities are your apartment and the 4 packages to be delivered. The actual numbering of the cities is interchangeable, we will consider city 0 as your apartment and the other 4 cities as the different packages. (Note that these are not real cities but abstract objects used in the model.) The next step in the solution is to calculate the time or cost of traveling between each pair of cities. There are a number of different ways of calculating the cost, one of which (and the one we will be using) is to only consider the time it takes to travel between a dropoff location and a pickup location (for a different package). We prefer to ignore the time it takes to deliver the packages because this is constant, but if you have included it you are still correct. It is also important to notice that it is incorrect to make a city for each pickup and dropoff location, since using these as...
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