Road Segment Endpoints Highway(s) Time Distance (Min) (Miles) Yellowstone N.P., WY Livingston, MT US-89 84 59 Yellowstone N.P., WY Idaho Falls, ID US-20 128 100 Livingston, MT Butte, MT I-90 100 104 Butte, MT Butte, MT Missoula, MT Idaho Falls, ID I-15 210 205 Missoula, MT I-90 110 119 Boise, ID US-12, US-95 475 371 Idaho Falls, ID Salt Lake City, UT I-15 206 208 Idaho Falls, ID Twin Falls, ID I-15, 1-86, I-84 155 161 Boise, ID Boise, ID Twin Falls, ID I-84 128 131 Winnemuca, NV US-95 303 256 Twin Falls, ID Wells, NV US-93 141 118 Salt Lake City, UT Salt Lake City, UT Wells, NV I-80 174 181 Ely, NV I-15, US-6 262 241 Wells, NV Winnemuca, NV 1-80 162 175 Wells, NV Ely, NV US-93 180 140 Winnemuca, NV Reno, NV 1-80 153 164 Ely, NV Bishop, CA US-6 337 283 Reno, NV Bishop, CA US-395 255 205 Reno, NV Sacramento, CA 1-80 152 133 Reno, NV Yosemite N.P., CA US-395, CA-120 225 154 Sacramento, CA Yosemite N.P., CA CA-99, CA-120 277 193 Bishop, CA Yosemite N.P., CA US-395, CA-120 132 65 Figure 1: Bi-directional Distance and Travel Time Data Sacramento 1-80 US-12, US-95 Missoula I-90 Butte 1-90 Livingston 1-15 US-89 Boise Idaho US-95 1-84 US-20 W Yellowstone Falls NP Twin 1-15, Falls I-86, I-84 US-93 Winnemuca I-15 1-80 Reno 1-80 I-80 Wells US-93 Salt Lake Ely 1-15, US 6 City US-395 CA-120 US-395 CA-99 CA-120 Yosemite NP US-395, CA-120 Bishop US-6
In this problem, we will consider problems of finding minimum cost paths in directed networks. You are performing logistics analysis for a company that distributes products from several distribution centers located around the US. You are considering adding a new distribution center to serve key cities in the Great Basin area. Currently, you operate single distribution center in Sacramento and serve all of the Great Basin cities from there. You are considering opening a new DC in Salt Lake City to improve service and reduce outbound transportation costs from the DC. See the map at the end of this assignment. Currently, your customers are located in all of the major and mid-sized cities represented by blue circles on the map. You have compiled data on the major highway routes that your truck fleet will use when traveling between your key customer areas and your distribution centers. Figure 1 summarizes the data. You have decided to collect both travel time and travel distance data. Travel distance will influence the costs of your truck transportation while travel time will allow you to understand you quickly you can deliver customer orders.
The map provided appears a bit like a network, but it is not a directed network useful for finding minimum cost paths between locations.
1. Consider the four cities, Idaho Falls; Twin Falls; Wells; and Salt Lake City. Consider the four highway segments that connect a pair of these cities. Draw a directed network representation of this subnetwork of the full network. Label each arc with its travel time from the data you have collected.
2. How many directed arcs did you draw?
3. Consider the arcs representing I-80 between Salt Lake City and Wells. Do both arcs have the same travel time? Is this a reasonable assumption in your view?
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