ISyE 3103 Introduction to Supply Chain Modeling: Transportation and Logistics Spring 2006 Homework 7 Assigned: March 30, 2006 Due: April 6, 2006

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1 ISyE 3103 Introduction to Supply Chain Modeling: Transportation and Logistics Spring 2006 Homework 7 Assigned: March 30, 2006 Due: April 6, 2006 This assignment is worth 50 points. You are to complete this work by yourself. Pipeline Network Design at Buckeye Pipe Line Company [20 points] Buckeye Pipe Line Company 1 is a major pipeline transportation provider in the Northeast, Mid- Atlantic, and Midwestern United States. The commodities the company hauls most often are refined petroleum products as well as propane, butane, refinery feedstocks, and blending components. Buckeye operates as a common carrier in accordance with published rates and rules tariffs. Buckeye also provides its customers with bulk storage services at many terminals throughout its service region. Since the company was founded over 100 years ago, many of its underground pipes are in need of repair and replacement. The pipes serving its Pennsylvania terminals (listed in Table 1) are especially worn, and Buckeye is considering a large-scale replacement of all of its pipes in the state. The firm would like to accomplish this project at the lowest cost. Since the pipes themselves are the most expensive part of the project, Buckeye wants to identify the best network design that uses the least amount of piping yet still connects all of the terminals in the state. Table 2 lists the possible connections and the associated distance 2 between pairs of terminals, and these possible connections are depicted in Figure 1. Table 1: Buckeye Pipe Line Company s Pennsylvania Terminal Facilities Node # City Node # City 1 Coraopolis 12 Highspire 2 Stowe Township 13 Philadelphia International Airport 3 Indianola 14 Mount Union 4 Midland 15 Exeter 5 Reading 16 Dupont 6 Tuckerton 17 Lancaster 7 East Freedom 18 Allentown 8 Malvern 19 Macungie 9 New Kingstown 20 Delmont 10 Carlisle 21 Greensburg 11 Halifax 1 For more details, see Buckeye s website at 2 These are the driving distances between the terminals, which are obviously different from the amount of pipe that would be needed to make the connections since the pipes are not restricted to traverse road routes. They will, however, serve as a good proxy of the required pipeline distance between the locations for the purposes of this assignment. ISyE 3103 Spring 2006 Homework 7 1

2 Table 2: Possible Connections and Distance between Buckeye Terminals Arc Mileage Arc Mileage Arc Mileage Arc Mileage (1,2) 11 (1,3) 31 (1,4) 24 (2,3) 21 (2,4) 34 (2,20) 31 (2,21) 40 (3,4) 62 (3,20) 24 (3,21) 33 (4,20) 64 (5,6) 10 (5,8) 42 (5,11) 79 (5,13) 71 (5,15) 100 (5,17) 27 (5,18) 37 (5,19) 34 (6,8) 44 (6,11) 84 (6,15) 93 (6,16) 89 (6,17) 33 (6,18) 30 (6,19) 27 (7,10) 106 (7,14) 56 (7,20) 76 (7,21) 77 (8.13) 33 (8,16) 114 (8,17) 45 (8,18) 58 (8,19) 43 (9,10) 8 (9,11) 34 (9,12) 19 (9,14) 67 (9,17) 47 (10,11) 41 (10,12) 28 (10,14) 67 (11,12) 31 (11,14) 85 (11,15) 101 (11,17) 59 (11,20) 205 (12,17) 30 (13,17) 88 (13,18) 69 (13,19) 75 (14, 20) 146 (15,16) 6 (15,17) 127 (15,18) 67 (15,19) 73 (16,18) 64 (16,19) 70 (18,19) 7 (20,21) 10 What You Are Asked To Do 1. Determine the network design that minimizes the total mileage of pipe utilized such that all 21 of the Buckeye terminals are connected. Use one of the algorithms we discussed in class to find this optimal network design. Be sure to include all of the iterations that the algorithm undergoes to determine the optimal solution. 2. Draw the arcs of your optimal pipeline network on the map provided in Figure The model we formulated to determine the optimal pipeline network design was a simplified version of the problem that Buckeye Pipe Line Company actually faces. Briefly discuss two practical considerations not represented in the model that Buckeye would have to consider when choosing the connections to include in its network. How could we have incorporated these considerations into the model above to provide a more realistic network design? ISyE 3103 Spring 2006 Homework 7 2

3 Figure 1: Map of Buckeye Pipe Line Company Facility Locations and Possible Connections ISyE 3103 Spring 2006 Homework 7 3

4 Figure 2: Optimal Pipeline Network Design ISyE 3103 Spring 2006 Homework 7 4

5 Yellowstone and Yosemite National Park Tour Bus Routing [30 points] Two of the United States most-visited national parks are Yellowstone National Park (located mostly in Wyoming, but extending slightly across the border into Idaho and Montana) and Yosemite National Park (located in California). Like many other national parks, Yellowstone and Yosemite are located away from major cities and thoroughfares, so that driving to and from either one may involve either roundabout travel or travel on smaller, slower roadways. A company specializing in nature tours offers two-location camping trips at Yellowstone and Yosemite. Customers drive to their choice of either of the two parks, and the company provides tours of the parks, as well as bus service between the parks. Every few days a bus drives from one park to the other. A bus from Yosemite to Yellowstone, for example, might have some Yosemitebased campers on their way to the second part of their tour, and also some Yellowstone-based campers who are heading back at the end of their tour. Using the Rand McNally road atlas, the company has identified all of the major roads that might be used as part of the bus route between the two parks. The roads include, in decreasing order of size and speed, interstate highways, U.S. highways, and state highways. Interstate highways are denoted by an I before the highway number, U.S. highways by US before the highway number, and state highways by the state s abbreviation (for example, CA ) before the highway number. A map of the highways, as well as a table of the city-to-city connections, is included below. The company s transportation director is unsure of the best path for the tour buses to take. Being a new, financially shaky company, they purchased older, heavily used buses. Therefore, minimizing the mileage that the buses travel is an important consideration. On the other hand, if the shortestmileage path results in longer travel times then the company s customers might be dissatisfied, so minimizing the travel time is also an important consideration. Part I In the data in the table and map, we assume that travel distances and times are the same in both directions along each arc. Is this a reasonable assumption? Why or why not? Based on this assumption, explain why, if you have found a shortest path from Yellowstone to Yosemite, reversing the path gives the shortest path from Yosemite to Yellowstone. Part II Use Dijkstra s algorithm to calculate the shortest-mileage route between Yellowstone and Yosemite. Show your work. Draw the network with the shortest-mileage tree clearly indicated on the network. Part III Use the Bellman-Ford algorithm to calculate the shortest-time route between Yellowstone and Yosemite. Show your work. Draw the network with the shortest-time tree clearly indicated on the network. Part IV Based on the limited data you have about the company, which route would you tentatively recommend, and why? ISyE 3103 Spring 2006 Homework 7 5

6 Location Data and Driving Distances Location X-Coord Y-Coord Yellowstone N.P., WY Livingston, MT Idaho Falls, ID Butte, MT Missoula, MT Boise, ID Salt Lake City, UT Twin Falls, ID Winnemuca, NV Wells, NV Ely, NV 28 8 Reno, NV 8 10 Bishop, CA 14 2 Sacramento, CA 2 6 Yosemite N.P., CA 10 4 Road Segment Endpoints Highway(s) Time (Min) Distance (Miles) Yellowstone N.P., WY Livingston, MT US Yellowstone N.P., WY Idaho Falls, ID US Livingston, MT Butte, MT I Butte, MT Idaho Falls, ID I Butte, MT Missoula, MT I Missoula, MT Boise, ID US-12, US Idaho Falls, ID Salt Lake City, UT I Idaho Falls, ID Twin Falls, ID I-15, I-86, I Boise, ID Twin Falls, ID I Boise, ID Winnemuca, NV US Twin Falls, ID Wells, NV US Salt Lake City, UT Wells, NV I Salt Lake City, UT Ely, NV I-15, US Wells, NV Winnemuca, NV I Wells, NV Ely, NV US Winnemuca, NV Reno, NV I Ely, NV Bishop, CA US Reno, NV Bishop, CA US Reno, NV Sacramento, CA I Reno, NV Yosemite N.P., CA US-395, CA Sacramento, CA Yosemite N.P., CA CA-99, CA Bishop, CA Yosemite N.P., CA US-395, CA ISyE 3103 Spring 2006 Homework 7 6

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8 Part II Shortest Distance From Yellowstone To Step Yellowstone Livingston Idaho Falls Butte Missoula Boise Salt Lake City Twin Falls Winnemuca Wells Ely Reno Bishop Sacramento Yosemite New Road Part III Shortest Time From Yellowstone To Step Yellowstone Livingston Idaho Falls Butte Missoula Boise Salt Lake City Twin Falls Winnemuca Wells Ely Reno Bishop Sacramento Yosemite New Road ISyE 3103 Spring 2006 Homework 7 8