HW 5: Discrete Location¶
ISE 754, Fall 2024
Assigned: Mon, 23 Sep (Individual Assignment)
Due: 10:00a, Mon, 7 Oct
Solve question 1 by hand (you can submit a scanned copy of your solution, or you can turn in a paper copy in class), and then, for the other questions, use the Code cells in this Jupyter Notebook to answer the questions. Please run all the cells in your notebook and then submit it as a .ipynb file, along with a .html or .pdf copy, via Moodle. (There is a Run All Cells command under the Run menu.)
(1) With respect to the Popco Bottling Company example, assume that now there are only two existing plants and the four 3-digit ZIP codes 813, 814, 815, and 829. The annual plant production is 84 and 61 tons, respectively, the annual production cost at each plant is \$21,346 and \$18,124, respectively, and the annual distribution cost at each plant is \$15,721 and \$10,351, respectively. Tables A–C, below, list the plant to ZIP-code centroid distances (mi), ZIP-code to ZIP-code centroid distances (mi), and the population and area of each ZIP code, respectively. Using the same modeling approach and assumptions using in the original example, determine the change in total costs associated with closing both plants and opening a single plant at the ZIP-code 815 centroid location.
(2) Gipfel, Inc., has wholesale distributors located throughout the continental U.S. that sell the products manufactured in its twelve plants. Each plant manufactures the same mix of products. Gipfel would like for you to determine if they should consider either constructing more plants and/or closing some of their existing plants. The 5-digit zip code and annual demand (in tons) for each wholesaler are provided in HW5data-cust.csv. In HW5data-plant.csv, the city, state, annual production and procurement cost, and the annual cost to distribute products to wholesalers are provided for each plant.
(3) UNCTV is planning to install new ATSC 3.0 TV broadcasting transmitters throughout North Carolina. The transmitters have a 50-mile maximum signal range and UNCTV would like to reach, at the least cost, as many people in North Carolina with a signal as possible, but they plan to install the transmitters only in cities with a population of at least 10,000. They would like you to recommend where transmitters should be installed, and how much of the state’s population would be covered. You do not need to consider any existing UNCTV facilities in your analysis.
(4) Continuing with the same example using in Loc 5 and Loc 8:
P = [50 150 220 295 420]'
r, f = 1, 1
w = r * f
k = [150, 200, 150, 150, 200]
C = w * D1(P, P)
(a) What would be the impact on the solution if each NF was limited to a processing two tons, where the demand of each EF, f, is one ton?
(b) What would be the impact on the solution if, in addition, one of the NFs was required to be located in Wilmington?