ISE 754 HW 5: Discrete Location solution

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Solve questions 1(a) by hand (you can submit a scanned copy of your solution, or you can just turn in a
paper copy in class) and then, for questions 1(b) to 4, create a script in Matlab that performs the
calculations needed to answer each question, one cell for each part of each question. Please submit
your script and either diary or “published” output file via Moodle.
1. The table below contains the variable costs associated with serving four EFs from a NF located at
one of four sites. If the fixed costs of locating a NF at any site are 50, (a) show, by hand, each
step of the UFLADD procedure used to determine the number and location of NFs, (b) use
Matlog’s UFLADD function to determine the solution, and (c) formulate as a MILP and solve.
1 2 3 4
1 0 92 50 56
2 92 0 80 74
3 50 80 0 18
4 56 74 18 0
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 is provided in worksheet Customers of spreadsheet HW5data.xlsx (see
Course Schedule for data link). In the Plants worksheet, the city, state, annual production and
procurement cost, and the annual cost to distribute products to wholesalers is provided for each
plant.
3. UNCTV is planning to install new ATSC 3.0 TV broadcasting transmitters throughout North
Carolina. The transmitters have a 30-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 20,000. 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. Modify EXAMPLE 4: UFL with n,m = 104 of script makeFacLoc7.m so that each NF
established can serve a maximum total population of 400,000 people. What is the impact of this
constraint?