HW 2: Single-Facility Location¶
ISE 754, Fall 2024
Assigned: Wed, 28 Aug (Individual Assignment)
Due: 10:00a, Mon, 9 Sep
First, please solve questions 1 and 2 by hand (you can submit a scanned copy of your solution, or you can turn in a paper copy in class), and then, for all three questions, use the Code cells in this Jupyter Notebook to answer the following questions. Please run all of 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) A new tool crib is to be located on the floor of a facility. Workers from eight different workstations will make 11, 46, 36, 20, 32, 23, 20, and 18 trips per shift to the tool crib. The 2-D locations of the workstations are shown in the figure below. Assuming rectilinear distance is a reasonable approximation of the actual travel distance, determine the optimal location for the tool crib that will minimize the total distance that the workers travel.
(2) A product will be produced at a single plant. Each ton of the product requires 2 tons of raw material A from a supplier located in Durham on the figure below, 0.55 tons of raw material B from a supplier located in Statesville, 1.2 tons of raw material C from a supplier located in Wilmington, and 0.35 tons of raw material D from a supplier located in Asheville. The annual demand for the product for the four customers in Asheville, Winston-Salem, Greensboro, and Raleigh are 10, 38, 20, and 46 tons, respectively. The cost per ton-mile to ship the raw materials A, B, C, and D to the plant is \$0.08, \$0.05, \$0.15, and \$0.03, respectively, and the cost per ton-mile to ship the finished goods from the plant to the customers is \$0.80. All scrap is disposed of locally. (a) Assuming that I-40 will be used for all travel, where should the plant be located to minimize transportation costs? (b) With respect to its monetary weight, is the product weight gaining or weight losing?
(3) Create ten random (real-number) points in the region defined by the rectangle [(2, 1), (10, 7)] using the random number seed 2073.
(a) Determine the location that minimizes the sum of the squared-Euclidean distances.
(b) Determine the location that minimizes the sum of the Euclidean distances.
(c) Determine the location that minimizes the maximum Euclidean distance.
(d) Determine the location that minimizes the sum of the Euclidean distances, with the restriction that the location cannot be within the rectangle defined by [(5,3) and (7,5)]. The straight line from the location to any point can cross the rectangle (e.g., if the location restriction is due to zoning, then travel across the zone can still occur).
(e) Determine the location that maximizes the minimum Euclidean distance, with the restriction that the location must be within the rectangle defined by [(2,1) and (10,7)].