HW 7: Networks¶
ISE 754, Fall 2024
Assigned: Mon, 28 Oct (Individual Assignment)
Due: 10:00a, Wed, 6 Nov
Solve question 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 the 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) Unless otherwise noted, each of the following questions builds upon the previous:
(a) Three DCs located in Zip codes 20002, 26149, and 36317 supply, in total, 40, 55, 35, 70, and 15 tons of a single product each year to customers located in Zip codes 30669, 32606, 30733, 23830, and 23061, respectively. Assuming that transport costs are proportional to great circle distance and that each DC can supply any amount of the product, determine the amount of product that should be supplied from each DC to each customer in order to minimize total ton-miles.
(b) What would be the change in total ton-miles if each DC was limited to supplying up to 80 tons per year of the product, in total, to all of the customers?
(c) What would be the change in total ton-miles if the amount of the product that could be transported across each lane (i.e., each DC-to-customer transport link) could not exceed 35 tons per year?
(2) The cost of each arc is shown in the network below. Determine the least cost path from node 3 to node 6.
(3) Create a 10 by 10 matrix containing the shortest NHS road distance between the ten Texas cities with the largest population.
(4) A single product is produced in a single-stage production process. A 13-week rolling horizon is used for planning production. The process has a capacity of 60 tons per week. The forecasted demand (ton) over the horizon is provided in HW7data-demand.csv. Production data for the past year is provided in HW7data-prod_cost.csv, where production (ton/wk) and cost (\$000/wk) are listed for the weeks the process was operating. The inventory carrying rate is estimated at 0.125 per week. Currently, there are 13 tons of finished product in storage, and this same amount should be in inventory at the end of the planning period. There is enough space to store up to 120 tons of finished product. Determine the best production plan over the planning horizon.
(5) A plant can use a three-stage process to produce three products. A 13-week rolling horizon is used for planning production. The products’ forecasted demand (ton) over the horizon is provided in HW7data-demand_2.csv.The plant can produce up to 600, 550, and 500; 500, 450, and 350; and 400, 350, and 300 tons per week for each stage of each product, respectively; has production costs of \$12, 75, and 35; 20, 130, and 60; and 16, 100, and 50 per ton for each stage of each product, respectively; and has costs of $4000, 900, and 500; 6000, 1100, and 600; and 5000, 1000, and 600 per set up for each stage of each product, respectively. The annual inventory carrying rate is 0.3. The plant is currently set up to produce each stage of the first product, and the first three weeks of demand for the other two products are being held as inventory at each stage. The final inventory for all stages of all products is zero. Determine the amount of each product that should be produced in order to for the total costs over the planning horizon to be within 1% of the optimal value.