HW 4: Network Modeling

OR/ISE 501 - Fall 2021

Assigned: Thu, 23 Sep (Groups of 2)
Due: 11:59p, Wed, 29 Sep

Group Members:

Please use the Code cells in this Jupyter notebook to answer each of the following questions. You can add additional cells for each question if that helps in organizing your solution. Please run all of the cells in your notebook and then submit it via Moodle. (There is a Run All Cells command under the Run menu.)

(1) Four warehouses at the (x,y) coordinates listed for locations 1-4 in the table below supply, in total, 40, 55, 35, 70, and 25 tons of a single product each year to customers at locations 4-8, respectively. Unless otherwise noted, each of the following questions builds upon the previous questions:

Location x y
1 -77.0300 38.8900
2 -80.8256 39.4833
3 -85.4043 31.6436
4 -83.1209 33.6721
5 -88.5150 35.0523
6 -84.7100 34.5600
7 -77.3951 37.0170
8 -76.4400 37.3900

image.png

(1a) Assuming that transport costs are proportional to Euclidean distance and that each warehouse can supply any amount of the product, determine the amount of product that should be supplied from each warehouse to each customer in order to minimize total cost.

(1b) In what unit of measure is the total cost given for this problem?

Your Answer:

(1c) What would be the change in the total cost if each warehouse was limited to supplying up to 60 tons per year of the product, in total, to all of the customers?

(1d) What would be the change in the total cost if the amount of the product that could be transported from each warehouse to each customer 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.

image.png

(3) Activity 5 takes six weeks and can start anytime after activity 2 is complete. Activity 8 takes four weeks and can start anytime after activities 2 and 9 are complete, and activity 2 takes eight weeks and can start after activities 7 and 10. Activity 9 takes seven weeks and can start after activity 1, activity 7 takes ten weeks and can start after activities 1 and 4, and activity 10 takes eight weeks and can start after activity 4. Activity 4 takes four weeks and can start after activity 3, and activity 1 takes six weeks and can start after activity 6 is complete. Activities 3 and 6 take five and eight weeks, respectively, and can start at any time. Determine the minimum number of weks required to complete all of the activities.

(4) A plant can use a three-stage process to produce a single product. A 13-week rolling horizon is used for planning production. The product's forecasted demand 13, 10, 10, 11, 23, 4, 14, 6, 13, 13, 6, 11, and 6 tons. The plant has production costs of \$600, \\$110, and \$60 per ton for each stage, respectively, can produce up to 25 tons per week at each stage subject to availability. Stage 1 will not be available weeks 3, 5, 8, 9, and 11; stage 2, weeks 4, 8, and 10; stage 3 will not be available weeks 2, 6, 8, 12. When not available to produce this product, the capacity will be used for other products or scheduled maintenance. The inventory costs are \\$3.50, \$4.00, and \\$4.40 per ton-month, for stages 1-3, respectively, and the initial and final inventory for all stages is five tons. Determine the amount of each product that should be produced to minimize total costs over the planning horizon.