691-901 CMSC/OPER Fall 2003 Homework 5 Assigned: November 6, 2003 Due: November 13, 2003
Oilco has oil fields in San Diego and Los Angeles. The San Diego field can produce up to 500,000 barrels per day, and the Los Angeles field can produce up to 400,000 barrels per day. Oil is sent from the fields to a refinery, either in Dallas or in Houston (assume each refinery has unlimited capacity). To refine 100,000 barrels costs $700 at Dallas and $900 at Houston. Refined oil is shipped to customers in Chicago and New York. Chicago customers require 400,000 barrels per day, and New York customers require 300,000 barrels per day. The costs of shipping 100,000 barrels of oil (refined or unrefined) between cities are shown in the following From/To table: Los Angeles San Diego Dallas Houston Dallas $300 $420 ------Houston $1100 $100 ------New York ------$450 $470 Chicago ------$550 $530
a. Formulate a minimum cost flow problem that can be used to determine how to minimize the total cost of meeting all demands. b. If each refinery had a capacity of 500,000 barrels per day, how would your minimum cost flow problem be modified? Chapter 9, problem 9.16 Chapter 9, problem 9.17 (b) (if you can get a solution to the maximum flow problem by visual inspection rather than running an algorithm, that's fine). Chapter 9, problem 9.20 (you do not have to answer the question "How many iterations does the primal-dual algorithm require to solve this problem?")