Problem 1 Facility Location. A paper products manufacturer has enough capital to build and manage some additional manufacturing plants in the United States in order to meet increased demand in three cities: New York City, NY; Los Angeles, CA; and Topeka, KS. The company is considering building in Denver, CO; Seattle, WA; and St. Louis, MO. Max Operating Capacity 400 tons/day 700 tons/day Denver Seattle $10/ton $17/ton $5/ton $11/ton.. $18/ton $28/ton Los Angeles . The cost of building plants in these cities is fi $10,000,000 in Seattle. Topeka New York City Figure 1: Graphical representation of the given data = Unmet Demand 300 tons/day 100 tons/day • Due to geographic constraints, plants in Denver and Seattle would have a maximum operating capacity k₂ of 400 tons/day and 700 tons/day respectively. 500 tons/day $5,000,000 in Denver and f2 = • The cost c¿j per ton of transporting paper from city i to city j is outlined in Figure [1] • The unmet demand d; for Los Angeles, Topeka, and New York City are 300 tons/day, 100 tons/day, and 500 tons/day, respectivey. The problem is to decide which plants to build, how much paper to produce in each plant, and how best to ship paper from the plants to the customers in the way which minimizes total expense.
Problem 1 Facility Location. A paper products manufacturer has enough capital to build and manage some additional manufacturing plants in the United States in order to meet increased demand in three cities: New York City, NY; Los Angeles, CA; and Topeka, KS. The company is considering building in Denver, CO; Seattle, WA; and St. Louis, MO. Max Operating Capacity 400 tons/day 700 tons/day Denver Seattle $10/ton $17/ton $5/ton $11/ton.. $18/ton $28/ton Los Angeles . The cost of building plants in these cities is fi $10,000,000 in Seattle. Topeka New York City Figure 1: Graphical representation of the given data = Unmet Demand 300 tons/day 100 tons/day • Due to geographic constraints, plants in Denver and Seattle would have a maximum operating capacity k₂ of 400 tons/day and 700 tons/day respectively. 500 tons/day $5,000,000 in Denver and f2 = • The cost c¿j per ton of transporting paper from city i to city j is outlined in Figure [1] • The unmet demand d; for Los Angeles, Topeka, and New York City are 300 tons/day, 100 tons/day, and 500 tons/day, respectivey. The problem is to decide which plants to build, how much paper to produce in each plant, and how best to ship paper from the plants to the customers in the way which minimizes total expense.
Computer Networking: A Top-Down Approach (7th Edition)
7th Edition
ISBN:9780133594140
Author:James Kurose, Keith Ross
Publisher:James Kurose, Keith Ross
Chapter1: Computer Networks And The Internet
Section: Chapter Questions
Problem R1RQ: What is the difference between a host and an end system? List several different types of end...
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(a) Model this problem as an Integer
(b) Ignoring any integer constraints, derive the dual of the IP you found in part (a). Hint: remember
that a binary constraint decomposes into ≥ 0, ≤ 1, and Integer.
Transcribed Image Text:Problem 1 Facility Location. A paper products manufacturer has enough capital to build and
manage some additional manufacturing plants in the United States in order to meet increased
demand in three cities: New York City, NY; Los Angeles, CA; and Topeka, KS. The company is
considering building in Denver, CO; Seattle, WA; and St. Louis, MO.
Max Operating
Capacity
400 tons/day
700 tons/day
Denver
Seattle
$10/ton
$17/tom
$5/ton
$11/ton...............
$18/ton
$28/ton
Los Angeles
Topeka
New York City
Figure 1: Graphical representation of the given data
Unmet Demand
300 tons/day
100 tons/day
500 tons/day
• Due to geographic constraints, plants in Denver and Seattle would have a maximum operating
capacity k of 400 tons/day and 700 tons/day respectively.
• The cost fi of building plants in these cities is f₁ = $5,000,000 in Denver and f2
$10,000,000 in Seattle.
• The cost cij per ton of transporting paper from city i to city j is outlined in Figure [1
• The unmet demand d; for Los Angeles, Topeka, and New York City are 300 tons/day, 100
tons/day, and 500 tons/day, respectivey.
The problem is to decide which plants to build, how much paper to produce in each plant, and how
best to ship paper from the plants to the customers in the way which minimizes total expense.
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