MIE376 Lec9 DWD Incomplete.page2

MIE376 Lec9 DWD Incomplete.page2 - there is some way of...

Info iconThis preview shows page 1. Sign up to view the full content.

View Full Document Right Arrow Icon
MIE376 Mathematical Programming Lecture Notes Daniel Frances 2011 2 Max 70Q 1 + 60Q 2 subject to 7Q 1 + 5Q 2 ≤ 30; 3 Q 1 + 2Q 2 ≤ 1 5; Q 1 + Q 2 4; Q i ≥ 0 Currently the optimal solution is for Quid to make 4 tons of Steel 1, no Steel 2, at revenue of $280. Its production limited by its furnace time availability. 2-Plant system Suppose that the two plants are purchased by one owner, who plans to share the availability of the iron ore among the two plants, starting with a total availability of 80 tons, and who wishes to maximize the overall revenue from the two plants. Max 90P 1 + 80P 2 + 70Q 2 + 60Q 2 s.t. 8P 1 + 6P 2 + 7Q 2 + 5Q 2 ≤ 80; 3 P 1 + P 2 ≤ 12; 2P 1 + P 2 ≤ 10; 3 Q 1 + 2Q 2 ≤ 15; Q 1 + Q 2 ≤ 4; P i , Q i ≥ 0 If we rewrite the new LP in a “neater” format we observe the following Max 90P 1 + 80P 2 + 70Q 1 + 60Q 2 subject to 8P 1 + 6P 2 + 7Q 1 + 5Q 2 ≤ 80; 3P 1 + P 2 1; 2P 1 + P 2 ≤ 10; 3Q 1 + 2Q 2 ≤ 15; Q 1 + Q 2 ≤ 4 P i , Q i ≥ 0 The two plant LPs are only linked through the objective and the iron ore constraint. The question arose if
Background image of page 1
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: there is some way of solving the two LPs in some coordinated fashion, or is it necessary to merge the two LPs into a single LP in order to obtain the overall optimal solution. Sketch of a Coordination approach Suppose there is some way to coordinate the operation of the two plants, without the necessity of merging all the data into a single LP. Suppose also, that the coordination process takes the form of an iterative process. • Each plant makes production offers of certain production at a given price. We will make up symbols for the quantities offered by each plant. The prices can easily be derived when we need them. Let Pi k the k th production offer from Plant 1 for steel i. Similarly let Qi k be the k th production offer from plant 2 for the two types of steel....
View Full Document

This note was uploaded on 07/10/2011 for the course MIE 376 taught by Professor Daniel during the Spring '11 term at University of Toronto.

Ask a homework question - tutors are online