15.053 Lecture Notes - Lecture 1: Linear Programming, Umber, Torte
Document Summary
Given a collection of numbers, partition them into two groups such that the difference in the sums is as small as possible. We split them into {7, 10, 13, 17} and {20, 22} The difference is 5, but we can do better. We can split them into {7, 17, 20} and {10, 13, 22} Excel solver, opensolver with cbc, opensolver with groubi. Algorithms, duality theory: obtaining bounds on distance form optimality, convex analysis. Decision variables: the elements that are under the control of the decision maker. The work schedules of each employee, the level of investments in a portfolio, what subjects a student should take each semester. Minimize cost, maximize expected return, make the last semester as enjoyable as possible. No worker can work more than 5 consecutive days. There is at most 2% investment in any stock portfolio. Students must take a prerequisite of a subject before taking the subject.
