Previously in IEMS 310 Notation of optimization problems
Previously in IEMS 310… • • • Notation of optimization problems Linear Programs Sensitivity Analysis Duality Piecewise linear functions Assignment Problems
Logistics • Hwk 2 due Friday • Yue prefers – “hard copy so I can mark on it, ” – “and email me the excel file in case I need to look through. ” • Please fill out survey
Yue’s Office Hours Options: 1. Fri 3 -5, (current) hwk due at 5 2. Thurs 9 -11, hwk due Fri in class 3. Thurs 1: 30 -3: 30, hwk due Fri in class
Economies of Scale • Related to piecewise linear functions • costs are concave – decreasing derivative cost – decreasing marginal costs • returns/profits are convex quantity profit quantity • Diseconomies of scale are the opposite
Hwk 1 Problem B • Design optimization – price, features, shape, packaging • • • Civil: price with safety constraint ME: air conditioning budgeting websites: load, reliability Chem Eng: reaction throughput
Agenda • Network Flow problem – transportation – staffing • Sequential Decision Processes – production problem
The Network Flow Problem • data: c 1 x 1 L 1, U 1 – network structure – bounds on flow through each link – cost/profit per unit flow on each link • decision variables: flow on links • constraints: – bounds on flow through links – conservation of flow • max profit / min cost x 2 x 3 x 5 x 6 x 4 x 7 x 8 x 9 L 1 ≤ x 1 ≤ U 1 x 1 - x 2 - x 5 = 0 min c 1 x 1 + c 2 x 2 + …
Network Flow • Recognize the structure – includes assignment problem jobs machines 2 1 3 7 3 2 5 0. 5 1. 1 jobs machines • LP • If the flow bounds (Li, Ui) are integer, then solution will be integer
4. 5 Transportation Problem ≤ 2500 Plants (supply) Depots (demand) =2000 ≤ 4000 =3000 ≤ 3500 =2500 =1500
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