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Previously in IEMS 310…

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,”

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Previously in IEMS 310…

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  1. Previously in IEMS 310… • Notation of optimization problems • Linear Programs • Sensitivity Analysis • Duality • Piecewise linear functions • Assignment Problems

  2. 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

  3. Yue’s Office Hours Options: • Fri 3-5, (current) hwk due at 5 • Thurs 9-11, hwk due Fri in class • Thurs 1:30-3:30, hwk due Fri in class

  4. cost quantity profit quantity Economies of Scale • Related to piecewise linear functions • costs are concave • decreasing derivative • decreasing marginal costs • returns/profits are convex • Diseconomies of scale are the opposite

  5. 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

  6. Agenda • Network Flow problem • transportation • staffing • Sequential Decision Processes • production problem

  7. x2 x1 x3 x4 x5 x6 x7 x8 x9 The Network Flow Problem c1 • data: • 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 L1,U1 L1 ≤ x1≤U1 x1 - x2 - x5 = 0 min c1x1 + c2x2 + …

  8. Network Flow • Recognize the structure • includes assignment problem • LP • If the flow bounds (Li,Ui) are integer, then solution will be integer jobs machines machines jobs

  9. 4.5 Transportation Problem Plants (supply) Depots (demand) ≤ 2500 =2000 ≤ 4000 =3000 ≤ 3500 =2500 =1500

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