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Previously in IEMS 310…

This document outlines key concepts related to optimization problems within IEMS 310, focusing on linear programs, sensitivity analysis, duality, piecewise linear functions, and assignment problems in logistics. It reviews the intricacies of economies and diseconomies of scale, emphasizing cost and profit implications. Detailed homework assignments, office hours, and related subjects like network flow problems and transportation challenges are addressed, providing students with a structured approach to design optimization in various engineering contexts.

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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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