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 1.Thurs 9-11, hwk due Fri in class 2.Thurs 1:30-3:30, hwk due Fri in class

4. 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 quantity cost quantity profit

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. The Network Flow Problem 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 x1x1 x2x2 x3x3 x4x4 x5x5 x6x6 x7x7 x9x9 x8x8 L 1 ≤ x 1 ≤ U 1 x 1 - x 2 - x 5 = 0 min c 1 x 1 + c 2 x 2 + … L 1,U 1 c1c1

8. Recognize the structure –includes assignment problem LP If the flow bounds (L i,U i ) are integer, then solution will be integer Network Flow 213 732 50.51.1 jobs machines jobsmachines

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