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Previously in IEMS 310…

Previously in IEMS 310…. Notation of optimization problems Linear Programs Sensitivity Analysis / Duality Assignment and Network Flow Problems Tricks: Piecewise linear functions. Agenda. Another trick: absolute value Another LP… Sequential Decision Processes

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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 • Assignment and Network Flow Problems • Tricks: • Piecewise linear functions

  2. Agenda • Another trick: absolute value • Another LP… • Sequential Decision Processes • … shortest path (Ch 5)and other dynamic programs

  3. Logistics • TA OH now Thurs 1:30-3:30 C236 • Hw deadline remains Fri 5pm • mailbox or in person in C236 • use Blackboard drop-box for excel files • Suggest start reading Ch 5.1-5.5 • Will discuss projects on Monday

  4. |errori| errori penaltyi errori Absolute Value Trick • from Hw 2 • errori = predicted by regression - yi • penalize overestimates

  5. Sequential Decision Process • Discretize Time • Variables for each period • for example: #workers Wk, inventory level Ik period k=1 2 3 4 5 …

  6. Production Planning (4.12) • List time periods • maybe add an extra at beginning and end • List variables (things to keep track of) • states and actions • Make timeline for a single period • Add constraints • “laws of motion”: constraints connecting a period to the next • Add objective • Solve

  7. Problem Summary • Producing snow tires • Monthly demand: Oct-March • Goal: cheaply meet demand • Decisions: • hire or fire, overtime, production quantity • Inventory cost, trainees are less productive

  8. Production Planning (4.12) • List time periods • maybe add an extra at beginning and end • List variables (things to keep track of) • states and actions • Make timeline for a single period • Add constraints • “laws of motion”: constraints connecting a period to the next • Add objective • Solve

  9. Production Planning (4.12) • List time periods • maybe add an extra at beginning and end • List variables (things to keep track of) • states and actions • Make timeline for a single period • Add constraints • “laws of motion”: constraints connecting a period to the next • Add objective • Solve

  10. Variables For each period • # hired Hk, #fired Fk • #trained and trainee workers • total #workers Wk, #trained workers Tk • units produced • overtime used • Rk units produced with regular hours, • Ok units produced with overtime • inventory Ik

  11. Production Planning (4.12) • List time periods • maybe add an extra at beginning and end • List variables (things to keep track of) • states and actions • Make timeline for a single period • Add constraints • “laws of motion”: constraints connecting a period to the next • Add objective • Solve

  12. Timeline Production Decision Rk #units with regular time Ok #units with overtime Period k Ik #units inventory prev. period next period Dk #units shipped Hk #hired Fk #fired Wk #workers Tk #trained workers

  13. Production Planning (4.12) • List time periods • maybe add an extra at beginning and end • List variables (things to keep track of) • states and actions • Make timeline for a single period • Add constraints • “laws of motion”: constraints connecting a period to the next • Add objective • Solve

  14. Constraints • Inventory: I1=0, Ik+1=Ik+Rk+Ok-Dk • Meeting Demand: Ik+1 ≥ 0 • Workforce W1=90, Wk+1=Wk+Hk-Fk Tk=Wk-Fk, T7=100 • Capacity Rk≤18Tk+8Hk Ok ≤(18/4)Tk • Nonnegativity

  15. Production Planning (4.12) • List time periods • maybe add an extra at beginning and end • List variables (things to keep track of) • states and actions • Make timeline for a single period • Add constraints • “laws of motion”: constraints connecting a period to the next • Add objective • Solve

  16. Objective • Hiring / Firing costs $3000*(H1+…+H7) $7000*(F1+…+F7) • Compensation $2600*(W2+…+W7) $2600*1.5*(O1+…+O7)/18 • Inventory $40*(I1+…+I7)

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