Transcript Yue’s Office Hours - Northwestern University

Previously in IEMS 310…
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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:
• 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
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
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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 x1
L1,U1
– 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
x2
x3
x5
x4
x6
x7
x8
x9
L1 ≤ x1 ≤ U1
x1 - x2 - x5 = 0
min c1x1 + c2x2 + …
Network Flow
• Recognize the structure
– includes assignment problem
jobs
machines
2
1
3
7
3
2
5
0.5
jobs
machines
1.1
• 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