REVIEW FOR EXAM 1

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REVIEW FOR EXAM 1

• Chapters 3, 4, 5 6

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Why models?

• Because all decisions are made, all actions are
  taken on the basis of models
• We dont have a choice

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Is model-building art or science?

• A little of both

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Three Decision Environments

• Certainty
• Risk Uncertainty
• Change, complexity and causality

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How do we determine which model paradigm to use?

• Optimization models or simulation models
• Deterministic models or probabilistic ones
• Static models or dynamic ones
• Linear models or nonlinear ones

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How do we decide what to include in our model?
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Methodology for Model Formulation

• Problem Definition
• Mathematical Modeling
• Solution of the Model
• Communication/Marketing of the Results

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Chapter 3

• Simple model formulation
• Where solutions occur on the feasible region
  defined by the constraints
• The optimal solution is always ______.
• Sensitivity
• Ranging reports
• reduced costs
• shadow prices
• complementary slackness

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Reduced cost

• If a decision variable is in the basis, its
  reduced cost is ????
• If a decision variable has an objective
  coefficient of 10 and a reduced cost of 5
• Is the variable in solution?
• If the obj. coeff is taken to 7, what happens?
• If the obj. coeff is taken to 4, what happens?

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Shadow price

• Measures the degree of sensitivity of the Obj.
  Fcn. to a unit change in a constraint RHS
• If a constraint has slack or surplus, then its
  shadow price is?
• If a constraint has a shadow price of 5 and its
  RHS is increased by 10 (within the range of
  feasibility), then the obj. fcn. Will increase by?

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Range of feasibility

• Applies to obj fcn, constraints, technology
  coefficients, WHAT???
• Remember these are ranges in which the solution
  is unchanged
• However, when you change RHS, variables in
  solution may have their values change

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Range of Optimality

• Again, this is a range over which the same
  variables remain in solution
• When within the range, do the basis variables
  (the variables in solution) change?
• However, the objective function value may change,
  right?
• Every time? For any coefficient?
• Look at the Practice exam
• Questions 55, 56

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Chapter 4--Robust LP

• More substantial models
• Definitional variables
• resulting in equality constraints that must be
  added
• Interpretation of the output
• Look at the exam
• Questions 59, 60
• Minimization models

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Chapter 6--Network Optimization

• Always an underlying network
• a decision variable for each arc
• a constraint for each node
• fast solution algorithms can solve large models
  on small computers
• Guaranteed integer solution values
• Always an associated linear programming model

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Frequency

• 80 of math programming probs are networks
• Concerned with the infrastructure that we.
• drive on
• ride on
• talk on
• telecommmunicate on
• e-anything on

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Network Model types

• Transportation
• Transhipment
• Assignment
• Production/Scheduling
• Shortest route
• Minimal spanning tree
• Traveling salesman
• Maximal flow

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Transportation

• 10 sources of supply, 15 destinations of demand
• How many decision variables?
• How many constraints?
• Solution algorithm gives us sensitivity
  information

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Transhipment

• Essentially a transportation problem with
  intervening transhipment nodes
• Solved using the out-of-kilter algorithm
  (generalized network model in WINQSB)

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Assignment

• A special case of the transportation problem with
  demand and supply numbers of 1
• But solvable with its own Hungarian assignment
  algorithm

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Production/Scheduling

• Formulated as a Transportation problem
• Tells you where and when to produce and when to
  ship so as to minimize costs, or maximize profits
  at the demand nodes
• SEE THE EXAM

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Shortest Route

• Should be able to find it for small models
• Use the node-labeling technique I showed you in
  class

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Minimal spanning tree

• To find what??
• Use the greedy algorithm

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Traveling salesman

• Hard to solve algorithmically
• Gives us the minimum distance or minimum cost
  tour
• that takes us through each node (city) exactly
  once
• 20 city problems have 500,000 constraints--to
  prevent subtours

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Maximal flow

• To find the bottleneck in an infrastructure

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Chapter 5--Integer programming

• Hardest to solve, algorithmically
• Rounding??
• Sensitivity data--NO

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Problem types

• Facility location
• Fixed charge
• Either/or
• Go/no go
• Discrete design--OPTIMIZED CURRICULUM
• Capital budgeting

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Model types

• Pure
• Mixed
• Binary

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Algorithm types

• Cutting planes--for pure problems
• Uses Simplex
• Branch Bound--for everything else
• Uses simplex

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What else??