1. REVIEW FOR EXAM 1
Chapters 3, 4, 5 & 6

2. Why models?
Because all decisions are made, all actions are taken on the basis of models
We don’t have a choice

3. Is model-building art or science?
A little of both

4. Three Decision Environments
Certainty
Risk & Uncertainty
Change, complexity and causality

5. 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

6. How do we decide what to include in our model?

7. Methodology for Model Formulation
Problem Definition
Mathematical Modeling
Solution of the Model
Communication/Marketing of the Results

8. 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

9. 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?

10. 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?

11. 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

12. 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

13. 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

14. 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

15. 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

16. Network Model types Transportation Transhipment Assignment
Production/Scheduling
Shortest route
Minimal spanning tree
Traveling salesman
Maximal flow

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

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

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

20. 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

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

22. Minimal spanning tree
To find what??
Use the greedy algorithm

23. 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

24. Maximal flow
To find the bottleneck in an infrastructure

25. Chapter 5--Integer programming
Hardest to solve, algorithmically
Rounding??
Sensitivity data--NO

26. Problem types Facility location Fixed charge Either/or Go/no go
Discrete design--OPTIMIZED CURRICULUM
Capital budgeting

27. Model types
Pure
Mixed
Binary

28. Algorithm types Cutting planes--for pure problems
Uses Simplex
Branch & Bound--for everything else
Uses simplex

29. What else??