Models
are used because 1) less expensive, time
consuming and risky, and more feasible. They are
abstraction of a real object can be (iconic (replica),
analog, or mathematical)
LP Assumptions:
Proportionality Assumption
Contribution of a variable is proportional to its value.
Additivity Assumptions
Contributions of variables are independent.
Divisibility Assumption
Decision variables can take fractional values.
Certainty Assumption
Each parameter is known with certainty.
Infeasible problem
has every possible solution
violate one or more constraints.
Unbounded problem is where Ob. function can
increase indefinitely without reaching a max value.
Multiple optimal solutions
can occur when the
objective function is parallel to a constraint line. And
when the feasible region is on a constraint.
Sensitivity range (Range of Optimality)
is the
range of coeff. values that will keep the current Opt.
Sol optimal.
To Find: equate the ratio of the current slope with the
slope of the constraint in question on that axis, the
difference between the current value of coeff and the
calculated level is the range.
Shadow price
is the amount of revenue associated
with another unit of the constraint. The total amount
of revenue that can be obtained at this marg. profit
level, is the shadow price * allowable increase. (0 for
nonbinding constraint)
Range of Feasibility
is range of RHS of constraints
that will 1) keep the shadow price the same and 2) it’s
the amount that a line can go before it changes it’s
binding/nonbinding status. (the allowable
increase/decrease).
Binding Constraint
: Remove and it changes the
feasible region and Opt. Solution.
NonBinding Constraint:
Remove and it changes
feasible region but not Opt. Sol. Shadow price is
always 0.
Redundant:
Remove changes neither feasible region
or Opt Sol.
Standard Form:
putting your constraints as
equalities using slack/surplus var’s,
Reduced Cost
is the amount that an obj function
coeff needs to improve by to make it part of the
solution (not cheap/profitable enough to use resources
on it). All used variables will have ‘0’ as reduced cost.
It is  for max, and + for min
Dual Cost
is the amount the objective function will
improve
per unit increase in constraint. (similar to
Shadow price, but
opposite sign for min
)
NonBasic Variable:
if reduced cost is 0, then an
alternative solution exists, Reduced cost will be ‘‘ or
‘0’ for max prob, and will be ‘+’ or ‘0’ for min problem.
Transshippment Prob:
Intermediate nodes to
accept and ship goods. Must have constraint that has
stuff going into to note = stuff going out.
Assignment Prob:
Make sure that value of
constraint<= 1, (only can do 1 job).
Multiple Objective Problems:
3 different
approaches – weighted approach, absolute priorities,
goal programming.
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 Fall '11
 serolbulkan
 Optimization, objective function

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