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[1] - Models are used because 1 less expensive time...

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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 non-binding 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/non-binding status. (the allowable increase/decrease). Binding Constraint : Remove and it changes the feasible region and Opt. Solution. Non-Binding 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 ) Non-Basic 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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