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Terms in this set (29)
Mathematical Programming (MP)
a technique for allocating limited resources most effectively when there are competing demands for these resources (often referred to as optimization)
Linear Programming
the simplest form of mathematical programming (LP)
What kind of Technique is LP, and why?
it is a deterministic technique because all of the input data and parameters are known with certainty
Characteristics of Optimization problems
-one or more decisions must be made
-goal of objective (max. profit/min. costs)
-restrictions or constraints placed on alternatives
What are the basic assumptions of an LP model
1. Certainty
2. Proportionality
3. Additivity
4. Divisibility
Steps in formulating LP models
1. Understand the problem
2.Identify decision variables
3. State the objective function
4. State the constraints
What is a feasible solution?
a solution that satisfies all the constraints
What is an infeasible solution?
a solution that does not satisfy one or more of the constraints
What is the optimal solution?
the feasible solution that results in the maximum/minimum objective
How would you get alternate optimal solutions?
the objective function would need to be parallel to the binding constraint and the solution would be a line segment
What two options do you need to change in solver?
1. Simplex LP
2. Make unconstrained variables non-negative
What does the sensitivity analysis tell us?
it provides a better picture of how the solution to a problem will change is different factors in the model change
what is the allowable inc./dec.?
it is the range of values for which the optimal solution will remain the same (corner point values will not change), but the value of the objective function and the slope of the profit line will change
constancy
assuming all other coefficients remain constant, underscores the fact that the allowable inc./dec. shown in the Sensitivity report apply only if all other coefficients in the LP do not change
What allowable inc./dec. would a solution that is a line segment yield?
0
Binding Constraints
constraints that have zero slack in the optimal solution to an LP problem
What does it mean to have a binding constraint?
this means that we can no longer improve the objective problem because we have used all of our resources.
What is the shadow price value?
it is the value of one additional unit of a scarce resource
What indicates a scarce resource?
a binding constraint with a non-zero shadow price
how do you calculate the possible gain with a scarce resource?
change in target cell = change in resource*shadow price (must be within the allowable inc./dec.)
what is a sunk/fixed cost?
1. one whose cost is not included in the target cell
2. one that stays the same regardless of quantity, we want excel solver to ignore them
what is a variable cost?
1. one whose cost is included in the target cell
i.e. shadow price is what you would gain net of the variable cost for one more unit of the resource
what is reduced cost?
it is the amount that profit would have to change by to make it worthwhile to make the product at the optimal solution (sales price inc./costs dec.)
how do you use reduced cost?
new profit = objective coefficient - reduced cost
when does a negative shadow price happen?
it occurs when the constraint is binding and is greater than or equal to in a maximization probem
how do you use a negative shadow price?
impact on profit = change in resource*shadow price
what is an ILP problem
when some or all of the decision variables in an LP problem are restricted to assuming only integer values
what two things do you need to do on excel for ILP problems
1. make all changing cells = integer
2. under options, unselect ignore integer constraints
characteristics and assumptions for transportation models
1. supply
2. demand/capacity
3. quantities
4. shipping cost
5. no transshipment
6. integer values
7. problem formulation
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