Theory Flashcards
What is a Mathematical Problem and what is its purpose?
- A math model is a quantitative representation of a real problem
- The purpose is to represent the problem in a concise form
What are the types of models? Elaborate
- Descriptive models; simply describe a situation
- Optimization model: model that suggest a desirable course of action
What are the proprieties of Linear Programming?
1) Proportionality
2) Divisibility
3) Additivity
Proportionality
Proportionality means that if the level of any activity is multiplied by a
constant factor, the contribution of this activity to the objective, or to any
of the constraints in which the activity is involved, is multiplied by the same
factor.
* Proportionality is a perfectly valid assumption in the product mix model,
but it is often violated in certain types of models.
* For example, in various blending models used by petroleum companies, chemical
outputs vary in a nonlinear manner as chemical inputs are varied.
Additivity
The additivity property implies that the sum of the contributions from the various activities to a particular constraint equals the total contribution to that constraint.
* The additivity property implies that the contribution of any decision
variable to the objective or to any constraint is independent of the levels of the other decision variables
Divisibility
The divisibility property simply means that both integer and non-integer
levels of the activities are allowed.
* In general, if you want the levels of some activities to be integer values,
there are two possible approaches:
1. You can solve the LP model without integer constraints, and if the solution turns
out to have fractional values, you can attempt to round them to integer values; or
2. You can explicitly constrain certain changing cells to contain integer values.
What are the 2 things that can go wrong in Solver? Elaborate
- Unboundedness; it be large or small as you like – the objective function
- Infeasibility- no feasible solution
Examples of LP applications
1) Blending model
2) Investment plan
3) Production process plan
What is a node?
Geographical location
what is an arc and arca capacity?
- An arc, indicated by an arrow,
generally represents a route for
getting a product from one node
to another. - Upper limits are called arc
capacities, and they can also be
shown on the model.
what is flow?
The decision variables are usually
called flows. They represent the
amounts shipped on the various
arcs. They can also contain the
unit shipping costs.
What is an inflow?
- An arc pointed into a node
What is an outflow?
- An arrow pointed out of a node
What is required for a typical transportation problem?
- capacities (or supplies),
- demands (or requirements), and
- unit shipping (and production)
costs.
What lines are the feasible solution in a graph? integer model
vertical lines
