LP deals with the optimization of a function of variables known as objective function/ cost function, subject to a set of linear equations and/or inequalities called constraints.
Assumptions in LP
- Proportionality: some sort of proportionality exists between the objective function and constraints.
- Continuity: decision variables can take any non-negative value that satisfies the constraints. However, some problems need integer values.
- Certainty: all LP problems are assumed to be deterministic.
- Finite Choices: a limited number of choices are available to the decision maker.
Formulation of LP problem.
Step 1: find the key-decision to be made by looking for variables.
Step 2: assume symbols for the variables and find the extents of variation.
Step 3: find feasible alternatives mathematically in terms of variables.
Step 4: mention the objective function quantitavely, as a linear function. Prepare a cost function.
Step 5: represent the influencing factors or constraints in mathematical terms.
Advantages of LP
- attain optimum use of productive factors
- improve quality of decisions
- can handle multiple constraints
- highlights the bottlenecks
Disadvantages of LP
- for large problems there are too many limitations and constraints, this makes the problem too difficult to solve even with computers
- the problems have to linearly approximated thus, the obtained results may be far from reality
- only static situations can be dealt with
- assume all values are known a priori with full certainty
- sometimes, the objective function and constraints cant be expressed in linear form
- multi-objective tasks cant be dealt with