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

  1. Proportionality: some sort of proportionality exists between the objective function and constraints.
  2. Additivity:
  3. Continuity: decision variables can take any non-negative value that satisfies the constraints. However, some problems need integer values.
  4. Certainty: all LP problems are assumed to be deterministic.
  5. 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

  1. attain optimum use of productive factors
  2. improve quality of decisions
  3. can handle multiple constraints
  4. highlights the bottlenecks

Disadvantages of LP

  1. for large problems there are too many limitations and constraints, this makes the problem too difficult to solve even with computers
  2. the problems have to linearly approximated thus, the obtained results may be far from reality
  3. only static situations can be dealt with
  4. assume all values are known a priori with full certainty
  5. sometimes, the objective function and constraints cant be expressed in linear form
  6. multi-objective tasks cant be dealt with