Optimization technique in Management science and Operation research
Linear programming (LP) is a powerful tool in modelling many applications. LP has attracted most of its attention in optimization during the last six decades for two main reasons: Applicability and Solvability.
Basic components of LP
- Decision variable: describe our choices that are under our control
- Objective functions: describes a criterion that we wish to minimize
- Constraints: describe the limitations that restrict our choices for decision variables
- Optimal solution: is one of the feasible solutions where the objective function is either maximum or minimum, for example, maximum profit or minimum cost. It is the best value of the objective function.
- A feasible solution is the set of possible values for decision variables that meets all of the constraints. LP problem is feasible if at least one solution is feasible.
- The infeasible solution is the set of possible values for decision variables that do not meet all the constraints, i.e., there is no optimal solution. LP problem is an infeasible solution if no solution exists that meets all of the constraints.
- The feasible region is a region which covered from all the possible set of values that meet the constraints or intersection of all the constraints. It includes all the inequalities, equalities, and integer constraints.
- Non-negativity constraints for decision variables which accept only non-negative values. Such constraints are greater than or equal to zero
