Home | | Business Maths 11th std | Summary of Operations Research

# Summary of Operations Research

Linear programming problem(LPP) is a mathematical modeling technique which is used to allocate limited available resources in order to optimize (maximize or minimize) the objective function.

Summary

Linear programming problem(LPP) is a mathematical modeling technique which is used to allocate limited available resources in order to optimize (maximize or minimize) the objective function.

Short form of LPP Objective function: A function Z = c1x 1 +c2x2 +…. +cnxn which is to be optimized (maximized or minimized) is called objective function.

Decision variable: The decision variables are the variables we seek to determine to optimize the objective function. xj , j = 1,2,3,…,n , are the decision variables.

Solution: A set of values of decision variables xj,j =1,2,3,…,n satisfying all the constraints of the problem is called a solution to that problem.

Feasible solution: A set of values of the decision variables that satisfies all the constraints of the problem and non-negativity restrictions is called a feasible solution of the problem.

Optimal solution: Any feasible solution which maximizes or minimizes the objective function is called an optimal solution.

Feasible region: The common region determined by all the constraints including non-negative constraints xj≥0 of a linear programming problem is called the feasible region ( or solution region) for the problem.

Linear programming problems which involve only two variables can be solved by graphical method.

It should be noted that the optimal value of LPP occurs at the corner points of the feasible region

Network is a diagrammatic representation of various activities concerning a project arranged in a logical manner.

An activity is a task or item of work to be done, that consumes time, effort, money or other resources

The beginning and end points of an activity are called events (or nodes).

Critical path: The longest path connected by the activities in the network is called the critical path. A path along which it takes the longest duration.

Tags : Maths , 11th Business Mathematics and Statistics(EMS) : Chapter 10 : Operations Research
Study Material, Lecturing Notes, Assignment, Reference, Wiki description explanation, brief detail
11th Business Mathematics and Statistics(EMS) : Chapter 10 : Operations Research : Summary of Operations Research | Maths