**Operational Research Handwritten Notes**

## What is Operational Research ?

Operations research (OR) is an analytical method of problem-solving and decision-making that is useful in the management of organizations. In operations research, problems are broken down into basic components and then solved in defined steps by mathematical analysis.

## What is Linear Programming ?

Linear programming is a powerful quantitative technique (or operational research technique) designs to solve allocation problem.

## What are Decision Variables ?

The decision variables refer to the economic or physical quantities, which are competing with one another for sharing the given limited resources.

## What is Objective function ?

The objective function of a linear programming problem is a linear function of the decision variable expressing the objective of the decision maker.

## What are Constraints ?

The constraints indicate limitations on the resources, which are to be allocated among various decision variables.

## What is non-negativity restriction ?

Non-negativity restriction indicates that all decision variables must take on values equal to or greater than zero

## What is Divisibility ?

Divisibility means that the numerical values of the decision variables are continuous and not limited to integers.

### Topics in our Operational Research Handwritten Lecture Notes PDF

In these “* Operational Research Handwritten Lecture Notes PDF*”, you will study the broad and in depth knowledge of a range of operation research models and techniques, which can be applied to a variety of industrial applications

The topics we will cover will be taken from the following list:

**Introduction to Operations Research:** Basics definition, scope, objectives, phases, models, and limitations of Operations Research. Linear Programming Problem – Formulation of LPP, Graphical solution of LPP. Simple Method, Artificial variables, big-M method, two-phase method, degeneracy, and unbound solutions.

**Transportation Problem:** Formulation, solution, unbalanced Transportation problem. Finding basic feasible solutions – Northwest corner rule, least cost method, and Vogel’s approximation method. Optimality test: the stepping stone method and MODI method.

**Assignment model:** Formulation. The Hungarian method for the optimal solution. Solving the unbalanced problem. Traveling salesman problem and assignment problem Sequencing models. Solution of Sequencing Problem – Processing n Jobs through 2 Machines – Processing n Jobs through 3 Machines – Processing 2 Jobs through m machines – Processing n Jobs through m Machines.

**Dynamic programming:** Characteristics of dynamic programming. Dynamic programming approach for Priority Management employment smoothening, capital budgeting, Stage Coach/Shortest Path, cargo loading and Reliability problems Games Theory. Competitive games, rectangular game, saddle point, min-max (max-min) method of optimal strategies, value of the game. Solution of games with saddle points, dominance principle. Rectangular games without saddle point – mixed strategy for 2 X 2 games.

**Replacement Models:** The Replacement of Items that Deteriorate whose maintenance costs increase with time without change in the money value. Replacement of items that fail suddenly: individual replacement policy, group replacement policy

**Inventory models:** Inventory costs. Models with deterministic demand – model (a) demand rate uniform and production rate infinite, model (b) demand rate non-uniform and production rate infinite, model (c) demand rate uniform and production rate finite.