**Operational Research Handwritten Notes**

In these “* Operational Research Handwritten 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.

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.

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

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

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

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

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

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