OPERATION RESEARCH / QUANTITATIVE TECHNIQUES FOR MANAGEMENT (PPT)

 

QUANTITATIVE TECHNIQUES FOR MANAGEMENT

Unit-I

 Linear Programming: Formulation of L.P. Problems, Graphical Solutions (Special cases: Multiple optimal solutions, infeasibility, unbounded solution); Simplex Methods (Special cases: Multiple optimal solutions, infeasibility, degeneracy, unbounded solution) Big-M method and Two-phase method; Duality and Sensitivity (emphasis on formulation & economic interpretation); Formulation of Integer programming, Zero-one programming, Goal Programming.

Linear Programming:

—  Introduction: Linear Programming is a technique to determine the optimal allocation of limited resources to meet the given objectives. The resources may be in the form of men, Materials and machines, etc. and the objective may be to maximize or minimize a given function.

—  Meaning: Linear Programming consists of two words, ‘linear’ and ‘Programming’. The term ‘linear’ implies that all the relations among the variable in the particular problem are linear (i.e., of degree one) and given straight lines when plotted graphically. 

—  The term ‘programming’ refers to the procedure of determining a mathematical program or plan of action.

—  Definition: According to Alpha C. Chiang “Linear Programming is the simpler variety of programming problems in which the objective function, as well as the constraint inequalities, are all linear.

—  The basic concept of Linear Programming:

—  (a) Objective function: An objective function of a linear programming problem states the determinants of the quantity to be maximized or to be minimized. 

—  (b) Constraints: There must be certain constraints or restrictions on the variable of the function of the problem.

—  (c) Non-Negativity Restrictions: The decision variable must not assume a negative value that represents the impossible situation.

—  (d) Feasible Region: The region which is common to all the constraints of a linear programming problem is called the feasible region of the problem.

—  (e) Feasible Solution: A feasible solution to a linear programming problem is the set of values of the variables which satisfies the set of constraints and the non-negative restrictions of the problem.

—  (f) Optimum solution: a feasible solution that satisfies both the conditions of the problem and also optimizes the objective function of the problem is called an optimum solution.

Assumptions of Linear Programming

—  1. Linearity: All the relationships in LPP, i.e., in both objective function and constraints are assumed to be linear. They are represented by straight lines.

—  2. Additivity: The value of the objective function for the given values of the decision variables and the total sum of resources used must be equal to the sum of the contributions (Profits or Costs) earned from each decision variable.

—  3. Divisibility: Divisibility simply means that the solution need not be in whole numbers(integers). 

—  4. Certainty: This assumption means that all parameters are known with certainty and do not change during the period being studied.

Business Applications of Linear Programming

—  1. Diet problems: To determine the minimum requirement of nutrients subject to the availability of food and their place.

—   2. Manufacturing Problems: to find the number of items of each type that should be manufactured so as to maximize the profits subject to production restrictions Imposed by limitations on the use of machinery and labor.

—  3. Transportation Problems: To find the least costly way of transporting shipments from the warehouses to customers. 

—  4. Production Problems: to decide the production schedule to satisfy demand and minimize cost in face of fluctuating rates and storage expenses.    

Unit II: (Exam Studies) 

—  Elementary Transportation: Formulation of Transport Problem, Solution by N.W. Corner Rule, Least Cost method, Vogel’s Approximation Method (VAM), Modified Distribution Method. (Special cases: Multiple Solutions, Maximization case, Unbalanced case, prohibited routes)

—  Elementary Assignment: Hungarian Method, (Special cases: Multiple Solutions, Maximization case, Unbalanced case, Restrictions on assignment.)

—  Unit III:(Exam Studies) 

Network Analysis: Construction of the Network diagram, Critical Path - float and slack analysis (Total float, free float, independent float), PERT, Project Time Crashing

—  Unit IV

—  Introduction to Game Theory: Pay off Matrix- Two-person Zero- Sum game, Pure strategy, Saddle point; Dominance Rule, Mixed strategy, Reduction of m x n game and solution of 2x2, 2 x s, and r x 2 cases by Graphical and Algebraic methods; Introduction to Simulation: Monte Carlo Simulation. 

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