# Phases In Solving Operation Research Problems

**Introduction:**

Operations Research is the study of administrative system pursued in the same scientific manner in which system in Physics, Chemistry and Biology are studied in natural sciences.

**Phases:**

**1. ****Formulation of the Problem**

The Operations Research analyst or team of experts first have to examine the situation and clearly define what exactly happening there and identify the variables and constraints. Similarly identify what is the objective and put them all in the form of statement. The statement must include

**a) **a precise description goals or objectives of the study,

**b) **identification of controllable and uncontrollable variables

**c) **restrictions of the problem

**Let us consider the following statement:**

**Statement**: A company manufactures **two products X and Y**, by using the

**three machines**Each unit of

*A*,*B*, and*C*.*X*takes

**1 hour**on machine A,

**3 hours**on machine B and

**10 hours**on machine

*C*. Similarly, product

*Y*takes

**one hour, 8 hours and 7 hours**on Machine

*A*,

*B*, and

*C*respectively. Inthe coming planning period,

**40 hours of machine**is available for production. Each unit of

*A*, 240 hours of machine*B*and 350 hours of machine*C***and**

*X*brings a profit of Rs 5/-**by the company**

*Y*brings Rs. 7 per unit. How much of*X*and*Y*are to be manufactured**for maximizing the profit**?The team of specialists prepares this statement after studying the system. As per requirement thismust include the variables, constraints, and objective function.

**2. ****Variables**

· The Company is manufacturing two products ** X and Y**. These are the two variables in the problem.

· When they are in the problem statement they are written in **capital letters***. *Once they are entered in the model small letters (lower case) letters are used (i.e., x and y). We have to find out how much of *X *and how much of *Y *are to be manufactured.

**3. ****Resources and Constraints**

a) There are three machines *A*, *B*, and C on which the products are manufactured. These are known as**resources**.

b) The capacity of machines in terms of machine hours available is the available resources.

c) The competing candidates have to use these available resources, which are limited in nature.

d) Now in the above statement, machine *A *has got available 40 hours and machine B has available a capacity of 240 hours and that of machine *C *is 350 hours.

e) The products have to use these machine hours in required proportion. That is one unit of product *X *consumes one hour of machine *A*, 3 hours of machine *B *and 10 hours of machine *C*.

f) Similarly, one unit of *Y *consumes one hour of machine *B*, 8 hours of machine *B *and 7 hours of machine *C*. These machine hours given are the available resources and they are limited in nature and hence they are **constraints **given in the statement.

**4. ****Objective of the Problem**

· To maximize the profit how much of *X *and *Y *are to be manufactured? That is **maximization of the profit or maximization of the returns **is the objective of the problem. For this in the statement it isgiven that the profit contribution of X is Rs 5/- per unit and that of product Y is Rs. 7/- per unit.

**5. ****To establish relationship between variables and constraints and build up a model**

**a) **Maximize Z = 5*x * 7*y ***Subject to a condition ****(written as ) OBJECTIVE FUNCTION.**

b) 1*x * 1*y *≤ 40

**c) **3*x * 8*y *≤ 240 **STRUCTURAL CONSTRAINTS.**

d) 10*x * 7*y *≤ 350 and

**e) **Both *x *and *y *are ≥ 0 **NON-NEGATIVITY CONSTRAINT.**

**6. ****Install and Maintain the Solution**

· Once we get the optimal values of x and y and objective function instructions are given to the concerned personal to manufacture the products as per the optimal solution, and maintain the same until further instructions.