Page 23 - DCOM303_DMGT504_OPERATION_RESEARCH

Operations Research

Notes
Table 2.1: T-type Classification of Advantages and Limitations

Advantages Limitations
1. It helps in proper and optimum 1. The treatment of variables having non-
utilization of the scarce resources linear relationships is the greatest
limitation of this LP
2. It helps in improving the quality of the 2. It can come out with non-integer solutions
decisions. too, which would be many a times
meaningless.
3. With the use of this technique, the 3. It rules out effect of time and uncertainty
decision-maker becomes more objective conditions.
and less subjective.
4. It even helps in considering other 4. Generally, the objective set will be single
constraints operating outside the and on the contrary, in the real life, there
problem. might be several objectives.
5. Many a times it hints the manager about 5. Large-scale problems tend to be
the hurdles faced during the production unaccomodative to solve under LP
activities.

2.4 Formulation of LP Models

Linear Programming Family

The family of LP consists of:
1. Formulation of Linear Programming Problems. (LPP)
2. LP – Graphical Solutions
3. LP – Simplex Solutions
4. LP – Assignment Problems
5. LP – Transportation Problems.

Steps for Formulating LPP

1. Identify the nature of the problem (maximization/minimization problem).
2. Identify the number of variables to establish the objective function.
3. Formulate the constraints.
4. Develop non-negativity constraints.

Example: A firm manufactures 2 types of products A & B and sells them at a profit
or ` 2 on type A & ` 3 on type B. Each product is processed on 2 machines G & H. Type a requires
1 minute of processing time on G and 2 minutes on H. Type B requires one minute on G &
1 minute on H. The machine G is available for not more than 6 hrs. 40 mins., while machine H is
available for 10 hrs. during any working day. Formulate the problem as LPP.
Solution:
Let x be the no. of products of type A
1
x be the no. of products of type B
2

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