Page 15 - DMGT209_QUANTITATIVE_TECHNIQUES_II

Quantitative Techniques-II

Notes has been. The problem of product development in which the decision-maker has to make decisions
at every decision point such as product design, test-market, full-scale production, etc. is an
example of dynamic model. Dynamic programming is the particular example of dynamic model.
Linear Models are those in which each component exhibits a linear behaviour. The word ‘linear’
is used to describe the relationship among two or more variables which are directly proportional.
For example, if our resources increase b some percentage, then it would increase the output by
the same percentage.

Did u know? What are non-linear models?
If one or more components of a model exhibit a non-linear behaviour, then such models are
called non-linear models.

A mathematical model of the form Z = 5 + 3 is called a linear model whereas a model of the form
2
Z = 5x + 3xy + y is called a non-linear model.
2
Procedure (or Method) of Solution

The type of procedure used to derive solutions to mathematical models divides them into two
categories: (i) analytical models, and (ii) simulation models.
An analytical model consists of a mathematical structure and is solved by known mathematical
or analytical techniques to yield a general solution.

Example: Network models (PERT/CPM), linear programming models, game theory
models, inventory control models.
A simulation model is the experimentation (Computer assisted or manual) on a mathematical
structure of real-life system. It is done by inserting into the given structure specific values of
decision variables under certain assumptions in order to describe and evaluate systems behaviour
over a period of time.

Example: We can test the effect of different number of service counters assuming different
arrival rates of customers on total cost of providing service to customers.
The following table summarises our discussion on classification of models.

You have read about certain standard techniques or prototype models of operations research
which can be helpful to a decision-maker in solving a variety of problems.

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