# Introduction to Decision Models

A decision model is an idealized representation of the problem.   Decision model refers to structured presentation of the problem, solution there to and stimulation of working of the solution.   The model’s purpose is to enable the decision analyst to forecast the effect of factors crucial to the solution of the problem.

### Types of Models

There are different types of models.   Ionic and Symbolic models are the prime two types.   Ionic Models are concretized.   It is a physical representation of any real life object on a different scale. Think of a prototype of a plane/car/machine/globe/idol and so on. Symbolic models re abstract models. A cost curve, a supply curve, marginal revenue curve, a production possibility curve, etc., is a symbolic model. A forecast profit and lost account is also a symbolic model. The statement symbolizes summary of financial effects of commercial activities planned over the next period. An equation is a symbolic model of variables, their relationship and effect of independent variables on the dependent variable.

Symbolic models can be classified into: 1) quantitative and qualitative, 2) standard and customized, 3) probabilistic and deterministic, 4) descriptive and optimizing, 5) static and dynamic, 6) simulative and realistic models.

1. In a quantitative model all variables are expressed in numbers, while in a qualitative model some or all of the variables are given only verbal expression.
2. Standard model is universalized.   Computers languages and operating systems are standardized, while application programmes are customized.   Nowadays customized-standardization is the order, powered by enormous computing powers of computers.   Mass customization is preferred.
3. Probabilistic model deals with situations where the outcomes of current action are not known, but their probability distribution is known.   Deterministic model deals with decision situations where certainty of outcomes is taken for granted.
4. Descriptive model describes the basic relationship between variables.   If Rs.10 and Rs. 12 are the contribution per unit of Product A and Product B, respectively and if a units of A and b units of B are produced, total contribution is described by: 10a + 12b.   In an optimizing model, ways to maximize the total contribution, given the resources and consumption and pattern of resources by A and B
5. Static model assumes, the set of conditions affecting the problem remains unchanged in a given frame time.   Linear programming is a static model.   Dynamic model assumes that the conditions keep changing with time.   Dynamic programming is a dynamic model.
6. Simulative model tries to replicate the real world situation either through a computer programme or through Monte Carlo Simulation System or through such other methods.   A realistic model is action play.   An advertisement campaign is full scale on.   The firm tries to evaluate the sales profit, awareness and brand equity effectiveness of the programme.

### Model Construction

The construct a model, one needs to know the variables, constants and constraints.   A verbal representation of the relationships among variables is then attempted.   Next, a model is constructed by developing a symbolic statement of the relationships among the variables and then these symbolic relationships are turned into a mathematical model which is tested with real-world data and evaluated.   But all decision situation do not lend them to modeling.

In the case of decision situations that requires an open system approach, accurate modeling is utopian, because the decision components are not fully known.   Hence, open decision systems are not perfectly modeled or structured.   Depending on individual situations, models vary from partly structured from, the decision model is an approximation of the real world situation.   Consider the case of sales forecasting, which is a typical dynamic decision exercise.   Sales response constant — ‘r’ advertisement effort as a function of time — A(t), sales saturation level — ‘M’, sales rate per time — ‘S’, and sales decay constant — ‘Z’, are some of the relevant variables identified. A simple model is developed using these variables which runs as follows: ds/dt = r.A(t).(M-S) MZS, where ds/dt is the rate of change in sales per unit time.   Many variables would affect the rate of sales, but a few only are considered important here.   Thus, the above model is only an approximation.

In certain cases of open decision models, no modeling, however much an approximation, is possible.   In such cases the system remains unstructured.   On the contrary, closed decision models are fully structured for reasons best known.   Even here, constructing a workable model may prove difficult in some cases.   The simulation technique is adopted then to develop the model.

In case of open decision making models, the environment s risky and stochastic and in such an environment as outcomes of decisions cannot be known with certainty, the objective criterion is one of satisfying.   In regards to closed systems, on the other hand, the functioning of the system is highly structured and that optimization is the ultimate goal.

### Enrichment and Evaluation of Model

The model must be enriched and evaluated.   Usually, to begin with a mathematical model is a simple version or an evolutionary design.   Step by step the model is enriched through incorporation of additional relevant elements of (variables and constants) and conditions and constraints.   But too many variables, constants, conditions and constraints might make model intractable (i.e., incapable of being solved) and imprecise.   Enrichment must be attempted to the extent of achieving a valid representation of the problem.

The validity of the model must be evaluated.   Content, context, construct, concurrent, predictive, convergent, divergent, nomological validities of the model must be evaluated.   Criterion for judging the validity of the model is whether or not the model measures what it is supposed to measure, predicts the effects of the alternative course of action with accuracy and so on.

Finally, reliability of the model must be evaluated.   A retrospective test may be performed here.   The test involves using historical data to reconstruct the past and then determining how will the model and resulting solution would have performed if it had been used.   If the results of the model mostly conform with the ex-post results, the model can be taken to possess reliability.   Further, with repeated applications, if the same results are turned out, the reliability of the model can be taken as established.

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