1. Introduction to Decision Analysis & Modeling
Dr. T. T. Kachwala

2. Decision Making Process
Slide 2
Decision Making Process
In an environment of uncertainty, a Decision Making Process leads a manager to one or more optimum solutions from amongst the alternates available, within the constraints of the available resources and such that the manager optimizes the value of the objective function and simultaneously minimizes the risk involved.
Operations Research or Management Science or Decision Science is a Science of application of Mathematical Models & Statistical Theories for the betterment or improvement of Management Decision Making Process

3. Statistical Theories & Mathematical Model
Slide 3
Statistical Theories & Mathematical Model
Statistical Theories refer to the Statistical Tools & Techniques like Mean, Standard Deviation, Regression & Normal Distribution which are used for Business Analysis
Mathematical Model is a Mathematical Equation which Simulates a Business situation to predict the possible outcome for known or assumed values of the Decision Variables.

4. Cost, Revenue & Volume Model.
Slide 4
Cost, Revenue & Volume Model.
Consider the Cost, Revenue & Volume Model.
Revenue & Volume; S = s*Q
Cost & Volume; C = F + v*Q
‘s’ is the selling price per unit
‘v’ is the variable cost per unit
‘Q’ is the level of output (assuming we produce only what we can sell)
‘F’ is the given Fixed cost

5. Cost, Revenue & Volume Model.
Slide 5
Cost, Revenue & Volume Model.
Profit & Volume;
S = F + V + P
S*Q = F + v*Q + P
(s – v)* Q – F = P
For a given selling price per unit, variable cost per unit & level of output (assuming we produce only what we can sell) and the given Fixed cost, we can calculate the Profits using the above model (equation).

6. Characteristics of Mathematical Model
Slide 6
Characteristics of Mathematical Model
A mathematical model or equation is characterized by a constant value & a variable component;
Example: In the Profit equation; P = (s – v)* Q – F, the fixed components are s, v & F & the variable component is Q.
A decision maker can use the above mathematical model to estimate the profit for given level of volume.
Example: for small levels of volume decision maker will incur a loss, for larger valves of volume, decision maker gains a profit and at breakeven sales the decision maker neither gains profit nor incurs a loss. Math Model BEAnalysis.xlsx

7. Characteristics of Mathematical Model
Slide 7
Characteristics of Mathematical Model
Such Mathematical Models are a critical part of any Quantitative Approach to Decision Making. They enable a Decision maker to make inferences about the real situation by studying and analyzing the model like an air plane designer who might test a new air plane model in a wind tunnel to learn about the potential flying characteristics of a full size plane.