Quantitative Techniques for Decision Making

Introduction

Decision making is crucial for survival of business. Businesses have to make decision considering the limited amount of information. Decision making problems are divided into two types deterministic and probabilistic.

Deterministic model of problem solving depends on the relationship between uncontrollable factors and continuing process of optimizing system performance. A model is developed in under assumption related to existing business condition. If the variables under assumption do not truly reflect the current business conditions, the model developed also will not reflect the reality.

Mathematical optimization utilizes mathematical equation to determine the business decision. The business decision derive is in a numerical form.

A business model for decision making is constructed by analyst based on inputs of a decision maker. A business model is developed over a period of time using a progressive approach method.

Optimization Modeling Process

Optimization model is developed in three steps, 1st step is describing the problem, 2nd step is elaborating the solution and 3rd step is controlling the problem.

The optimized problem of the 1st step can be classified into linear and non-linear depending upon on nature of variables. Optimization problem has three following aspects:

• An objective function to maximize or minimize.
• A set of variables which affect the value of the objective function.
• A set of uncontrollable factors referred as parameters.

The solution of optimized problem satisfying all parameters and constraints is referred as feasible solution. The objective of an optimization process is to value of variables, which minimize or maximize objective giving out an optimal solution.

Linear Programming

Linear programming is a mathematical procedure of determining linear allocation of business variables. For constructing linear program following factors are essential:

• The objective function needs to be linear.
• The objective must be to either maximize or minimize a linear function.
• The constraints in the program should also be linear.

In formulating a linear program certain variables are integer in nature, such as function with integer variable is known as integer programming.

Decision Tree

In a certain decision-making process, probability plays an important role. On the decision model based upon probability is decision trees.

Scenario modeling

Business environment is always unpredictable and can throw up unusual situation more than often. Thus, organizations find themselves in the middle of dynamic environment. Here model and methods like sensitivity analysis, stability analysis, what-if analysis, scenario modeling, etc. is utilized.

Therefore, model under used uncertainties are as follows:

• Scenario Analysis: this model assumes a different scenario a business may find itself with certain value of parameters.
• Worst Case Analysis: this model assumes an extreme case scenario in computing different variables.
• Monte-Carlo Model: this model assumes uncertainty through statistical distribution.

Theory of Constraints

Theory of constraints is a management concept which helps organization deal with situation, which hampers its growth and march towards higher level of performance. Theory of constraint encourages an organization to deal one constraint at a time and consist of following steps:

• Identifying constraints of the existing system.
• Identifying was to potential extract more out of system constraints.
• Exploiting constraints to its fullest potential should be made priority.
• As the company overcomes 1st constraint, it should look forward to working upon other constraints.