Introduction
Quantitative techniques are methods of analyzing numerical data. They are meant to be the vital components in business risk evaluation for some decision-making purposes. The quantitative analysis puts assumptions into the real-life scenario to simulate what may happen in the actual environment. The use of a theoretical approach may be needed because data is not always available as it is required for making some important decision. In such a case, a good example is a situation in which a motor company wants to ascertain the number of drivers who are driving a particular model of automobile in Australia at a particular time. It would be unfeasible to establish the data without the total collaboration of every individual driver apart from the exorbitant amount of resources. This calls for the need for the application of quantitative techniques to create a picture of the real business world, though without real data.
Quantitative Techniques and Problem Solving
Linear Programming
We can describe linear programming as a mathematical model that might be used in decision-making and problem-solving to aid in choosing a better decision to be applied. The term “linear program” means that it consists of a linear objective function and a set of linear constraints. One of the uses of linear programming is to implement it in the scheduling of production processes in large and busy manufacturing plants. Here is a sample illustration of linear programming. The manager of manufacturing estimates that 730 hours of cutting and dyeing time, 700 hours of sewing time, 808 hours of finishing time, and 235 hours of inspection and packaging time will be available for the production of bags for the next three months. In such a case, the main problem of Rex LTD is to determine how many standard handbags should be produced in the given period aiming to maximize the profit received.
Letting A1 be the number of standard production by Rex LTD, then A2 will be the number of handbags produced by Rex LTD. Using the following mathematical model, we seek to find the arrangement of A1 and A2 that suits all the limits and yields a value for the objective function that is greater than or equal to the value given by any other viable solution.
- Max 10 A 1 + 9 A2
- 7/10 A 1 + 1 A 1 <_ 730 Cutting and Dyeing
- 1/2 A 1 + 5/6 A 2 <_ 700 Sewing
- 1 A 1 + 2/3 A 2 <_ 808 Finishing
- 1/10 A 1 + 1/4 A 2 <_ 235 Inspection / Packaging
- Where A1 >_ 0 and A2 >_ 0.
The solution implies that we minimize on A1 and A2 to yield maximum profit.
Probability Distributions and Decision Making
Probability, in simple terms, is the likelihood of the occurrence of an event. We focus a particular interest on one probabilistic ratio known as the expected demand and try to figure out how it can assist in business management. Here is an example. Company Y sells electric motors type B. During a given week, demand for Company Y’s A motor is 0, 1, or 4. The distribution described below is as follows.
What is Company Y’s expected demand for a week?
(0)(0.45)+ (1) (0.70) + (4) (0.075) = 1.00.