# Quantitative Analysis

DOI: 10.4018/978-1-5225-5264-2.ch001
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## Abstract

The first chapter presents concepts about quantitative models for decision making; the process that follows is used when constructing a model and definitions of queueing theory: work in process, cycle time, and congestion. Also presented and explained is the Kendall notation that will be used throughout the book. The chapter shows some examples of waiting line systems at the end.
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## Quantitative Analysis

Quantitative analysis is defined as the scientific approach to problems or conflictive situations in a system, where the administrator has to make a decision.

Systems consist of a variety of components or elements. Each element is connected to the others and together they form an entity that produces an answer. Systems, in decision-making, are those entities that are under the responsibility of an administrator who has to make a series of decisions that should generate the answer needed to achieve an objective.

The systems of interest are organizations with production and distribution targets. Some examples of systems that have only a few components are grocery stores, cafeterias, stationery stores, small supermarkets, small restaurants, bakeries. In these cases the managers are often the owners themselves and are in charge of all the business’ planning, buying, contracting, selling, accounting and dispatching jobs. Given that these systems do not have a lot of personnel, the quantity of consumables is small and the variety of products on offer is low, they are usually relatively simple to manage.

Some examples of systems with a lot of components are car manufacturers, airports, supermarkets, universities, airlines, online sales companies. In these cases, the systems have a huge variety of components, each of which involves several people. There will often be someone in charge of each area, which shall, in turn, be coordinated by an entity consisting of a single person or by a board composed of several officers with specialist duties. In these systems, decisions may be complex.

In quantitative analysis there are a set of tools that reduce the uncertainty associated with decision-making. These tools are often mathematical models that enable us visualize how each of the components of the system (variables) is connected to the others.

### Models

Models are representations of systems and describe the characteristics that are of interest for the decisions that the administrator has to make. The process of creating a model is known as modeling. Models can be any of three types: physical, mental or symbolic.

• Physical Models: Physical models are scale models of airplanes, houses or cities, for example. This way of representing systems was one of the first to be applied for system analysis. During the two World Wars, people used scale representations of the battlefields. These models were built with the detailed location of the trenches, gunner positions, roads, cities, together with the location of each of the divisions that made up the armies or of the squadrons of enemy fighter planes and bombers.

• Mental: This is one of the first representations of systems ever used and is called the imagination. As children we have all used this representation intensively.

• Symbolic: A symbolic model shows the relationships between each component of a system through the use of symbols or operators. The best known ones are mathematical models. A supply equation is a symbolic representation of the behavior of demand in respect of the price of an item or product. A queueing formula is a representation of the behavior of the cycle time in respect of the demand for a service (for example, in a cafeteria) and the service capacity of the server (the cashier who takes the order and charges).

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