Contents
Definition of Mathematical Model Types of Variables The Mathematical Modeling Cycle Classification of Models

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Definitions of Mathematical Model
Mathematical modeling is the process of creating a mathematical representation of some phenomenon in order to gain a better understanding of that phenomenon. It is a process that attempts to match observation with symbolic statement. A mathematical model uses mathematical language to describe a system. Building a model involves a trade-off between simplicity and accuracy. The success of a model depends on how easily it can be used and how accurate are its predictions.

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Types of Variables
A mathematical model usually describes a system by a set of variables and a set of equations that establish relationships between the variables. The variables represent some properties of the system. There are four basic groups of variables: – – – – Input variables Parameters Random variables Decision variables (output variables)

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The Mathematical Modeling Cycle

Simplify Real World Problem
Interpret

Mathematical Model

Program

Conclusions Simulate

Computer Software

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The Mathematical Modeling Cycle
1. Identify and understand the problem, draw diagrams 2. Define the terms in your problem 3. Identify important variables and constants and determine how they relate to each other. 4. State the assumptions as you focus on particular aspects of the phenomenon. 5. Develop the equation(s) that express the relationships between the variables and constants.

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The Mathematical Modeling Cycle
The Real World
A non-mathematical setting

The Mathematical World
An abstract representation

Representation Pose a question Create a model
Identify relevant variables, determine the form of the answer and the objects that best capture the relationships between the variables

...definition for a model
According to Wilson’s definition a model is the explicit interpretation of one’s understanding of a situation, or simply of one’s idea about that situation. It can be expressed in mathematics, symbols or words. But it is essentially a description of entities, process or attributes and the relationships between them. It may be prescriptive or illustrative, but about all, it must be useful.
Describe the purpose and uses ofmodels
There are various use of models; here I am going to focus on seven of them:
Firstly, a model helps us concentrate on the essentials of a complex problem, designing a model force us to think logically and clearly. We have to consider what we know, what we don't know, and what data we have available.
Secondly models are used to illustrate a concept, which help us to understand the problem situation better, they can also reveal part of the bigger picture and even show what’s missing.
Thirdly, models are used to defining structure, process and behaviors, it reveal complexity in simple systems like the structure of a virus.
Fourthly, models can be used as prerequisite to design.
Fifthly, model is a tool for communication, for example map communication tools will help us to identify the communication between stakeholders and enable us to understand, motivate and...

...Types of Models in Economics
From the definition of a model, it has been said that models in economics have the wide range of forms including graphs, diagrams, and mathematicalmodels. Economists use these models in different purposes; it depends on many factors such as what type of raw data they have, how they can represent the data, and what they want from the model they use. In this section it will be more explanation about what is the main role of these different models and also some important examples in economics.
Flow Chart
Flow chart is a diagram that shows the connections between the different stages of a process or parts of a system. Economists use a flow chart to explain how the economy is organized and how participants in the economy interact with one another. If people follow the right connections in the flow chart diagram It will be easier for them to understand the relationship between participants in the economy.
One of the important flow chart using in economics is called the circular-flow diagram, presented in
Figure 1. Circular-flow diagram is a visual model of the economy that shows how dollars flow
through market among households and firms.
Graph
Graph is a planned drawing, consisting of a line or lines, showing how two or more sets of numbers are related to each other. In general the different types of graphs can be...

...Mathematicalmodel
A mathematicalmodel is a description of a system using mathematical language. The process of developing a mathematicalmodel is termed mathematical modelling (also writtenmodeling). Mathematicalmodels are used not only in the natural sciences (such as physics, biology, earth science, meteorology) and engineering disciplines (e.g. computer science,artificial intelligence), but also in the social sciences (such as economics, psychology, sociology and political science); physicists, engineers, statisticians, operations research analystsand economists use mathematicalmodels most extensively.
Mathematicalmodels can take many forms, including but not limited to dynamical systems, statistical models, differential equations, or game theoretic models. These and other types of models can overlap, with a given model involving a variety of abstract structures.
Examples of mathematicalmodels
Population Growth. A simple (though approximate) model of population growth is the Malthusian growth model. A slightly more realistic and largely used population growth model is the logistic function, and its extensions.
Model of a...

...Mathematical modelling of a hyperboloid container
Mathematicalmodel is a method of simulating real-life situations with mathematical equations to forecast their future behaviour. Eykhoff (1974) defined a mathematicalmodel as 'a representation of the essential aspects of an existing system (or a system to be constructed) which presents knowledge of that system in usable form'. Mathematicalmodels are used particularly in the natural sciences and engineering disciplines (such as physics, biology, and electrical engineering) but also in the social sciences (such as economics, sociology and political science); physicists, engineers, computer scientists, and economists use mathematicalmodels most extensively.
Mathematical modelling uses tools such as decision-theory, queuing theory, and linear programming, and requires large amounts of number crunching. Mathematical modelling approaches can be categorized into four broad approaches: Empirical models, simulation models, deterministic models, and stochastic models. The first three models can very much be integrated in teaching high school mathematics. The last will need a little stretching. Empirical modelling involves examining data related to the problem with a view of formulating or...

...Mathematics Modeling
Introduction
Mathematics finds its root way back more than 5000 years. Mathematics has helped people solve complex problems, represent different problems and transfer knowledge and skill about the different problems. Mathematicalmodels have often being developed to solve and represent these problems especially in natural sciences and engineering disciplines (Arnold 2000). Mathematicalmodels can be defined as a mathematical language that would describe the behavior of a system or rather a problem. Mathematical modeling can be done to develop scientific understanding, test a system for change and help in making decision (Anon 2005).
Urban Population change
The urban population change represents one of the most important aspects that define a city. The household composition and their nature differentiate the urban population from that in the area. Urban population is growing much faster than the population as a whole. It is prospected that, in the next century, more than half the population will be living in the urban centers. The changes of the population have shaped the cities to function as social, economic and cultural centers. The urban population growth has been witnessed more in the developing countries especially in Africa and Asia continents. The large change in urban population can be attributed to the industrial revolution. Rural to urban migration...

...Mathematical modeling is commonly used to predict the
behavior of phenomena in the environment. Basically,
it involves analyzing a set of points from given data
by plotting them, finding a line of "best fit" through
these points, and then using the resulting graph to
evaluate any given point. Models are useful in
hypothesizing the future behavior of populations,
investments, businesses, and many other things that
are characterized by fluctuations. Amathematicalmodel usually describes a system by a set of variables
and equations which form the basis of the
relationships between the variables.
The variables represent independent and dependent
properties of the system. Models are classified in a
variety of ways. One of these ways is "linear versus
nonlinear." A linear model is any system whose
behavior can be explained or predicted using a linear
equation or an entire set of linear equations. On the
other hand, a nonlinear model uses at least one
nonlinear equation to describe its behavior. Models
may also be classed as either deterministic or
probabilistic. A deterministic model always performs
the same way under a given set of initially occurring
conditions, while a probabilistic model is
characterized by randomness. Another way of evaluating
models is to determine whether it is static or...

...Research Project
Mathematical Programming Based Modeling
For Supply Chain Management Control
Muhammad Faisal
Department of Engineering Management, Abasyn University, Islamabad, Pakistan.
Abstract
Economic globalization has forced and is still forcing enterprises to develop new global manufacturing and distribution concepts. A growing number of products are produced in multiple plants dispersed around the globe. This paper designs and discusses amathematicalmodel of international supply chain which leads to a better understanding of the complex process flows within a multi-location enterprise’s production network. Besides the consumption during production activities, this system also takes into account the consumption caused due to the dispersed feature of the supply chain, i.e., the transportation costs. After that, a linear programming model based on input-output account is applied to find the optimal solutions of the production and distribution decisions for Walmart supply chain. Conclusions are given at the end of this paper.
Index Terms: Mathematical Programming Based Modeling, mixed integer linear programming model, supply chain management, input output model.
I. Introduction.
A supply chain can be defined as an integrated process consists of a number of various business entities including suppliers, manufacturers, distributors,...