# Linear prog and simulation mod

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• Publicado : 4 de septiembre de 2010

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Synopsis
This document presents the use of linear programming and simulation modelling with definitions, successful uses of these techniques in the past and two examples; one for linear programming and one for simulation modelling, both related to the transport business.
The use of these techniques has been used for decades, the company should think about using these tools in order to improveour operations.

1 INTRODUCTION 1

2 LINEAR PROGRAMMING 2

2.1 Definition 2

2.2 Benefits 2

3 SIMULATION MODELING 3

3.1 Definition 3

3.2 Benefits 3

4 SUCCESESFUL USES OF LINEAR PROGRAMMING IN THE PAST 4

4.1 The Taiwan example: Cement transportation planning (Li-Hsing, 1998) 5

4.2 The Ireland example: Railway projects prioritisation forinvestment (Ahern, 2006) 5

4.3 The UK example: displacement problem and dynamically scheduling aircraft landings (Beasley, 2004) 6

5 EXAMPLES 7

5.1 Linear programming 7

5.2 Simulation modelling 8

6 SUMMARY 10

7 REFERENCES 11

1. INTRODUCTION
In today’s market and business world, two quantitative statistic methods, Linear Programming and Simulation, are mathematical modellingtechniques that have been widely applied to work out the best solutions for business. The wide application of two techniques have been successfully employed in the transport and logistics sector for a number of decades and many managers in the transport and logistics sector appreciate the benefits brought about from the comprehensive and systematic quantitative model.

This report is welldesigned to have brief introduction about the two quantitative statistic methods, key benefits in use and application analysis of the model which has been successfully used in the history. Two models based on transport and logistics, will be built to illustrate how to solve problems with these two techniques in the last part. The LP model will be employed to optimize cost-efficiency strategy (Rose &Beck, 2007). In addition the model would produce a specific set of results showing how well the solution performed by various measures. (Rose & Beck, 2007)

2. LINEAR PROGRAMMING

1 Definition

Linear Programming (LP) is a widely applied mathematical technique in computer modelling to find the best possible solution in allocating resources, such as energy, machines, materials, money, space,personnel, time, etc. to achieve maximum profits or minimum costs (Rose & Beck, 2007). It can help users to solve a variety of problems related to management from scheduling, media selection, financial planning, capital budgeting, transportation and many others and achieve the expectation of maximise or minimise some quantity.

2 Benefits

One of key benefits of Linear Programming is to solveproblems of maximising profits with given inputs or minimising costs with given outputs (Rose & Beck, 2007). Looking at inventory management for example, most companies keep continuous material flows in order to offer sufficient resources for the production process. However, it brings a great number of costs such as space, labour, pack, ship, damage and obsolescence (Muller, 2003). The idealinventories should be kept at the minimum level to avoid over-stocking and over-investment (Piet, 2007). Therefore, the objective is to minimise the total cost of holding inventory including capital costs, inventory risk costs, storage costs and inventory service costs. The application of LP will help managers to solve the problems that minimise the over-inventories and meet the future unexpected demandat same time (Rose & Beck, 2007).

3. SIMULATION MODELING

3 Definition

Historically, simulations have been used in a number of different fields. During the 20th century, studies of system theory across are done mainly on computers. It has allowed for a more systematic view of the concept. Simulation is a technique to duplicate the features of a real world. Its essence is ‘to imitate a...