Dr. Mohammed Al-Dujaili
Department of Ceramics Engineering and Building Materials
Faculty of Materials Engineering
University of Babylon
Academic year 2016-2017
Chapter 5: Department of Mechanical Engineering
Chapter 6: Department of Non-Metallic Materials Engineering
Stage: Forth
Subject: Industrial Engineering
Linear Programming, Transportation Models and Maintenance Engineering
Operation Research Engineering (ORE)
ORE: is designed to provide a techniques and modeling concepts needed to analyze and design complex systems. That s mean, it is a discipline that deals with the application of advanced analytical methods to help make better decisions. It is often considered to be a sub-field of mathematics.
Steps of Operation Research Engineering
A. Problem Definition
B. Data Collection.
C. Model Formulation
D. Model Solution
E. Validation and Analysis
F. Implementation and Monitoring
The following diagram is explaining the steps of operation research.
Diagram to the Operation Research Steps
1. Linear Programming
Linear programming (LP), or linear optimization) is a method to achieve the best outcome (such as maximum process or lowest process) in a mathematical model whose requirements are represented by linear relationships. LP is a special case of mathematical programming (mathematical optimization). More formally, LP is a technique for the optimization of a linear objective function, subject to linear equality and linear inequality constraints. It s feasible region is a convex polyhedron, which is a set defined as the intersection of finitely many half spaces, each of which is defined by a linear inequality. Its objective function is a real-valued affine function defined on this polyhedron. A LP algorithm finds a point in the polyhedron where this function has the smallest (or largest) value if such a point exists.
Augmented form (slack form)
Linear programming problems must be converted into augmented form before being solved by the simplex algorithm. This form introduces non-negative slack variables to replace inequalities with equalities in the constraints. The problems can then be written in the following block matrix form:
Maximize Z:
x, xs ? 0
Where: xs are the newly introduced slack variables, and Z is the variable to be maximized.
Assumptions of linear programming
1. There are restrictions on the freedom of the use of resources and facilities available at the company as working hours or quantities of raw materials or semi-processed the plant or machinery.
2. Available several alternatives to a combination of resources and capabilities down to the goal sought by the involved company.
3. The relationships among the linear variables.
4. Provide the accuracy and reliability of the information and planning data, which will make the optimization decision in its light.
Methods and techniques the linear programming
1. Graphical Method
2. Algebraic method
3. Simplex method
4. Transportation method
5. Assignment method
Simplex Method
The Simplex Method is "a systematic procedure for generating and testing candidate vertex solutions to a linear program. The Simplex Method selects the variable that will produce the largest change towards the minimum (or maximum) solution. That variable replaces one of its compatriots that is most severely restricting it, thus moving the Simplex Method to a different corner of the solution set and closer to the final solution. In addition, the Simplex Method can determine if no solution actually exists. Note that the algorithm is greedy since it selects the best choice at each iteration without needing information from previous or future iterations. This method will give the following benefits
1. Provides an efficient procedure for solving such large problems
2. It uses methods from linear algebra
3. The study of systems of linear equations
4. Using matrices
Flowchart for the Solution Process According to Simplex Method
Transportation method
Is simplified meaner helps of determining the best transportation programs which reduce of the costs to the lowest possible. Represents the problem basically in the case of a multiple sources, and places of destination required transport between them, where the multiplicity of means of access from the supply centers for demand centers. Using linear programming according to the iterative solutions in the search for a possible solution.
In this case, we can define TM: the transportation problem can be solved as an ordinary linear programming problem, its special structure can be exploited, resulting in a special-purpose algorithm, the so-called transportation method. Therefore, the problem can be formulated as;
.
Critical path method (CPM)
The critical path method (CPM) is a step-by-step project technique for process planning that defines critical and non-critical tasks with the goal of preventing time-frame problems and process bottlenecks. The CPM is ideally suited to projects consisting of numerous activities that interact in a complex manner.
In applying the CPM, there are several steps that can be summarized as follows:
1. Define the required tasks and put them down in an ordered (sequenced) list.
2. Create a flowchart or other diagram showing each task in relation to the others.
3. Identify the critical and non-critical relationships (paths) among tasks.
4. Determine the expected completion or execution time for each task.
5. Locate or devise alternatives (backups) for the most critical paths
المادة المعروضة اعلاه هي مدخل الى المحاضرة المرفوعة بواسطة استاذ(ة) المادة . وقد تبدو لك غير متكاملة . حيث يضع استاذ المادة في بعض الاحيان فقط الجزء الاول من المحاضرة من اجل الاطلاع على ما ستقوم بتحميله لاحقا . في نظام التعليم الالكتروني نوفر هذه الخدمة لكي نبقيك على اطلاع حول محتوى الملف الذي ستقوم بتحميله .
الرجوع الى لوحة التحكم
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