...SIMPLEX METHOD Devharajan Rangarajan Department of Electronic Engineering National University of Ireland, Maynooth devharajan.rangarajan.2016@mumail.ie Abstract— An optimization problem consists of maximizing or minimizing a real function by systematically choosing input values from within an allowed set and computing the value of the function. This pays way to a new world of constrained optimization. This paper focuses on one such optimization technique known as Linear programming and one of its method known as Simplex method in detail with examples. cTx = c1x1 + · · · + cnxn The subject of linear programming can be defined quite concisely. It is concerned with the problem of maximizing or minimizing a linear function whose variables are required to satisfy a system of linear constraints, a constraint being a linear equation or inequality. The subject might more appropriately be called linear optimization. Problems of this sort come up in a natural and quite elementary way in many contexts but especially in problems of economic planning. (or Ax ≤ b) I. INTRODUCTION Linear programming is the process of taking various linear inequalities relating to some situation, and finding the "best" value obtainable under those conditions. A typical example would be taking the limitations of materials and labour, and then determining the "best" production levels for maximal profits under those conditions. In "real life", linear programming is part...
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...computer-based, visual or verbal representations are used. The range of problems and issues to which management science has contributed insights and solutions is vast. It includes scheduling airlines, both planes and crew, deciding the appropriate place to site new facilities such as a warehouse or factory, managing the flow of water from reservoirs, identifying possible future development paths for parts of the telecommunications industry, establishing the information needs and appropriate systems to supply them within the health service, and identifying and understanding the strategies adopted by companies for their information systems. Scientific Planning Successful management relies on careful coordination, often using scientific methods in project planning. For example, critical path analysis allows us to identify which tasks in a project will take the longest or adversely affect the length of other tasks, permitting us to focus on those tasks. Computer models can also help we determine utilization and recommend more effective usage. In addition, this type analysis allows us to develop proactive strategies for handling outages and...
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...Literature survey 3 Research Methods 4 Research Justification 7 Conclusion 7 Bibliography 8 Statement of research problem The purpose of this study is to find out if the adoption of Extreme programming in a learning environment has improved student productivity. It is a software development process used by small teams who have rapidly changing requirements. With regard to students, all students that are studying software development modules are also faced with this problem where by the requirements are continuously changing as they get deeper within their project. This paper is to show if extreme programming is actually helping students become more productive regardless of the ever changing requirements. Context or background to the research problem In this day and age the most widely used form of agile development in software development is extreme programming which was proposed by Kent Beck in 1996. Many parameters contribute to the success of XP. Researchers concluded that using XP in an educational domain has many benefits, where they have seen that less skilled students were able to show more progress than they would have if a traditional methodology were used.(Assassa, Mathkour, & Al Dossari). XP offers a number of practices, values and principles which are advised to be adopted in order to run a software development project(Assassa et al., 2006). These values include communication, simplicity, feedback and courage. Extreme programming has four stages which are...
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...The Importance of Alice to New Programmers Programming is the act of writing computer programs or software in one or more of a set of programming languages. It seems highly abstruse and technical to the untrained. Learning it is a delicate process that requires a lot of care and diligence. If this learning process is rushed or mismanaged, the required basics would not be picked up and this would make programming much harder later on. When a person wants to learn anything new, it is considered essential that the person start from the rudiments. For example, when a person is learning how to play a musical instrument, he must first learn about its structure, then how to play basic melodies before delving into symphonies or even self-composition. For a person learning programming, it is advised that he begin with a simple language such as Python or Ruby so as to obtain a good foundation in the methods of programming without being discouraged by the complexities of the more advanced ones such as C++ or Java. An equally effective approach is to use tutoring software such as Alice. Alice is like the training wheels for programmers. It is a software environment that allows its users to manipulate objects in three-dimensional space, with the aid of visual scripting elements. No real programming is done. However, the procedures required to get work done in Alice are similar in logic to the ones used in actual programming and as a result of this, the prospective programmers are able to...
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...• Linear Programming Supplement E TRUE/FALSE 1. Linear Programming Linear programming is useful for allocating scarce resources among competing demands. Answer: True Reference: Introduction Difficulty: Easy Keywords: linear programming, scarce resources, competing demands A constraint is a limitation that restricts the permissible choices. Answer: True Reference: Basic Concepts Difficulty: Moderate Keywords: constraint, limit Decision variables are represented in both the objective function and the constraints while formulating a linear program. Answer: True Reference: Basic Concepts Difficulty: Moderate Keywords: constraint, decision variable, objective function A parameter is a region that represents all permissible combinations of the decision variables in a linear programming model. Answer: False Reference: Basic Concepts Difficulty: Moderate Keywords: parameter, decision variable, feasible region In linear programming, each parameter is assumed to be known with certainty. Answer: True Reference: Basic Concepts Difficulty: Moderate Keywords: parameter, assumption, certainty The objective function Maximize Z = 3x + 4y is appropriate for linear programming. Answer: False Reference: Basic Concepts Difficulty: Moderate Keywords: linearity, assumption, proportionality 2 2. 3. 4. 5. 6. 199 Copyright ©2010 Pearson Education, Inc. Publishing as Prentice Hall Supplement E • Linear Programming 7. One assumption of linear programming is that...
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...CAPITOL UNIVERSITY College of Computer Studies Introduction to Programming Activity Book Compiled by: Mark Godfrey D. Torres 2012 Introduction to Programming ii Table of Contents Weeks 1 to 3 – Creating Your First Java Classes ....................................................................................... 1 Objectives ........................................................................................................................................... 1 Summary ............................................................................................................................................ 1 The Don’ts........................................................................................................................................... 2 Key Terms ........................................................................................................................................... 3 Seatwork............................................................................................................................................. 6 Where to Save Your Files ................................................................................................................. 6 Configuring Windows to Work with the Java SE Development Kit................................................... 6 Your First Application ........................................................................................................................
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...Running head: GROUP SOFTWARE DEVELOPMENT Team Programming Environments Information Technology for Teams Course Team Programming Environments Programming teams are achieving advances in deployment of more modular software products through the use of adaptive techniques in software development. Companies implementing large scale enterprise planning and control systems, product data management tools and complex back office systems for global service and support are finding these techniques to be more cost effective, adaptable and lean improving user requests for changing software functionality, processes and improved deployment strategies (Applegate, Austin, & McFarlan, 2002). This paper will compare and contrast three team oriented programming environments including Rational, Unified Modeling and Extreme Programming and will describe the impact of these programming environments on group software development. Literature Review of Software Trends The traditional methods of systems planning and investment decision making in the last century have given pause to leaders who witnessed costs in design, implementation and deployment of software skyrocket, created armies of support teams to operate and manage the software products and forced many firms into bankruptcy. Companies who have successfully implemented enterprise systems are now seeking more adaptive infrastructure deployments, software end-user functional value, and more adaptable...
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...Operations Research and its Prospects in Pakistan Prof. Dr. Shoaib ud Din Mathematics Department Punjab University, Lahore, Pakistan Operations Research has had an increasingly great impact on the management of organizations in the recent years. In fact, with the exception of advent of electronic computer, the extent of this impact seems to be unrivalled by that of any other recent development. However, all the development in this field has gone almost unnoticed in most developing countries including Pakistan. This article is an effort to introduce Mathematics community in the country to the subject and its achievements. A brief history In order to appreciate the importance of OR in the world today it is important that we know something of its history and evolution. Although roots of Operations Research can be traced back many decades, it is generally agreed that this discipline began during World War II. During the War team of British scientists with diverse background were called upon to study the strategic and tactical problems associated with air and land defense of the country. The establishment of this scientific team marked the first formal Operations Research activity. Their efforts were allegedly instrumental in winning the Air Battle of Britain, The Island Campaign in the Pacific, the Battle of the North Atlantic, and so on. The name Operations Research-Operational Research in the United Kingdom – was apparently coined because the problems assigned to this team...
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...ASSIGNMENT ON OPERATION RESEARCH ( FIN – 3104 ) 3RD YEAR , 1ST SEMESTER BBA – 3RD BATCH DEPARTMENT OF FINANCE JAGANNATH UNIVERSITY TOPIC Quantitative Analysis for Optimization : Using Linear Programming & Transportation Problem Group Name Name & ID No. of the Group Members: |Sl. No. |Name |ID No. | | | | | |01 |Suman Chandra Mandal (Group Leader) |091557 | | |Md. Nahid Islam |091604 | |02 | | | | | | | |03 |Mahbuba Mehreen |091619 ...
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...A look at linear programming, using the simplex method Earlier in the class we were introduced to linear programming and now we are going to introduce a different method using a more geometric version called the simplex method. First, I am going to have to explain theory of the simplex method and then we’ll explain the real world uses of this algebraic math Ok, so earlier in the class we were introduced into liner equations and inequalities. With the simplex method we are going got look for what is called “The Optimum Solution”, but in order to find the optimum solution we need to change the linear equation so that it can be recognized differently and computer in geometric form as well as on our graph. We are now going to use a special matrix or TABLEAU to find the many variables and to solve for an optimum solution by substituting some of our variables into our sometimes large programming problem. I must say that the problem could sometimes result in a solution or it may also have no solution at all. Once we find that some of the test are confirmed with the simplex method and we come to the optimal solution the process itself stops. With this method we don’t have to consider that the amount of corner point will increase with the amount of variables, since we are only looking for the optimal solution. In the text we are given many examples of what this simplex method of linear programming problems. As I have read throughout the chapters I see that the most probable applications...
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...School PGDM Batch 2015-17 Semester II Course Outline 1 Shanti Business School, Ahmedabad PGDM 2015-17: Program Structure Semester-1 Semester-2 Semester-3 Semester-4 Course credit Course credit Course credit Language Skills @ Written Analysis & Communication @ Soft skills II @ Employability Skills @ IT & MIS 2 Soft skills I @ Computing skills 2 Social Media Marketing @ 2 Legal Aspects of Business 2 Business Strategy 3 Management Control Systems 3 Micro Economics 3 Macro Economics 3 Business Environment 3 Business Ethics & Corporate Governance 2 Quantitative Methods-1 3 Business Research Methods 3 Quantitative Methods-2 3 Core Elective-1 3 Core Elective1 3 Core Elective-2 3 Core Elective2 3 Elective-1 3 Elective-1 3 Elective-2 3 Elective-2 3 Grand Project-1 3 Grand Project-2 3 Principles of Management Basic Building Blocks Autumn Break Executive Skills Organisational Behavior Human Resources Management 3 Marketing Management 1 3 Marketing Management -2 3 Understanding Financial Statements 3 Financial Mgt 3 Operation Management Management Domain 3 3 Basics of Business Planning 2 Electives Credits Autumn Break credit SUMMER INTERNSHIP Course S 1 22 S 2 ...
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...www.VLCglobal.com/support VLC Course Descriptions Quantitative Analysis for Decision Making Quantitative Analysis for Decision Making An Immersive Virtual Reality Learning Experience 2011-2012 Course Description This course provides the student with the concepts, methods and tools for the application of logical and quantitative analysis to business decision making and problem solving. It familiarizes the student with a wide range of software and other classical and contemporary resources related to decision and problem analysis, including basics of logic and decision making, principles of optimization, probabilistic distributions, linear programming, simplex, queuing and transportation problems, break even analysis, inventory management, forecasting and simulation. The course highlights the benefits as well as the limits of quantitative analysis in a real-world context. This course may be adapted for the graduate and undergraduate levels. Materials Readings, assignments, problems and assessments are integrated into the courseware. Any additional materials will be assigned by the instructor at the start or during the course. Course Outline & Assignments Assignments will change from time to time as new resources become available, contemporary events have bearing on the topics, or the social, legal, or economic environments change. FUNDAMENTALS OF DECISION MAKING AND PROBLEM SOLVING (Module One, 4-6 hours) • • • • • • • • • • • • • • ...
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...than less than or equal to greater than greater than or equal to equal to not equal Logical Operators && || ! ^ short circuit AND short circuit OR NOT exclusive OR if Statements if (condition) { statements; } if (condition) { statements; } else { statements; } if (condition1) { statements; } else if (condition2) { statements; } else { statements; } switch Statements switch (intExpression) { case value1: statements; break; ... case valuen: statements; break; default: statements; } loop Statements while (condition) { statements; } do { statements; } while (condition); for (init; condition; adjustment) { statements; } Companion Web site: www.pearsonhighered.com/liang Java Quick Reference Frequently Used Static Constants/Methods Math.PI Math.random() Math.pow(a, b) System.currentTimeMillis() System.out.println(anyValue)...
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...uni-magdeburg.de 1) 2) 3) 1 A Comparison of Solution Procedures for the Flow Shop Scheduling Problem with Late Work Criterion Abstract In this paper, we analyze different solution procedures for the two-machine flow shop scheduling problem with a common due date and the weighted late work criterion, i.e. for problem F2 | dj = d | Yw, which is known to be binary NP-hard. In computational experiments, we compare the practical efficiency of a dynamic programming approach, an enumerative method and a heuristic list scheduling procedure. Test results show that each solution method has its advantages and none of them can be rejected from the consideration a priori. Keywords: flow shop, late work, dynamic programming, enumerative method, list scheduling 2 1. Introduction The process of investigating every new optimization problem follows the same well known scheme (cf. e.g. (Błażewicz, Ecker, Pesch, Schmidt & Węglarz, 2001), (Brucker, 1998)). If researchers have failed in constructing an optimal polynomial-time method solving the problem under consideration, they attempt to prove the hardness of the problem....
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...of the different projects. TRUE/FALSE 4. If a maximization linear programming problem consist of all less-than-or-equal-to constraints with all positive coefficients and the objective function consists of all positive objective function coefficients, then rounding down the linear programming optimal solution values of the decision variables will ______ result in a(n) _____ solution to the integer linear programming problem. A) always, optimal B) always, non-optimal C) never, non-optimal D) sometimes, optimal E) never, optimal 5. The branch and bound method of solving linear integer programming problems is an enumeration method. TRUE/FALSE 6. In a mixed integer model, all decision variables have integer solution values. TRUE/FALSE 7. For a maximization integer linear programming problem, feasible solution is ensured by rounding _______ non-integer solution values if all of the constraints are less-than -or equal- to type. A) up and down B) up C) down D) up or down 8. In a total integer model, all decision variables have integer solution values. TRUE/FALSE 9. The 3 types of integer programming models are total, 0 - 1, and mixed. TRUE/FALSE 10. The branch and bound method of solving linear integer programming problems is _______. A) an integer method B) a relaxation method C) a graphical solution D) an enumeration method 11. The linear programming relaxation contains...
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