...WAN optimization tools are used mainly in application delivery networks which consist of WAN Optimization Controllers (WOCs) and Application Delivery Controllers (ADCs). On the data center end Application Delivery Controllers are present to distribute the traffic among servers based on application specific criteria. In the branch office portion of Application Delivery Controllers, WDC are present that uses its advanced compression and flow optimization capabilities to provide application availability, security, visibility, and acceleration. WAN Optimization mitigates the latency and bandwidth limitations of the WAN to provide remote users with access to applications in the data center. IT departments have been trying to take initiatives to meet their business objectives to reduce costs and consolidate resources. WAN optimization...
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...in the product kind. Organizations have already adopted solutions with varying degrees of planning and scheduling capabilities. Yet, operations executive acknowledge that these same systems are becoming out dated, lacking the speed, flexibility and responsiveness to manage their increasing complex production environment. Optimization techniques are applied to find out whether resources available are effectively utilized in order to achieve optimum profit from the activities of the firm. There should be consistency in the use of various resources and the mix should be such that it brings down the cost for ensuring profit. Therefore, it is the duty of the management to exercise control over the resources and to see that the resources are effectively utilized. Similarly, organizations in general are involved in manufacturing a variety of products to cater the needs of the society and to maximize the profit. While doing so, they need to be familiar with different combinations of product mix which will maximize the profit. Or alternatively minimize the cost. The techniques such as ratio analysis, correlation and regression analyses, variance analysis, optimization and projection methods can be adopted for ascertaining the extend of resource utilization and selection of practically viable and profitable product mixes by taking in to account all possible constraints. Tulsan, P.C, and Vishal pandey, (2002: 231). The ratio analysis helps to evaluate the performance of the organization...
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...corresponding elements, then adds the results. Example: [pic] If the row vector and the column vector are not of the same length, their product is not defined. Example: [pic] The Product of a Row Vector and Matrix When the number of elements in row vector is the same as the number of rows in the second matrix then this matrix multiplication can be performed. Example: [pic] If the number of elements in row vector is NOT the same as the number of rows in the second matrix then their product is not defined. Example: [pic] Linear programming (LP; also called linear optimization) is a method to achieve the best outcome (such as maximum profit or lowest cost) in a mathematical model whose requirements are represented by linear relationships. Linear programming is a special case of mathematical programming (mathematical optimization). More formally, linear programming is a technique for the optimization of a linear objective function, subject to linear equality and linear inequality constraints. Its feasible region is a convex polytope, 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...
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...Steepest Descent Direction in Optimization - Application and Algorithm Hemanand. T Department of Chemical Engineering, St. Joseph’s College of Engineering, Chennai – 600 119 Abstract: An analytical solution to identify the minimum value of a function used for optimization based on steepest descent technique was extensively discussed with applications in a process. The properties of gradient vector, the oscillation of function values and overshoot were analyzed in a function for the search of minimum. The best step size in each iteration was found by conducting a one-D optimization in the steepest descent direction. The five steps in the algorithm for steepest descent direction were done for the effective search for the minimum included (i) estimate of a starting design and set the iteration counter, (ii) selection of a convergence parameter, calculation of the gradient of function f(x) at the point, (iii) then stop the iteration process at the minimum point, otherwise, search for minimum by next iteration, (iv) calculation of step size to minimize and (v) updation of the design with the new values which yield minimization of an optimization process. Keywords: Gradient Vector, Overshoot, One-D optimization, Convergence Parameter, Oscillation. 1. Introduction: In mathematics, optimization, or mathematical programming, refers to choosing the best element from some set of available alternatives. In the simplest case, this means solving problems in which one...
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...Linear Programming: Using Solver in Excel Linear Programming was conceptually developed before World War II by the outstanding Russian mathematician A.N.Kolmogorov and gained its popularity ever since the development of Simplex method by George B. Dantzig in 1947. Linear programming deals with problems of maximizing or minimizing a linear function in the presence of linear equality and/or inequality constraints. In these problems, we find the optimal, or most efficient way of using limited resources to achieve the objective of the situation. Linear Programming enables users to model large and complex problems and solve in a short amount of time by the use of effective algorithm, hence it is a powerful and widely used tool in various fields such as science, industrial engineering, financial planning and management decision making. Nowadays, with the development of technology, most of the real world Linear Programming problems are solved by computer programs. Excel Solver is a popular one. We work through different examples to demonstrate the applications of linear Programming model and the use of Excel Solver for various decision making in operation and supply chain management. Components of Linear Programming model To solve the linear programming problems, we first need to formulate the mathematical description called a mathematical model to represent the situation. Linear programming model usually consists of the following components * Decision variables: These represent...
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...Boulder, CO: Westview Press, 209-229. An earlier version of this paper also appeared in Foresight and National Decisions: The Horseman and the Bureaucrat (Grant 1988). A S KEPTIC'S GUIDE TO COMPUTER MODELS 2 The Inevitability of Using Models........................................................................3 Mental and Computer Models..............................................................................2 The Importance of Purpose..................................................................................3 Two Kinds of Models: Optimization Versus Simulation and Econometrics.......4 Optimization.............................................................................................4 Limitations of Optimization..........................................................5 When To Use Optimization..........................................................8 Simulation................................................................................................9 Limitations of Simulation.............................................................11 Econometrics............................................................................................13 Limitations of Econometric...
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...Email aypolat@ku.edu.tr gulermis@ku.edu.tr Office Hours Office Location Course Description Introduction to modeling with integer variables and integer programming; network models, dynamic programming; convexity and nonlinear optimization; applications of various optimization methods in manufacturing, product design, communications networks, transportation, supply chain, and financial systems. Course Objectives The course is designed to teach the concepts of optimization models and solution methods that include integer variables and nonlinear constraints. Network models, integer, dynamic and nonlinear programming will be introduced to the students. Students will be exposed to applications of various optimization methods in manufacturing, product design, communications networks, transportation, supply chain, and financial systems. Several different types of algorithms will also be presented to solve these problems. The course also aims to teach how to use computer programs such as Matlab and GAMS to solve mathematical models. Learning Outcomes Students are expected to model real life problems using mathematical models including integer variables and nonlinear equations. Students will be able to apply mathematical modeling techniques such as dynamic, integer and nonlinear programming to different types of problems. They will also be able to model and solve transportation and network problems such as shortest path, maximum flow and minimum cost network flow...
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...DECISION MODELING DECISION WITH WITH MICROSOFT EXCEL MICROSOFT Linear Optimization Linear Optimization A constrained optimization model takes the form of a constrained performance measure to be optimized over a range of feasible values of the decision variables. The feasible values of the decision variables are determined by a set of inequality constraints. constraints Values of the decision variables must be chosen such that the inequality constraints are all satisfied while either maximizing or minimizing the desired performance variable. These models can contain tens, hundreds, or thousands of decision variables and constraints. Linear Optimization Very efficient search techniques exist to optimize constrained linear models. constrained These models are historically called linear programs linear (LP). In this chapter we will: 1. Develop techniques for formulating LP models 2. Give some recommended rules for expressing LP models in a spreadsheet that facilitates application of Excel’s Solver 3. Use Solver to optimize spreadsheet LP models Formulating LP Models Every linear programming model has two important features: Objective Function Constraints A single performance measure to be maximized or minimized (e.g., maximize profit, minimize cost) Constraints are limitations or requirements on the set of allowable decisions. Constraints may be further classified into physical, economic, or policy limitations or ...
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...bed scheduling, portering operations, emergency transport, accident trend analysis and treatment optimization. In the service sector, OR techniques have been found especially helpful when dealing with variability in service delivery such as call centres, queues for service and medical wait times. A sampler of typical OR applications includes: • • • • • • • • • • • • Optimization of LTL trucking (Yellow Freight) Optimal package designs (Domtar Packaging, Ltd) Manpower planning models (Treasury Board Secretariat) Aircraft operations (Delta Airlines) Surgical bed optimization (Fraser Health Authority) Pre-board passenger screening (Vancouver International Airport ) Switching network studies (Bell-Northern Research, Ltd) Maintenance Strategies for the US Coast Guard Revenue Management (American Airlines) Resource allocation in a mental health hospital (Douglas Hospital) Routing of Waste Trucks (Waste Management Inc.) Rail Car Optimization (CP Rail) Successful OR applications can be found in a broad array of industries dealing with challenges such as OR has been applied in many industry sectors including the following: Transport and Travel. OR techniques are used by airlines and rail companies to offer varying fares and make higher revenues by filling more seats at different prices - an OR technique known as Yield Management. All airlines depend on the effective use of OR techniques to make them operate at a profit. Retailing. In supermarkets, data from store loyalty card schemes...
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...of Economic Sciences, Tehran, Iran d Department of Industrial Engineering, South-Tehran Branch, Islamic Azad University, Tehran, Iran b a r t i c l e i n f o a b s t r a c t Considering the trade-offs between conflicting objectives in project scheduling problems (PSPs) is a difficult task. We propose a new multi-objective multi-mode model for solving discrete time–cost–quality trade-off problems (DTCQTPs) with preemption and generalized precedence relations. The proposed model has three unique features: (1) preemption of activities (with some restrictions as a minimum time before the first interruption, a maximum number of interruptions for each activity, and a maximum time between interruption and restarting); (2) simultaneous optimization of conflicting objectives (i.e., time, cost, and quality); and (3) generalized precedence relations between activities. These assumptions are often consistent with real-life projects. A customized, dynamic, and self-adaptive version of a multiobjective evolutionary algorithm is proposed to solve the scheduling problem. The proposed multi-objective evolutionary algorithm is...
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...equilibrium and has no incentive to alter his expenditure pattern. 3. Linear programming (LP, or linear optimization) is a mathematical method for determining a way to achieve the best outcome (such as maximum profit or lowest cost) in a given mathematical model for some list of requirements represented as linear relationships. Linear programming is a specific case of mathematical programming (mathematical optimization). 4. Utility is a measure of the total worth of a particular outcome; it reflects the decision maker's attitude toward a collection of factors such as profit, loss, and risk. Researchers have found that as long as the monetary value of payoffs stays within a range that the decision maker considers reasonable, selecting the decision alternative with the best expected monetary value usually leads to selection of the most preferred decision. However, when the payoffs become extreme, most decision makers are not satisfied with the decision that simply provides the best expected monetary value. 5. The Delphi method (/ˈdɛlfaɪ/ DEL-fy) is a structured communication technique, originally developed as a systematic, interactive forecasting method which relies on a panel of experts. Delphi is based on the principle that forecasts (or decisions) from a structured group of individuals are more accurate than those from unstructured groups.[6] The technique can also be adapted for use in face-to-face meetings, and is then called mini-Delphi...
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...Key quantitative techniques essential for analyzing and improving business operations. Spreadsheet modeling of business decision problems, both with and without data uncertainty. Linear and integer programming optimization models. Elementary applied probability modeling and Monte Carlo simulation. COURSE MATERIALS Required Textbook(s): Introduction to Management Science, 11/E (Available in Book Store) Bernard W. Taylor ISBN - 10: 0132751917 ISBN - 13: 9780132751919 Course items in Blackboard LEARNING GOALS AND OBJECTIVES LGO1. Students will understand and be able to apply Key quantitative techniques essential for analyzing and improving business operations A. Students will be able to use spreadsheet modeling of business decision problems, both with and without data uncertainty in preparing assignments, projects, or term papers in other courses in the functional area business disciplines as well as in research projects in the workplace. B. Students will be able to employ spreadsheet software (e.g. Microsoft Excel) as a tool to assist in the solution of business problems. C. Students will have an awareness of ethical issues in conducting research, in optimization problems and in the presentation of results. LGO2. Students will be able to understand risk from the perspective of Elementary applied probability modeling and Monte Carlo simulation. LGO3. Students will be familiarized with model - building for purposes of Optimization and forecasting...
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...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 of a very important area of mathematics called "optimization techniques". This field of study (or at least the applied results ...
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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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...60 | Office Hours | 30 | Contact Details | 09811033937 | Course eMail | r.s.reaches@gmail.com | Course Descriptor Course Overview(200 words) | Quantitative Methods-II, focuses on ‘Operations Research’ tools which helps in solving problems in different functional domain of business. It also helps to optimize business operations/processes. The Quantitative Method-II tools act as aids to decision makers to take best decision for effective & efficient use of resources which ultimately lead to profit maximization or to achieve multiple goals or objective. | Course must be aligned with a strategic objective of the program Prerequisites/Co-requisites | Quantitative Methods I | Learning Objectives | To learn basic optimization techniques and their managerial applications with a focus on methodologies such as Linear Programming, Transportation models, Assignment Models, Transhipment Models, Games Theory, Queuing Models, Goal Programming, Integer Programming, Non-linear Programming, Simulation and Decision Theory. | Learning objectives must be aligned with learning outcomes of the course Teaching Methods | Modeling, Case study, Software-based solutions | Refer academic policies and procedures handbook For Internal Use Only Session Plan* | SESSION-1: Overview on Operations Research modelling (OR modelling): meaning, definition, steps involved in OR modelling; Session-2: Overview on Linear Programming (LP): LP meaning, various applications,...
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