...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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...studied mathematical formulas that would allow me to find the optimal solution. In this paper, I will use both linear optimization and goal programming to take a number of sets of data to analyze and discover the optimal use of various constraints of resources. The paper will be divided into three different sections with a specific method applied in the first two sections, and a final section to describe the possible errors in the solutions presented in the prior two sections. In the first section, I will use linear optimization to take various sets of resources and distribute them appropriately among various products to find the best allocation to achieve maximum revenues. Linear optimization is the name of a branch of applied mathematics that deals with solving optimization problems of a particular form.1 Put simply, linear programming is finding the best outcome possible using a linear mathematical model. The constraints are linear inequalities of the variables used in the cost function. This method is the best available and of the most use given the present goal of achieving the maximum revenue possible for the company. In the second section, I will use goal programming to take into account the second set of constraints that faces many companies—labor. Since ALDI was a private company that sold its 1 Schulze, Mark A. "Linear programming for optimization." Perceptive Scientific Instruments, Inc (1998). 3 own manufactured products, I also had to study the labor that was...
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...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 of a very important area of mathematics called "optimization techniques". This field of study (or at least the applied...
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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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...Introduction of Linear Programming (LP) To understand LP , first we need to understand mathematical programming thoroughly. So what is mathematical programming (MP). MP is the branch of management science that deals with solving optimization problem, in which we want to maximize function (such as profit, expected return or efficiency) or minimize the function( such as cost. time or distance), Usually in a constrained environment. The recommended course of action is known as program : hence, the term MP is used to describe such problems. MP consist of 3 components (Elaborate 3 function) 1. Decision variable: - Which is controlled or determined by the decision maker 2. Objective Function:- Its to be maximize or minimize 3. Constraints:- Restrictive set of conditions that must be satisfied by any solution to the model. The most widely used mathematical model are LP models. LP models A LP model is model that seeks to maximize or minimize a linear objective functions subject to a set of linear constraints. Large company such as the San Miguel corporation, Texaco, American airlines and general motors have used linear models to affect efficiency and improve the bottom line . But LP can also be applied in smaller venues. In fact a wide variety of cases lend themselves to linear modeling , including problems from such diverse areas such as manufacturing, marketing, investing , advertising, trucking, shipping, agriculture, nutrition, E-commerce, restaurant and...
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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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...1 Mathematical Programming The Mathematical Programming Add-in constructs models that can be solved using the Solver Add-in or one of the solution add-ins provided in the collection. When the Math Programming add-in is installed, several new command lines are added to the OR_MM menu. The menu items under the title Math Programming create models of the different types. Selecting an item from this list causes a dialog box to be presented which constructs a mathematical programming model. The models created by the add-in are solved with the Excel Solver, the Jensen Network Solver or the Jensen LP/IP Solver. All are Excel add-ins. Documentation for these programs can be reached by clicking the links on the lower left. The Solver add-in comes with Excel, and it can solve linear programming, integer programming and nonlinear programming models. The Math Programming add-in automatically builds Solver models and calls the computational procedures that solve the problems. All four model types can be can be solved in this way. The Jensen LP/IP Solver solves linear or integer programming problems. It is available for the Linear/Integer Programming and Network Flow Programming model types. The Jensen Network Solver can solve pure or generalized network flow models. Both linear and integer problems can be solved. It is available for the Network Flow Programming or Transportation model types. Parametric analysis can be applied to any of the math programming models. Here one parameter...
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...Technical Supplement 1 Linear Programming with Transportation in Operations Management LEARNING OBJECTIVES After studying this technical supplement, you should be able to: 1. Explain the importance of optimization to operations management 2. Demonstrate how to develop linear programming models 3. Show how linear programming models can be solved using EXCEL 4. Demonstrate 0-1, transportation, and assignment models LINEAR PROGRAMMING MODELS IN OPERATIONS MANAGEMENT Linear programming (LP) is one of the most powerful analytic tools available to improve operations management. LP provides the optimal, or best possible, solution to problems that can be formulated by a linear function subject to a set of linear constraints. This has proven extremely useful in many operations management applications, some of which are described in Table 1. TABLE 1 Linear Programming Models |Type of Model |Variables |Function to Optimize |Typical Constraints | |Product Mix |Number of products to produce |Maximize contribution to |Resource limits, such as time, | | | |profit |labor, material; Maximum or | | | | |minimum quantities | |Blending |Amount of materials to combine |Minimize cost |Resource limits; Demand...
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...Linear Programming (LP) Linear programming, simply put, is the most widely used mathematical programming technique. It has a long history dating back to the 1930s. The Russian mathematical economist Leonid Kantorovich published an important article about linear programming in 1939. George Stigler published his famous diet problem in 1945 (“The Cost of Subsistence”). Of course, no one could actually solve these problems until George Dantzig developed the simplex method, which was published in 1951. Within a few years, a variety of American businesses recognized that they could save millions of dollars a year using linear programming models. And in the 1950s, that was a lot of money. In his book Methods of Mathematical Economics (Springer-Verlag, 1980), Joel Franklin talks about some of the uses of linear programming (LP). In fact, about half of his book is devoted to LP and its extensions. Today, we will analyze one of the examples provided in that book. The example comes from a 1972 article published in the Monthly Review of the Federal Reserve Bank of Richmond. Alfred Broaddus, the author, was trying to explain to bankers how Bankers Trust Company used linear programming models in investment management. His example was simple and effective. The bank has up to 100 million dollars to invest, a portion of which can go into loans (L), and a portion of which can go into securities (S). Loans earn 10%, securities 5%. The bank is required to keep 25% of its invested...
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...Assignment MIS This project involves packaging nails so that you make the most profit possible (this is a profit maximizing problem). Say you have six types of nails and can make as many as you need of each. These nails are in 4-inch, 3.5-inch, 3-inch, 2.5-inch, 2-inch, and 1.5-inch nails. The cost of making each type of nail depends on how big a nail it is. Those cost and selling prices are listed in the table below along with the weights. The nails will be sold in boxes of up to 30 nails. There must be no more than 10, but no less than 5, of each of three types of nails in each box. The nails in each box should weigh no more than 20 ounces. You're looking for the combination with the highest profit using a trial-and-error method. A spreadsheet would be helpful for completing this project. You'll most likely find that you identify some promising paths to follow right away and will concentrate on those to reach the best one. |Nail |Weight |Cost |Selling price | |4 inch |1 oz |4 cents |8 cents | |3.5 Inch |0.85 oz |3,5 cents |7 cents | |3 inch |0.7 oz |3 cents |6 cents | |2.5 inch |0.5 oz |2.5 cents |4 cents | |2 inch |0.25 oz |2 cents |3 cents | |1.5 inch |0.1 oz ...
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...these codes: - Allgod=god mode for you and your team Allammo=Infinite ammo easy=Easy difficulty ewww=Kill all enemies Submitted By: Karo Bonas Helicopter Crash Entry Location: In boarder crossing get past the first complex and carry on down the road it should say that there is a helicopter on its way get to a safe place and when its out of range follow it it should start to descend and it will hit the ground and bounce into landing position trust me its funny Submitted By: craig Re-Supply Hint Entry Location: In the 8th level (Re-supply), When u get out of the truck, just run straight without stopping. U will see some big green containers placed near the wall. Get on top of one of it with the help of the wooden box kept in between. When u r on top, try to jump above the wall with ur mouse pointer a little up. Try it a few times and u will be able to jump above the wall and get outside. Ur first objective will be complete without going in the building and not even killing anyone. Submitted By: DaViD jOnEs -...
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...5/15/13 shipping container home Select Language Pow ered by Translate s h i p p i n g Hom e Freew are Cyber Education Energy/Minerals Processes/Structures Fossils/Tim e/Space Flooding Expeditions Aboriginal Links Brow se to Bach c o n t a i n e r h o m e building a shipping container home go to step by step constuction Remote accomodation is always a challenge in difficult terrain. What follows is an example of using two conventional shipping containers to create 90 square meters of living space in dense rainforest adjoining World Heritage Rainforest. The facility, on a nature refuge is used for rainforest research. The terrain is extremely difficult and accessed via a narrow track made by woodcutters in 1928. The techniques are simple and require only very basic skills. They produce a dry, durable ,vermin proof, comfortable, removable facility with a low ecological impact. See also the excellent container home site: KTainer (external link) http://www.geeksville.com/~kathy/ktainer.html (Earth Science Australia thanks the following sponsors for their support) For the best deals on shipping containers visit www.containers.com.au New and used shipping containers for sale visit www.portcontainerservices.com.au High quality water tanks visit www.bushrangerwatertanks.com.au Click on any image for larger image. Step by Step Construction earthsci.org/education/fieldsk/container/container.html 1/11 5/15/13 shipping container home We cleared...
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...Data Gathering Procedure The data for this research were collected using a survey questionnaire. The survey was created using suitable questions modified from related research and individual questions formed by the researcher. The survey was comprised of 20 to 25 questions, which were related to the participant’s perception regarding for the reject products of corrugated box in well pack. In the questionnaire, Likert scale was used to determine if the respondent agreed or disagreed in a statement. After the professor validated the questionnaire, these were distributed to the 4th year Industrial Engineering students of Quezon City Polytechnic University . The researchers assured confidentiality of their survey sheets since the identities are not important. The researchers also understood that people’s consciousness may also affect their honesty and effectiveness in answering the survey, and so, the researchers gave people the option of being anonymous. Participants were given time to respond and then the researchers collected the surveys the next day. There were no incentives offered for participating in the research. Next, the researchers planned the questions that they would be asking to the interview. The researchers interviewed certain number of workers in the company regarding to the reject products. Statistical Treatment of Data In getting the sample size, the group used the Solving formula which is, n= , N stands for the whole population of the workers who where work...
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...In this beautiful world, many forces that can’t be identified by our naked eye surround us like anything...and some people do not even realize their existence. Forces like magnetism, electricity, gravity etc. have been a constituent of earth science. The spinning of the earth and things like gravity force etc. is due to the earth’s magnetism property. Here we are introducing a simple DIY science project for students or hobbyist – Maglev Train. Magnetic suspension, Maglev and Magnetic levitation are an approach by which a thing or any object is hanging without any support apart from the magnetic fields. This magnetic levitation approach is utilized for designing this simple maglev train. Actually the original maglev trains are very complex in design, but here we try to design a simple maglev train, which uses some permanent magnets, cardboard or wooden boards etc. Working Principle of Maglev Trains: The basic principle behind the magnetic levitation is to use the magnetism property to levitate any objects. Magnetism is a part of our elementary science, and the principle is that “the like/same poles repel each other but the unlike/opposite poles attract each other”. Actually our Maglev Train works on this principle of magnetism. The train floats on the guide rail due to this principle of magnetism that the magnetic forces. Materials Required for Maglev Trains: The materials required for the construction of Maglev Train model are listed below. * Wooden block : 5" x...
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...| [pic] | |DAVAO PACKAGING CORPORATION | |BO. A.O. FLOIRENDO, PANABO CITY | |Corporate Profile | |COMPANY BACKGROUND | |INTRO | |Davao Packaging Corporation (DAPACOR) is the premier producer of world class packaging products targeting the agricultural, | |industrial, and consumer markets. | |DAPACOR's core products include: corrugated carton boxes, plastic films and sheets, synthetic twine, sticker labels, and | |recycled resins. DAPACOR is an organization of skilled individuals dedicated to the pursuit of Quality, Excellence and | |Innovation. It has highly-advanced and state-of-the-art equipment that boost its capabilities to exceed its customers' | |expectations. ...
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