...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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...Overview and examples from Finite Mathematics Using Microsoft Excel® Revathi Narasimhan Saint Peter's College An electronic supplement to Finite Mathematics and Its Applications, 6th Ed. , by Goldstein, Schneider, and Siegel, Prentice Hall, 1997 Introduction In any introductory mathematics course designed for non-mathematics majors, it is important for the student to understand and apply mathematical ideas in a variety of contexts. With the increased use of advanced software in all fields, it is also important for the student to effectively interact with the new technology. Our goal is to integrate these two objectives in a supplement for the text Finite Mathematics and Its Applications, by Goldstein, Schneider, and Siegel. The package consists of interactive tutorials and projects in an Excel workbook format. The software platform used is the Microsoft Excel 5.0 spreadsheet. It was chosen for the following reasons: • • • suited to applications encountered in a finite math course widespread use outside of academia ease of creating reports with a professional look Use of Excel 5.0 was put into effect in the author's sections of the Finite Mathematics II course in the Spring 1996 semester. It was expanded to cover the Finite Mathematics I course for the Fall semester of 1996. Using a combination of specially designed projects and tutorials, students are able to analyze data, draw conclusions, and present their analysis in a professional format. The mathematical...
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...LINEAR PROGRAMMING II 1 Linear Programming II: Minimization © 2006 Samuel L. Baker Assignment 11 is on page 16. Introduction A minimization problem minimizes the value of the objective function rather than maximizing it. Minimization problems generally involve finding the least-cost way to meet a set of requirements. Classic example -- feeding farm animals. Animals need: 14 units of nutrient A, 12 units of nutrient B, and 18 units of nutrient C. Learning Objective 1: Recognize problems that linear programming can handle. Linear programming lets you optimize an objective function subject to some constraints. The objective function and constraints are all linear. Two feed grains are available, X and Y. A bag of X has 2 units of A, 1 unit of B, and 1 unit of C. A bag of Y has 1 unit of A, 1 unit of B, and 3 units of C. A bag of X costs $2. A bag of Y costs $4. Minimize the cost of meeting the nutrient requirements. To solve, express the problem in equation form: Cost = 2X + 4Y objective function to be minimized Constraints: 2X + 1Y $ 14 nutrient A requirement 1X + 1Y $ 12 nutrient B requirement 1X + 3Y $ 18 nutrient C requirement 8 8 Read vertically to see how much of each nutrient is in each grain. X $ 0, Y $ 0 non-negativity Learning objective 2: Know the elements of a linear programming problem -- what you need to calculate a solution. The elements are (1) an objective function that shows the cost or profit depending on what choices you make, (2) constraint inequalities...
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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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...Solver: A solver is a generic term indicating a piece of mathematical software, possibly in the form of a stand-alone computer program or as a software library, that 'solves' a mathematical problem. A solver takes problem descriptions in some sort of generic form and calculates their solution. In a solver, the emphasis is on creating a program or library that can easily be applied to other problems of similar type. Types of problems with existing dedicated solvers include: * Linear and non-linear equations. In the case of a single equation, the "solver" is more appropriately called a root-finding algorithm. * Systems of linear equations. * Nonlinear systems. * Systems of polynomial equations, which are a special case of non linear systems, better solved by specific solvers. * Linear and non-linear optimisation problems * Systems of ordinary differential equations * Systems of differential algebraic equations * Logic/satisfiability problems * Constraint satisfaction problems * Shortest path problems * Minimum spanning tree problems * Search algorithms Excel Solver, introduced by Microsoft in 1991, is a powerful optimization application used in finance, production, distribution, purchasing and scheduling. It is part of the data analysis tools used for what-if analysis--a process of identifying changes in a cell by adjusting related cells. If your boss has asked you to find ways to increase company's profits by determining...
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...Spreadsheet Analysis & Modeling MIS-505 Questions for Final Exam 1. What is name range? How can ranges be named? What are its uses? 2. What is lookup in Excel? What are the different kinds of lookup functions? What are its uses? 3. What is Index function? Write down the procedure of index function. What are its uses? 4. What is Match function? How you can write an Index and Match functions in a nested way? What are its uses? 5. Describe different kinds of text functions in Excel (such as left, right, mid). 6. How can you put date in Excel? What are its uses? 7. What is NETWORKINGDAYS function in Excel? What is NETWORKINGDAYS.INT function in Excel? What are its uses? 8. What is workday and WORKDAY.INT functions in Excel? What are its uses? 9. What is Net Present Value? How do NPV and XNPV function work in Excel? What are its uses? 10. What is internal rate of return (IRR)? How do IRR, XIRR, and MIRR work in Excel? What are its uses? 11. What is present value? How does PV function work? What are its uses? 12. What is Future Value? How does FV function work? What are its uses? 13. Write down the functions of PMT, PPMT, IPMT. How can you use these functions to prepare a loan amortization schedule? 14. Write down the function of IF Statement, AND, OR and XOR. 15. Describe different Time functions. What are its uses? 16. What is What If Analysis? Describe different kind of what if analysis. What are its uses...
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... | |Student Course Guide | |Prerequisite: MAT 300 | |INSTRUCTIONAL MATERIAL – Required | |( including all mandatory software) | |Taylor, B. M. (2010). Introduction to management science (10th ed.). Upper Saddle River, NJ: Pearson/Prentice Hall. | |Treeplan add-on for Excel. This software is available in the Open Lab at Strayer campuses, and can also be downloaded from the textbook's | |companion Website. http://wps.prenhall.com/bp_taylor_introms_10/112/28870/7390752.cw/-/7390754/index.html | | | |COURSE DESCRIPTION | |Applies quantitative methods to systems management (Decision Theory), and / or methods of decision-making with respect to sampling, | |organizing, and analyzing empirical data. ...
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...ads are important; hence they wish to run the equivalent of at least eight weekday and at least two Sunday ads during August. (Assume that a fractional ad would simply mean that a smaller ad is placed on one of the days; that is, 3.5 ads would mean three full-page ads and one half-page ad. Also, assume that smaller ads reduce exposure and costs proportionately.) This August has 26 weekdays and 5 Sundays. The objective is to determine the optimal placement of ads by PMA in the newspaper during August so as to maximize the cumulative total exposure (as measured by circulation) for the month of August. a) Formulate the linear programming model for the problem. b) Use the Graphical method to find the optimal solution. Show all steps. c) Use Excel Solver to find the optimal solution. Copy and paste your spreadsheet and the Answer report in its entirety from Excel. Remember to not delete/modify any part of the Answer Report. Problem 2 (50 Points) Missouri Mineral Products (MMP) purchases two unprocessed ores from Bolivia Mining, which it uses in the production of various compounds. Its current needs are for 800 pounds of copper, 600 pounds of zinc, and 500 pounds of iron. The amount of each mineral found in each 100 pounds of the...
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...Cement On August 26, 2012, Dr. Hitesh Arora asked me to submit an end term project as part of the Decision Making Models course curriculum. The project was supposed to be prepared on any of the topic or concept taught as part of the course curriculum. Attached to this cover memorandum is a report that picks up the transportation problem at Shaktiman Cement and strives to provide a solution to the problem. The transportation problem at Shaktiman Cement consists of three production plants and three construction sites. The company has to figure out a way to satisfy the demands of the three construction sites using the cement it produces and transport the cement from its plants to the construction sites at the minimum transportation cost possible. The solution to the transportation problem was arrived at by solving the problem using the ‘Solver’ tool in Microsoft Excel. I would like to thanks Dr. Hitesh Arora for guiding me through with the course curriculum of Decision Making Models. The project would not have been possible without his valuable inputs and methodical teaching pedagogy. Cordially, Shantanu Mittal 211134, Sec-C FMG-21 ii CONTENTS ii 1 2 3 10 10 Cover Memorandum............................................................................................ 1. Transportation Problems...................................................................................... 2. The...
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...com/login. Major assignment handouts, sample workbooks, etc. are made available in https://sjsu.instructure.com/login. You are responsible for regularly checking the Calendar and Course News in Canvas to keep up with ongoing developments during the course. Course Description .Quantitative models and optimization systems used in problemsolving. Studies of decision criteria, statistical decision making, linear programming, inventory control, Project Scheduling/Management Theory, PERT/CPM, simulation, and other techniques used in management. Course Goals and Student Learning Objectives. The course will emphasize basic principles of mathematical modeling, computational algorithms and spreadsheet computer solutions of optimization, decision analysis, simulation and network based methods applied to business problems. I. Students will learn various aspects of Linear Programming How to formulate word problems algebraically How to obtain Graphical Solutions to problems with two variables How to set up Linear Programming problems in the spreadsheet How to use the Excel Solver to solve LP problems in the spreadsheet How to read and interpret the Answer and Sensitivity reports...
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...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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...Chapter 5 Modeling with Linear Programming 5.1 Introductory Example SilComputers makes quarterly decisions about their product mix. While their full product line includes hundreds of products, we will consider a simpler problem with just two products: notebook computers and desktop computers. SilComputers would like to know how many of each product to produce in order to maximize pro t for the quarter. There are a number of limits on what SilComputers can produce. The major constraints are as follows: 1. Each computer either notebook or desktop requires a Processing Chip. Due to tightness in the market, our supplier has allocated 10,000 such chips to us. 2. Each computer requires memory. Memory comes in 16MB chip sets. A notebook computer has 16MB memory installed so needs 1 chip set while a desktop computer has 32MB so requires 2 chip sets . We received a great deal on chip sets, so have a stock of 15,000 chip sets to use over the next quarter. 3. Each computer requires assembly time. Due to tight tolerances, a notebook computer takes more time to assemble: 4 minutes versus 3 minutes for a desktop. There are 25,000 minutes of assembly time available in the next quarter. Given current market conditions, material cost, and our production system, each notebook computer produced generates $750 pro t, and each desktop produces $1000 pro t. There are many questions SilComputer might ask. The most obvious are such things as How many of each type computer should SilComputer produce...
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...and second parts, put them in a report format with the instructions given (executive summary, etc.) and submit. 2. Expected situation: Setup the spreadsheet model and provide brief answers to part I questions within the Excel worksheet. I provide feedback, and you will be working on the rest of the questions until December 9. If there is any mistake in your progress submission, I will provide specific instructions on how to fix them, and in the following weeks after that, you may submit additional progress reports to make sure you are on the right track. I will provide feedback on your progress if you ask for it. 3. Flexible situation: Read/understand the case, have some ideas about what method you will use to solve it and how you will set up the Excel model, and have a feasible plan that will help you finish the case by the final deadline. In this case, you can submit a draft or partially-complete Excel worksheet and I will provide feedback based on your submission. Case: Location, Distribution, and Capacity Expansion at a Beer Manufacturer A Case Study of Location, Distribution, and Capacity Expansion Decisions at Anadolu Efes Case Description and Objectives This case study involves the application of linear programming and integer linear programming methods in solving a distribution and capacity planning problem at Anadolu Efes Beverage Group. Faced with intense competition and anticipated increase in beer demand that will surpass the current production capacity, the...
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...Images of Microsoft® Excel dialog boxes © Microsoft. All rights reserved. This content is excluded from our Creative Commons license. For more information, see http://ocw.mit.edu/help/faq-fair-use/. 1 Tool for Solving a Linear Program: Excel has the capability to solve linear (and often nonlinear) programming problems. The SOLVER tool in Excel: May be used to solve linear and nonlinear optimization problems Allows integer or binary restrictions to be placed on decision variables Can be used to solve problems with up to 200 decision variables 2 How to Install SOLVER: The SOLVER Add-in is a Microsoft Office Excel add-in program that is available when you install Microsoft Office or Excel. To use the Solver Add-in, however, you first need to load it in Excel. The process is slightly different for Mac or PC users. Microsoft: 1. Click the Microsoft Office Button , and then click Excel Options. 2. Click Add-Ins, and then in the Manage box, select Excel Add-ins and click Go. 3. In the Add-Ins available box, select the Solver Add-in check box, and then click OK. If Solver Add-in is not listed in the Add-Ins available box, click Browse to locate the add-in. If you get prompted that Solver is not currently installed, click Yes to install it. 4. After you load Solver, the Solver command is available in the Analysis group on the Data tab. MAC: 1. Open Excel for Mac 2011 and begin by clicking on the Tools menu. 2. Click Add-Ins, and then in the Add-Ins...
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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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