Optimization Modeling for Inventory Logistics Engineering & Technology Management ETM 540 – Operations Research in Engineering and Technology Management Fall 2013 Portland State University Dr. Tim Anderson Team: Logistics Noppadon Vannaprapa Philip Bottjen Rodney Danskin Srujana Penmetsa Joseph Lethlean Optimization Modeling for Inventory Logistics Contents Abstract .............................................................................................................
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Mathematical logic is something that has been around for a very long time. Centuries Ago Greek and other logicians tried to make sense out of mathematical proofs. As time went on other people tried to do the same thing but using only symbols and variables. But I will get into detail about that a little later. There is also something called set theory‚ which is related with this. In mathematical logic a lot of terms are used such as axiom and proofs. A lot of things in math can be proven‚ but there
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Introduction to Optimization Course Notes for CO 250/CM 340 Fall 2012 c Department of Combinatorics and Optimization University of Waterloo August 27‚ 2012 2 Contents 1 Introduction 1.1 An example . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.1.1 1.1.2 1.2 1.3 1.2.1 1.3.1 1.3.2 1.4 1.4.1 1.4.2 1.5 1.5.1 1.5.2 1.6 1.6.1 1.6.2 1.6.3 1.7 1.8 2 The formulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . Correctness . . . . . . . . . . . . . . . .
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LECTURE NOTES ON MATHEMATICAL INDUCTION PETE L. CLARK Contents 1. Introduction 2. The (Pedagogically) First Induction Proof 3. The (Historically) First(?) Induction Proof 4. Closed Form Identities 5. More on Power Sums 6. Inequalities 7. Extending binary properties to n-ary properties 8. Miscellany 9. The Principle of Strong/Complete Induction 10. Solving Homogeneous Linear Recurrences 11. The Well-Ordering Principle 12. Upward-Downward Induction 13. The Fundamental Theorem of Arithmetic
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such as "maximize contribution" becomes a(n) -objective function. Choosing the best alternative in the face of random states of nature is referred to as -decision thoery Linear programming is part of larger body of knowledge referred to as optimization -True One requirement of a linear programming problem is that the objective function must be expressed as a linear equation. -True Which of the following is not one of the steps in setting up a LP formulation> -calculate the objective
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maximizing a monotonically increasing function of a variable is equivalent to maximizing the variable itself. Therefore ln(Q)=(2/3)ln(L)+(1/3)ln(K)‚ a more convenient expression‚ is the same as maximizing Q. Therefore the objective function for the optimization problem is ln(Q)=(2/3)ln(L)+(1/3)ln(K). Step 1: Form the Langrangian function by subtracting from the objective function a multiple of the difference between the cost of the resources and the budget allowed for resources; i.e.‚ G= ln(Q) -
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Infeasibility 4 14 Unbounded 4 11 Spreadsheet Example 2 REVIEW 1. A mathematical programming problem is one that seeks to maximize an objective function subject to constraints. If both the objective function and the constraints are linear‚ the problem is referred to as a linear programming problem. 2
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Technical Aspects of ITVEM Systems Optimization Associated with the ITVEM optimization model‚ it will be the optimization of the cost minimization‚ although the optimization can also be in terms of maximizing the performance. To do so‚ Figure V.5 can assist to be a chart reference‚ whereas it should also develop several assumptions regarding the optimization process‚ for example‚ the Cobb-Douglas production function (Lin and Kao‚ 2014) replaces each the desired output (the starred y*it‚ i = 1
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Mathematical modeling is commonly used to predict the behavior of phenomena in the environment. Basically‚ it involves analyzing a set of points from given data by plotting them‚ finding a line of "best fit" through these points‚ and then using the resulting graph to evaluate any given point. Models are useful in hypothesizing the future behavior of populations‚ investments‚ businesses‚ and many other things that are characterized by fluctuations. A mathematical model usually describes a
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Mathematical Model of a Transportation Problem where m … number of sources n … number of destinations ai … capacity of i-th source (in tons‚ pounds‚ liters‚ etc) bj … demand of j-th destination (in tons‚ pounds‚ liters‚ etc.) cij … cost coefficients of material shipping (unit shipping cost) between i-th source and j-th destination (in $ or as a distance in kilometers‚ miles‚ etc.) xij … amount of material shipped between i-th source and j-th destination (in tons‚ pounds‚ liters etc.)
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