introduction to mathematical modeling and ibm ilog cplex
... • A combinatorial optimization problem (COP) is a discrete optimization problem in which we seek to find a solution in a finite set of solutions that maximizes or minimizes an objective function. This type of problem usually arises in the selection of a finite set of mutually exclusive alternatives ...
... • A combinatorial optimization problem (COP) is a discrete optimization problem in which we seek to find a solution in a finite set of solutions that maximizes or minimizes an objective function. This type of problem usually arises in the selection of a finite set of mutually exclusive alternatives ...
Math 678. Homework 5 Solutions. #1 Consider a
... from the above we will have M = v(x0 , t0 ) ≤ n v(y, s) dyds ≤ 4r (t − s)2 E(x,t;r M . Equality is only possible when u ≡ M in the heat ball. Then we can cover the domain with such balls as in the proof of Theorem 4 and conclusion follows. (c) Let v = φ(u) with φ being convex and u a solution to the ...
... from the above we will have M = v(x0 , t0 ) ≤ n v(y, s) dyds ≤ 4r (t − s)2 E(x,t;r M . Equality is only possible when u ≡ M in the heat ball. Then we can cover the domain with such balls as in the proof of Theorem 4 and conclusion follows. (c) Let v = φ(u) with φ being convex and u a solution to the ...
Solutions
... triangles along the line from (b, c) to (a, 0). Consider the left triangle and its median from (0, 0) to its opposite side. The ...
... triangles along the line from (b, c) to (a, 0). Consider the left triangle and its median from (0, 0) to its opposite side. The ...
Pest control may make the pest population explode
... this model to explain a measured increase in the shark population and decrease in the population of food fish during the decreased fishing activity caused by the first world war. The use of mathematical models for predicting the effect of human actions has continued since then. For example, the abov ...
... this model to explain a measured increase in the shark population and decrease in the population of food fish during the decreased fishing activity caused by the first world war. The use of mathematical models for predicting the effect of human actions has continued since then. For example, the abov ...
Introduction to Discrete Optimization
... accounts for its known or inferred properties and maybe used for further study of its characteristics. ...
... accounts for its known or inferred properties and maybe used for further study of its characteristics. ...
The Utility Frontier
... Example 3: The Pareto problem (P-Max), max u1 (x1 ) subject to u2 (x2 ) = u2 , . . . , un (xn ) = un , x∈F ...
... Example 3: The Pareto problem (P-Max), max u1 (x1 ) subject to u2 (x2 ) = u2 , . . . , un (xn ) = un , x∈F ...
Multiple-criteria decision analysis
Multiple-criteria decision-making or multiple-criteria decision analysis (MCDA) is a sub-discipline of operations research that explicitly considers multiple criteria in decision-making environments. Whether in our daily lives or in professional settings, there are typically multiple conflicting criteria that need to be evaluated in making decisions. Cost or price is usually one of the main criteria. Some measure of quality is typically another criterion that is in conflict with the cost. In purchasing a car, cost, comfort, safety, and fuel economy may be some of the main criteria we consider. It is unusual that the cheapest car is the most comfortable and the safest one. In portfolio management, we are interested in getting high returns but at the same time reducing our risks. Again, the stocks that have the potential of bringing high returns typically also carry high risks of losing money. In a service industry, customer satisfaction and the cost of providing service are two conflicting criteria that would be useful to consider.In our daily lives, we usually weigh multiple criteria implicitly and we may be comfortable with the consequences of such decisions that are made based on only intuition. On the other hand, when stakes are high, it is important to properly structure the problem and explicitly evaluate multiple criteria. In making the decision of whether to build a nuclear power plant or not, and where to build it, there are not only very complex issues involving multiple criteria, but there are also multiple parties who are deeply affected from the consequences.Structuring complex problems well and considering multiple criteria explicitly leads to more informed and better decisions. There have been important advances in this field since the start of the modern multiple-criteria decision-making discipline in the early 1960s. A variety of approaches and methods, many implemented by specialized decision-making software, have been developed for their application in an array of disciplines, ranging from politics and business to the environment and energy.