![]() I have enjoyed serving as the Chair for the Wagner competition in 20, and I have participated in the Edelman Award as a judge and coach. I selected most of the examples from the Edelman Award and the Wagner Prize competitions. For most of these examples, I will identify their decision variables, objective, and constraints and provide a close description of the meaning of the decision variables and the constraints, since providing the exact definition would involve writing the mathematical models. In this article, I will provide several examples describing the problem to be solved. That definition hints that optimization problems are expressed as mathematical models and to solve them requires specialized training. More properly (and succinctly), one can say that an optimization problem searches the decision variables which maximize or minimize an objective function under several conditions or constraints. In a Humanitarian Operation the goal would be to reach as many affected people as quickly as possible to distribute resources water, food, and medical services by designing optimal routes. In Marketing, the goal can be to maximize the profit obtained by targeting the right customers under budget and operational conditions. In a hospital, the goal can be to minimize the wait time for patients in the emergency room before they are seen by a doctor where the resources are the doctors, the nurses, the rooms, the equipment, etc. oil refinery) where the resources are labor, raw materials, etc. In an optimization model, the goal can be to minimize cost in a production system (i.e. Optimization is at the heart of the Prescriptive stage indicating how to use resources efficiently to achieve the best possible goal under a series of conditions. Gartner Analytics Maturity Model proposes four phases: Descriptive (What Happened?), Diagnostic (Why did it happen?), Predictive (What will happen?) and Prescriptive (How can we make it happen). As you read, think about the implications of combining these algorithms and the vast computational power currently available. In this article, I provide several examples that will help people identify situations where Optimization can be applied, while avoiding mathematical jargon as much as possible. Mathematical Optimization, also known as Mathematical Programming, Operations Research, or simply Optimization, is a discipline that solves a great variety of applied problems in diverse areas: medicine, manufacturing, transportation, supply chain, finance, government, physics, economics, artificial intelligence, etc. ![]() They are used, for example, by GPS systems, by shipping companies delivering packages to our homes, by financial companies, airline reservations systems, etc. I will ask the question in a different way here: What is the least amount of surface area possible? as this will tell us how much material is needed to make one bottle.In our daily lives, we benefit from the application of Mathematical Optimization algorithms. I am trying to design a cylindrical bottle of 1.5 L that will serve as a packaging material for a mass production product, my goal is to use the minimum amount of material for this bottle in order to reduce its cost as much as possible. These words mean that we are looking for a function's local maximum or minimum. In any of these cases we should notice the words Minimize and Maximize. We may be trying to reduce the distance travelled to choose the best warehouse location, or maximize a storage area. We may be trying to decide for a business strategy that will minimize manufacturing cost or maximize profit. ![]() And not just in physics, this applies to business too! I certainly can't promise that everyone reading this will use math everyday in their chosen careers, but it is really very easy to demonstrate the endless real world applications of calculus which allow anyone to see exactly how powerful this discipline is when it comes to solving complex problems. One of the most common phrases we hear in mathematic classrooms is "Why do I need to know this?" ![]()
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