Linear optimization: Mathematical formulations of complex problems (How to) 2: Unterschied zwischen den Versionen
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Most of the student think that linear programming is simply a synonym for computer programming or geometry or even a type of “hard maths”. But the fact is, that a basic grasp of mathematics is just needed. The concept of linear optimization is simple, because they are really about finding solutions to problems which are expressed in terms of an entity which needs to be optimized with given constraints. Due to this linear optimization is perhaps the most successful discipline of Operations Research. The following chart shows a structured linear optimization solution model paired with an easy introductory example. | Most of the student think that linear programming is simply a synonym for computer programming or geometry or even a type of “hard maths”. But the fact is, that a basic grasp of mathematics is just needed. The concept of linear optimization is simple, because they are really about finding solutions to problems which are expressed in terms of an entity which needs to be optimized with given constraints. Due to this linear optimization is perhaps the most successful discipline of Operations Research. The following chart shows a structured linear optimization solution model paired with an easy introductory example. | ||
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| + | Example-case: | ||
| + | A company makes two products using two machines. Each product produced requires 50 minutes processing time on the 1st and 30 minutes processing time on the 2nd machine. Each unit of one product that is produced requires 24 minutes processing time on the 1st machine and 33 minutes processing time on the 2nd machine. | ||
| + | At the start of the current week there are 30 units of the 1st product and 90 units of the 2nd product in stock. Available processing time on the 1st machine is forecast to be 40 hours and on 2nd machine is forecast to be 35 hours. | ||
| + | The demand for the 1st in the current week is forecast to be 75 units and for 2nd is forecast to be 95 units. Company policy is to maximize the combined sum of the units of the 1st product and the units of the 2nd in stock at the end of the week | ||
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[[Datei:Chart_analytic.JPG|Analytic Solution Scheme]] | [[Datei:Chart_analytic.JPG|Analytic Solution Scheme]] | ||
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| + | [[Datei:Chart_example_optimum.jpg]] | ||
Version vom 28. Juni 2013, 00:16 Uhr
Theory
Most of the student think that linear programming is simply a synonym for computer programming or geometry or even a type of “hard maths”. But the fact is, that a basic grasp of mathematics is just needed. The concept of linear optimization is simple, because they are really about finding solutions to problems which are expressed in terms of an entity which needs to be optimized with given constraints. Due to this linear optimization is perhaps the most successful discipline of Operations Research. The following chart shows a structured linear optimization solution model paired with an easy introductory example.
Example-case: A company makes two products using two machines. Each product produced requires 50 minutes processing time on the 1st and 30 minutes processing time on the 2nd machine. Each unit of one product that is produced requires 24 minutes processing time on the 1st machine and 33 minutes processing time on the 2nd machine. At the start of the current week there are 30 units of the 1st product and 90 units of the 2nd product in stock. Available processing time on the 1st machine is forecast to be 40 hours and on 2nd machine is forecast to be 35 hours. The demand for the 1st in the current week is forecast to be 75 units and for 2nd is forecast to be 95 units. Company policy is to maximize the combined sum of the units of the 1st product and the units of the 2nd in stock at the end of the week
