BUS 660 –lecture aid6

BUS 660 –lecture aid6 - BUS 660 lecture aid...

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BUS 660 –lecture aid Introduction to Optimization Modeling Introduction The models covered thus far in this course have been descriptive, that is,they provide useful input to decision making but do not quite provide the decision itself. This week's linear optimization modeling technique is prescriptive in that it is normally used to determine the best decision, one that optimizes a measurable objective under given quantitative constraints. Linear optimization techniques are used to solve a wide array of optimization problems. This lecture describes the general approach to setting up and solving linear optimization problems. Some common types of problems are indicated that lend themselves to this modeling approach. Understanding the theory and concepts behind linear programming can require one to use complex mathematical reasoning. Excel© can be used to set up and solve linear optimization problems easily; however, some basic math is still needed in order to set up the variables and constraints. What is a Linear Optimization Model? A linear optimization model essentially comprises: 1) Variables - whose values are to be determined 2) Constraints - that those variables are under 3) An objective function that is a linear combination of the variables and represents a measure (such as profit, cost, resources, etc.) that is being optimized. Note that the word optimize is to be interpreted as maximize or minimize . Clearly, if the measure were profit, the desire is to maximize it. On the other hand, if the measure were cost, the desire would typically be to minimize it. A linear optimization model seeks to find those values of the variables that optimize (maximize or minimize) the objective function, subject to certain constraints on the variables. It is important to note that the constraints and the objective function need to be expressed in exact mathematical terms. Subjectivity and intuition cannot be accommodated. This is a modeling technique that thrives on mathematical precision. The term linear optimization usually refers to linear programming or integer programming . In the latter case, the variables can take on only integer values. For example, with a variable that represents number of workers assigned to machine A
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BUS 660 –lecture aid6 - BUS 660 lecture aid...

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