OMIS 327 Lecture 3. LP Formulation

OMIS 327 Lecture 3. LP Formulation - OMIS 327 Lecture 3...

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1 OMIS 327 Lecture 3 Linear Programming: Problem Formulation Instructor: Dr. Lee, Jung Young
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2 Today’s Learning Goals Basic assumptions and properties of linear programming (LP) LP problem formulation
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3 Introduction A production schedule and an inventory policy to satisfy demand and to minimize the total costs An investment portfolio to maximize the return The best media mix that maximizes advertising effectiveness A transportation plan to minimize total transportation costs
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4 Introduction Many management decisions involve trying to make the most effective use of limited resources. Linear programming Linear programming ( LP LP ) is a widely used mathematical modeling technique designed to help managers in planning and decision making relative to resource allocation . This belongs to the broader field of mathematical mathematical programming. programming. In this sense, programming programming refers to modeling and solving a problem mathematically.
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5 Requirements of a Linear Programming Problem 1. All problems seek to maximize maximize or minimize minimize some quantity (the objective function objective function ). 2. Restrictions or constraints constraints that limit the degree to which we can pursue our objective are present. 3. There must be alternative courses of action from which to choose. 4. The objective and constraints in problems must be expressed in terms of linear linear equations or inequalities. inequalities.
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6 Basic Assumptions of LP We assume conditions of certainty certainty exist and numbers in the objective and constraints are known with certainty and do not change during the period being studied. We assume proportionality proportionality exists in the objective and constraints. We assume additivity additivity in that the total of all activities equals the sum of the individual activities. We assume divisibility divisibility in that solutions need not be whole numbers (integers).
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