08 Linear Programming

# 08 Linear Programming - Lesson 08 Linear Programming A...

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08 - 1 Lesson 08 Linear Programming A mathematical approach to determine optimal (maximum or minimum) solutions to problems which involve restrictions on the variables involved.

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08 - 2 Linear programming (LP) has been used to: . establish locations for emergency equipment and personnel that minimize response time . determine optimal schedules for planes . develop financial plans . determine optimal diet plans and animal feed mixes . determine the best set of worker-job assignments . determine optimal production schedules . determine routes that will yield minimum shipping costs Linear Programming Applications
08 - 3 Aggregate planning Production, Staffing Distribution Shipping Inventory Stock control, Supplier selection Location Plants or warehouses Process management Stock cutting Scheduling Shifts, Vehicles, Routing POM Applications

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08 - 4 Type 2 How many of each type do I make to maximize/minimi ze company profits/costs? A computer manufacturer makes two models of computers Type 1, and Type 2. The computers use many of the same components, made in the same factory by the same people and are stored in the same warehouse. The Basic LP Question Type 1
08 - 5 What Constrains What We Make? Materials Labor Time Cash Storage Space Shipping Customer Requirements Etc. What Limits Us?

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08 - 6 Objective (e.g. maximize profits , minimize costs , etc.) Decision variables - those that can vary across a range of possibilities Constraints - limitations for the decision variables Parameters - the numerical values for the decision variables Assumptions for an LP model . linearity - the impact of the decision variables is linear in both constraints and objective function . divisibility - non-integer values for decision variables are OK . certainty - values of parameters are known and are Components of Linear Programming
08 - 7 x = quantity of product 1 to produce x = quantity of product 2 to produce x = quantity of product 3 to produce 1 2 3 Decision Variables……………. .. Objective Function ( maximize profit) ………………… 5x x x 1 2 3 + + 8 4 Subject To Labor Constraint ……………………………. . Material Constraint…………………………… Product 1 Constraint…………………………. Non- negativity Constraint…………………… Linear Programming Formulation Maximize Maximize 2x x x 250 7x x x 100 x 10 x x x 0 1 2 3 1 2 3 1 1 2 3 + + + + 4 8 6 5 , ,

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08 - 8 Relationships must be stated in terms of a relationship to a bound. Suppose you have a ratio relationship as follows. x
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## This note was uploaded on 09/10/2011 for the course ECON 101 taught by Professor Halcrow,b during the Spring '08 term at Antelope Valley College.

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08 Linear Programming - Lesson 08 Linear Programming A...

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