Modelos de Optimizacion stituto Tecnológico y de Estudios

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      Instituto Tecnológico y de Estudios

    Superiores de Monterrey

Campus Guadalajara

Models of optimization

Group 2

Noviembre 16, 2017

Profesor: Juan Antonio Orozco

Escuela de diseño Ingeniería y Arquitectura

Departamento de Física, Matemáticas y Química

Proyecto Final

Alam Osvaldo Ruiz López A01223526

Mauricio de Jesús Cooper Barrera A01630042

Paulo Valdovinos Uribe A01229076

Practical Case I: Auto Assembly

Automobile Alliance, a large automobile manufacturing company, organizes the vehicles it

manufactures into three families: a family of trucks, a family of small cars, and a family of

mid-sized and luxury cars. One plant outside Detroit, MI, assembles two models from the family of mid-sized and luxury cars. The first model, the Family Thrillseeker, is a four-door sedan with vinyl seats, plastic interior, standard features, and excellent gas mileage. It is marketed as a smart buy for middle-class families with tight budgets, and each Family Thrillseeker sold generates a modest profit of $3,600.00 USD for the company. The second model, the Classy Cruiser, is a two-door luxury sedan with leather seats, wooden interior, custom features, and navigational capabilities. It is marketed as a privilege of affluence for upper-middle class families, and each Classy Cruiser sold generates a healthy profit of $5,400.00 USD for the company.

Rachel Rosencrantz, the manager of the assembly plant, is currently deciding the production

schedule for the next month. Specifically, she must decide how many Family Thrillseekers and how many Classy Cruisers to assemble in the plant to maximize profit for the company. She knows that the plant possesses a capacity of 48,000 labor-hours during the month. She also knows that it takes 6 labor-hours to assemble one Family Thrillseeker and 10.5 labor-hours to assemble one Classy Cruiser.

Because the plant is simply and assembly plant, the parts required to assemble the two models are not produced at the plant. They are instead shipped from other plants around Michigan area to the assembly plant. For example, tires, steering wheels, windows, seats, and doors all arrive from various supplier plants. For the next month, Rachel knows that she will be able to obtain only 20,000 doors (10,000 left-hand doors and 10,000 right-hand doors)) from the door supplier. A recent labor strike forced the shutdown of that particular supplier plant for several days, and that plant will not be able to meet its production schedule for the next month. Both the Family Thrillseeker and the Classy Cruiser use the same door part.

In addition, a recent company forecast of the monthly demands for different automobile models suggests that the demand for the Classy Cruiser is limited to 3,500 cars. There is no limit on the demand for the Family Thrillseeker within the capacity limits of the assembly plant.

1. Formulate and solve a LP problem to determine the number of Family Thrillseekers and the number of Classy Cruisers that should be assembled.

Sets

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Decision Variable

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Linear Program (LP)

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Subject to the following constraints

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We can feed the model to an Excel Solver:

As we can see the maximum profit we can earn is (Zmax= $ 26,640,000 USD) when we produce 3,800 Thrillseeker and 2,400 Classy Cruiser.

Before she makes her final production decisions, Rachel plans to explore the following

questions independently except where otherwise indicated:

1. The marketing department knows that it can pursue a targeted $500,000.00 USD advertising campaign that will raise the demand for the Classy Cruiser next month by 20 percent. Should the campaign be undertaken?

For the moment, the plant doesn’t produce as much Classy Cruiser that are demanded, there is not point in paying an advertising campaign to increase the demand if we do not raise our production.

1. Rachel knows that she can increase next month’s plant capacity by using overtime labor. She can increase the plant’s labor-hour capacity by 25 percent. With the new assembly plant capacity, how many Family Thrillseekers and how many Classy Cruisers should be assembled?

With the extra labor-hour capacity we get the next model

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Subject to the following constraints

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We can feed the model to an Excel Solver to get the following solution:

As we can see the maximum profit we can earn is (Zmax= $ 30,600,000 USD) when we produce 3,250 Thrillseeker and 3,500 Classy Cruiser.

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