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homework - Industrial Engineering Operations Research...

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Industrial Engineering Spring Operations Research – Optimization Homework Last updated: February , Guide ines • Homework assignments are always due on Mon days at : pm. • Remember that end-of-class quizzes might be based on the most recently due homework. • Solutions to each homework assignment will be posted on Blackboard the day a er it is due. • Homework is not collected or graded. ere are some instructions common to several problems. See the endnotes on page . Assignments Due date Problems / , , , , , / , , , / , , , , / , , , , / , , , , , , / / , , , / , , , , / / , , , / , , , , , , / , , , , , / / , , , , , / , , , , / , , ,

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Prob ems Prob em . Read the syllabus carefully. Familiarize yourself with the course components and the policies on makeup quizzes and exams, regrading, collaboration, and academic honesty. Prob em (Rardin, Exercise - ) . A factory has two production lines available to make a product. e rst can produce one lot of the product in t hours at cost c , and the second requires t hours and cost c . e plant manager wishes to nd the least costly way to produce b lots in a total of at most T hours. An integer number x will be produced on line , and an integer number x will be produced on line . Identify each of the following for this design problem: (a) the decision variables (b) the data, or input parameters (c) the objective function (d) the constraints Prob em . A rm wants to choose the site of a new warehouse that will simultaneously serve four retail branches. e average daily transportation need of the four retail branches from the warehouse are: Retail branch Coordinates Number of daily deliveries Ashmouth ( , ) Bedsbottom ( , ) Cadillac ( , ) Danhunt ( , ) Suppose that travel costs are per mile, and trucks can travel a straight line between the new warehouse and the retail branches. e rm would like to determine where to locate the new warehouse in a way that minimizes the daily transportation cost. (a) Formulate an optimization model to determine the new warehouse’s location. Remember that a delivery is a round-trip. (b) Suppose that zoning laws restrict the location of the new warehouse to lie in the four-sided shaded region in the gure below. Formulate a new optimization model to determine the new warehouse’s location, taking these additional restrictions into consideration. x y Ashmouth ( , ) Bedsbottom ( , ) Cadillac ( , ) Danhunt ( , ) ( , ) ( , ) ( , ) ( , )
Prob em (Rardin, Exercise - ) . An engineer is working on a design problem with n parameters to be chosen, and each has possible values. A highly valid descriptive model is available, and he is thinking of choosing the best design simply by using the model to evaluate the e ect of every combination of design parameter values. (a) Explain why this approach will require running the descriptive model on n combinations of decision- variable values. (b) For n = , , , , compute the time a computer would require to check all the combinations, assuming that it runs hours per day, days per year, and that it requires second to apply the model for any particular choice of design parameters.

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