02_LP2 - More Linear Programming Models 1 MIT and James...

Info icon This preview shows pages 1–9. Sign up to view the full content.

View Full Document Right Arrow Icon
MIT and James Orlin © 2003 1 More Linear Programming Models
Image of page 1

Info icon This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
MIT and James Orlin © 2003 2 Overview Applications personnel scheduling production and inventory management Goals get practice in recognizing and modeling linear constraints (and non-linear constraints) use of models in practice
Image of page 2
MIT and James Orlin © 2003 3 Overview 5 in 7 scheduling problem The model Practical enhancements or modifications Two non-linear objectives that can be made linear A non-linear constraint that can be made linear
Image of page 3

Info icon This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
MIT and James Orlin © 2003 4 Overview 5 in 7 scheduling problem The model
Image of page 4
MIT and James Orlin © 2003 5 Scheduling Postal Workers Each postal worker works for 5 consecutive days, followed by 2 days off, repeated weekly. Day  Mon  Tues  Wed  Thurs  Fri  Sat  Sun  Demand  17  13  15  19  14  16  11    Minimize the number of postal workers (for the time being, we will permit fractional workers on each day.)
Image of page 5

Info icon This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
MIT and James Orlin © 2003 6 Formulating as an LP Select the decision variables Let x 1 be the number of workers who start working on Monday, and work till Friday Let x 2 be the number of workers who start on Tuesday … Let x 3 , x 4 , …, x 7 be defined similarly.
Image of page 6
MIT and James Orlin © 2003 7 Minimize z = x 1 + x 2 + x 3 + x 4 + x 5 + x 6 + x 7 subject to x 1 + x 4 + x 5 + x 6 + x 7 17 Day  Mon  Tues  Wed  Thurs  Fri  Sat  Sun  Demand  17  13  15  19  14  16  11    x 1 + x 2 + x 5 + x 6 + x 7 13 x 1 + x 2 + x 3 + x 6 + x 7 15 x 1 + x 2 + x 3 + x 4 + x 7 19 x 1 + x 2 + x 3 + x 4 + x 5 14 x 2 + x 3 + x 4 + x 5 + x 6 16 x 3 + x 4 + x 5 + x 6 + x 7 11 x j 0 for j = 1 to 7
Image of page 7

Info icon This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
MIT and James Orlin © 2003 8 On the selection of decision variables Would it be possible to have y j be the number of workers on day j?
Image of page 8
Image of page 9
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

What students are saying

  • Left Quote Icon

    As a current student on this bumpy collegiate pathway, I stumbled upon Course Hero, where I can find study resources for nearly all my courses, get online help from tutors 24/7, and even share my old projects, papers, and lecture notes with other students.

    Student Picture

    Kiran Temple University Fox School of Business ‘17, Course Hero Intern

  • Left Quote Icon

    I cannot even describe how much Course Hero helped me this summer. It’s truly become something I can always rely on and help me. In the end, I was not only able to survive summer classes, but I was able to thrive thanks to Course Hero.

    Student Picture

    Dana University of Pennsylvania ‘17, Course Hero Intern

  • Left Quote Icon

    The ability to access any university’s resources through Course Hero proved invaluable in my case. I was behind on Tulane coursework and actually used UCLA’s materials to help me move forward and get everything together on time.

    Student Picture

    Jill Tulane University ‘16, Course Hero Intern