Results 1 to 2 of 2

Thread: 0-1 integer programming problem - Greatest Resource Utiliazation

  1. #1

    0-1 integer programming problem - Greatest Resource Utiliazation

    Hello all!

    Can somebody please explain the following aspect of the added problem: 'bt dimension q x 1'
    This problem is about creating the greatest utilization of available resources within an organization.



    . . .[tex]\displaystyle \mbox{max}\, \sum_j\, c_j\,x_j[/tex]

    . . . . .[tex]\mbox{subject to }\, R^t\ \underline{x}\, \leq\, \underline{b^t}[/tex]

    . . . . . . .[tex]\mbox{with }\, x_j\, \in\, \{0,\, 1\}[/tex]

    Also:

    . . . . .[tex]\displaystyle b_i^t\, :\, \mbox{resource }\, i\, \mbox{ available at time }\, t;[/tex]

    . . . . . . . . .[tex]b^t\, \mbox{ dimension }\, q\, \times\, 1[/tex]

    . . . . .[tex]\displaystyle c_j\, =\, \sum_{i=1}^q\, r_{ij}[/tex]

    . . . . .[tex]\displaystyle r_{ij}\, :\, \mbox{resource }\, i\, \mbox{ required by }\, a_j[/tex]

    . . . . .[tex]\displaystyle R^t\, :\, \mbox{matrix of resources req'd by all }\, a_j\,[/tex]

    . . . . . . . . .[tex]\displaystyle \mbox{which can be scheduled at time }\, t.[/tex]



    Thanks in advance!!!
    Attached Images Attached Images
    Last edited by stapel; 11-30-2017 at 04:03 PM. Reason: Typing out the text in the graphic.

  2. #2
    Elite Member
    Join Date
    Apr 2005
    Location
    USA
    Posts
    8,922
    Quote Originally Posted by michel89 View Post
    Hello all!

    Can somebody please explain the following aspect of the added problem: 'bt dimension q x 1'
    This problem is about creating the greatest utilization of available resources within an organization.



    . . .[tex]\displaystyle \mbox{max}\, \sum_j\, c_j\,x_j[/tex]

    . . . . .[tex]\mbox{subject to }\, R^t\ \underline{x}\, \leq\, \underline{b^t}[/tex]

    . . . . . . .[tex]\mbox{with }\, x_j\, \in\, \{0,\, 1\}[/tex]

    Also:

    . . . . .[tex]\displaystyle b_i^t\, :\, \mbox{resource }\, i\, \mbox{ available at time }\, t;[/tex]

    . . . . . . . . .[tex]b^t\, \mbox{ dimension }\, q\, \times\, 1[/tex]

    . . . . .[tex]\displaystyle c_j\, =\, \sum_{i=1}^q\, r_{ij}[/tex]

    . . . . .[tex]\displaystyle r_{ij}\, :\, \mbox{resource }\, i\, \mbox{ required by }\, a_j[/tex]

    . . . . .[tex]\displaystyle R^t\, :\, \mbox{matrix of resources req'd by all }\, a_j\,[/tex]

    . . . . . . . . .[tex]\displaystyle \mbox{which can be scheduled at time }\, t.[/tex]



    Thanks in advance!!!
    Please show YOUR work on the problem. You have to start somewhere.
    Last edited by stapel; 11-30-2017 at 04:03 PM. Reason: Copying typed-out graphical content into reply.
    "Unique Answers Don't Care How You Find Them." - Many may have said it, but I hear it most from me.

Bookmarks

Posting Permissions

  • You may not post new threads
  • You may not post replies
  • You may not post attachments
  • You may not edit your posts
  •