0-1 integer programming problem - Greatest Resource Utiliazation

[michel89]

Hello all!

Can somebody please explain the following aspect of the added problem: 'b^t dimension q x 1'
This problem is about creating the greatest utilization of available resources within an organization.

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. . .\(\displaystyle \displaystyle \mbox{max}\, \sum_j\, c_j\,x_j\)

. . . . .\(\displaystyle \mbox{subject to }\, R^t\ \underline{x}\, \leq\, \underline{b^t}\)

. . . . . . .\(\displaystyle \mbox{with }\, x_j\, \in\, \{0,\, 1\}\)

Also:

. . . . .\(\displaystyle \displaystyle b_i^t\, :\, \mbox{resource }\, i\, \mbox{ available at time }\, t;\)

. . . . . . . . .\(\displaystyle b^t\, \mbox{ dimension }\, q\, \times\, 1\)

. . . . .\(\displaystyle \displaystyle c_j\, =\, \sum_{i=1}^q\, r_{ij}\)

. . . . .\(\displaystyle \displaystyle r_{ij}\, :\, \mbox{resource }\, i\, \mbox{ required by }\, a_j\)

. . . . .\(\displaystyle \displaystyle R^t\, :\, \mbox{matrix of resources req'd by all }\, a_j\,\)

. . . . . . . . .\(\displaystyle \displaystyle \mbox{which can be scheduled at time }\, t.\)

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Thanks in advance!!!

 

[tkhunny]

Hello all!

Can somebody please explain the following aspect of the added problem: 'b^t dimension q x 1'
This problem is about creating the greatest utilization of available resources within an organization.

---

. . .\(\displaystyle \displaystyle \mbox{max}\, \sum_j\, c_j\,x_j\)

. . . . .\(\displaystyle \mbox{subject to }\, R^t\ \underline{x}\, \leq\, \underline{b^t}\)

. . . . . . .\(\displaystyle \mbox{with }\, x_j\, \in\, \{0,\, 1\}\)

Also:

. . . . .\(\displaystyle \displaystyle b_i^t\, :\, \mbox{resource }\, i\, \mbox{ available at time }\, t;\)

. . . . . . . . .\(\displaystyle b^t\, \mbox{ dimension }\, q\, \times\, 1\)

. . . . .\(\displaystyle \displaystyle c_j\, =\, \sum_{i=1}^q\, r_{ij}\)

. . . . .\(\displaystyle \displaystyle r_{ij}\, :\, \mbox{resource }\, i\, \mbox{ required by }\, a_j\)

. . . . .\(\displaystyle \displaystyle R^t\, :\, \mbox{matrix of resources req'd by all }\, a_j\,\)

. . . . . . . . .\(\displaystyle \displaystyle \mbox{which can be scheduled at time }\, t.\)

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Thanks in advance!!!

Please show YOUR work on the problem. You have to start somewhere.