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

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.

. . .$\displaystyle \mbox{max}\, \sum_j\, c_j\,x_j$

. . . . .$\mbox{subject to }\, R^t\ \underline{x}\, \leq\, \underline{b^t}$

. . . . . . .$\mbox{with }\, x_j\, \in\, \{0,\, 1\}$

Also:

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

. . . . . . . . .$b^t\, \mbox{ dimension }\, q\, \times\, 1$

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

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

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

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

2. Originally Posted by michel89
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.

. . .$\displaystyle \mbox{max}\, \sum_j\, c_j\,x_j$

. . . . .$\mbox{subject to }\, R^t\ \underline{x}\, \leq\, \underline{b^t}$

. . . . . . .$\mbox{with }\, x_j\, \in\, \{0,\, 1\}$

Also:

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

. . . . . . . . .$b^t\, \mbox{ dimension }\, q\, \times\, 1$

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

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

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

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