# 0-1 integer programming problem - Greatest Resource Utiliazation

#### michel89

##### New member
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.

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

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

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

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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#### tkhunny

##### Moderator
Staff member
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.

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

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

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

Also:

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

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

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

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

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

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