Lines Matching refs:left
51 $K_{0}=\sum_{i=1}^{m}\left\lceil b_{i}/\left\lfloor
72 \left.\begin{array}{@{}l}
91 \left.\begin{array}{@{}l}
92 %\left.\begin{array}{@{}l}
95 %\left.\begin{array}{@{}l}
98 %\left.\begin{array}{@{}l}
100 \left\{0,\ldots,l\right\}\\
101 \left\{0,\ldots,h_{i}\right\}\quad\forall i\\
103 %\left.\begin{array}{@{}l}
104 \left\{0,\,1\right\}
109 where $h_{i}=\left\lfloor l/l_{i}\right\rfloor$. This problem formulation is modeled and solved in \eclipse\ as follows:
179 q_{i}&\in&\left\{0,\ldots,\left\lfloor l/l_{i}\right\rfloor\right\}\qquad i=1,\ldots,m
182 where $L_{0}=\left\lceil\sum_{i=1}^{m}b_{i}l_{i}/l\right\rceil$ and $K_{0}=\sum_{i=1}^{m}\left\lceil b_{i}/\left\lfloor l/l_{i}\right\rfloor\right\rceil$ are initial bounds on the number of stock boards required, $c_{\mathbf{q}}=l-\sum_{i=1}^{m}{l_{i}q_{i}}$, the subproblem objective function coefficients $\mathbf{u}$ represent the benefit obtained by producing boards of each type, and the subproblem is simply a general integer knapsack problem maximizing the benefit due to the boards produced by a cutting. The problem is modeled and solved as follows: