Alternative Equation Formats

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MathML

\begin{aligned} minimize & \sum_{a \in A} \sum_{d \in D} (f_{a d}^{+} + f_{a d}^{-}) \\ subject to & c_{a d}^{x} \sum_{t \in T} c_{t} x_{a t} + c_{a d}^{y} y_{a} + \\ c_{a d}^{z} \sum_{t \in T} c_{t} x_{a t} y_{a} + c_{a d}^{u} u_{a} + c_{a d} - w_{a d} & = f_{a d}^{+} - f_{a d}^{-} & a \in A, d \in D \\ \sum_{t \in T} x_{a t} & = 1 & a \in A \\ \sum_{a \in A} (f_{a d}^{+} - f_{a d}^{-} + w_{a d}) & \leq B_{d} & d \in D \\ f_{a d}^{-} & \leq w_{a d} v_{a d} & a \in A, d \in D \\ \sum_{d \in D} v_{a d} & \leq K_{a} & a \in A \\ y_{a} & \in [0, 1] & a \in A \\ u_{a} & \geq 0 & a \in A \\ f_{a d}^{+} & \geq 0 & a \in A, d \in D \\ f_{a d}^{-} & \in [0, w_{a d}] & a \in A, d \in D \\ v_{a d} & \in {0, 1} & a \in A, d \in D \\ x_{a t} & \in {0, 1} & a \in A, t \in T \end{aligned}

MathML rendered with MathJax

\begin{aligned} minimize & \sum_{a \in A} \sum_{d \in D} (f_{a d}^{+} + f_{a d}^{-}) \\ subject to & c_{a d}^{x} \sum_{t \in T} c_{t} x_{a t} + c_{a d}^{y} y_{a} + \\ c_{a d}^{z} \sum_{t \in T} c_{t} x_{a t} y_{a} + c_{a d}^{u} u_{a} + c_{a d} - w_{a d} & = f_{a d}^{+} - f_{a d}^{-} & a \in A, d \in D \\ \sum_{t \in T} x_{a t} & = 1 & a \in A \\ \sum_{a \in A} (f_{a d}^{+} - f_{a d}^{-} + w_{a d}) & \leq B_{d} & d \in D \\ f_{a d}^{-} & \leq w_{a d} v_{a d} & a \in A, d \in D \\ \sum_{d \in D} v_{a d} & \leq K_{a} & a \in A \\ y_{a} & \in [0, 1] & a \in A \\ u_{a} & \geq 0 & a \in A \\ f_{a d}^{+} & \geq 0 & a \in A, d \in D \\ f_{a d}^{-} & \in [0, w_{a d}] & a \in A, d \in D \\ v_{a d} & \in {0, 1} & a \in A, d \in D \\ x_{a t} & \in {0, 1} & a \in A, t \in T \end{aligned}

Math as LaTeX Source

\begin{align*} & \text {minimize} & \sum _{a \in A} \sum _{d \in D} \left(f^+_{ad} + f^-_{ad}\right) \\ & \text {subject to} & c^ x_{ad} \sum _{t \in T} c_ t x_{at} + c^ y_{ad} y_{a} + \\ & & c^ z_{ad} \sum _{t \in T} c_ t x_{at} y_{a} + c^{u}_{ad} u_{a} + c_{ad} - w_{ad} & = f^+_{ad} - f^-_{ad} & & a \in A,\ d \in D \\ & & \sum _{t \in T} x_{at} & = 1 & & a \in A \\ & & \sum _{a \in A} \left(f^+_{ad} - f^-_{ad} + w_{ad} \right) & \leq B_ d & & d \in D\\ & & f^{-}_{ad} & \leq w_{ad} v_{ad} & & a \in A,\ d \in D \\ & & \sum _{ d \in D} v_{ad} & \leq K_ a & & a \in A\\ & & y_{a} & \in [0,1] & & a \in A\\ & & u_{a} & \geq 0 & & a \in A \\ & & f^+_{ad} & \geq 0 & & a \in A,\ d \in D\\ & & f^-_{ad} & \in [0,w_{ad}] & & a \in A,\ d \in D\\ & & v_{ad} & \in \{ 0,1\} & & a \in A,\ d \in D\\ & & x_{at} & \in \{ 0,1\} & & a \in A,\ t \in T \end{align*}