From 8ea50128b88936b0972cfef9ab7aa286d2876898 Mon Sep 17 00:00:00 2001 From: Alinson S Xavier Date: Fri, 21 Aug 2020 17:25:04 -0500 Subject: [PATCH] Docs: Add complete model --- src/docs/model.md | 48 +++++++++++++++++++++++++++++++++++++++++++++-- 1 file changed, 46 insertions(+), 2 deletions(-) diff --git a/src/docs/model.md b/src/docs/model.md index e391e09..e54782b 100644 --- a/src/docs/model.md +++ b/src/docs/model.md @@ -129,6 +129,50 @@ In the third line, we have the disposal costs. & \forall p \in P, t \in T \\ & y_{lpt} \geq 0 & \forall l \in L, p \in P, t \in T \\ - & m^\text{disp}_{pmt} \geq z_{mpt} \geq 0 - & \forall m \in M, p \in P, t \in T \\ + & m^\text{disp}_{mpt} \geq z_{mpt} \geq 0 + & \forall m \in M, p \in P, t \in T \end{align} + +### Complete optimization model + +\begin{align*} + \text{minimize} \;\; & + \sum_{t \in T} \sum_{p \in P} \left[ + c^\text{open}_{pt} u_{pt} + + c^\text{f-base}_{pt} x_{pt} + + \sum_{i=1}^t c^\text{f-exp}_{pt} w_{pi} + + c^{\text{exp}}_{pt} w_{pt} + \right] + \\ + & + \sum_{t \in T} \sum_{l \in L} \sum_{p \in P} \left[ + c^{\text{tr}}_t d_{lp} + c^{\text{var}}_{pt} + \right] y_{lpt} + \\ + & + \sum_{t \in T} \sum_{p \in P} \sum_{m \in M} c^{\text{disp}}_{pmt} z_{pmt} \\ + \text{subject to } & \sum_{p \in P} y_{lpt} = m^\text{initial}_{lt} + & \forall l \in L, t \in T \\ + & \sum_{l \in L} y_{lpt} \leq m^\text{base}_p x_p + \sum_{i=1}^t w_p + & \forall p \in P, t \in T \\ + & \sum_{i=1}^t w_p \leq m^\text{max}_p x_p + & \forall p \in P, t \in T \\ + & q_{mpt} = \alpha_{pm} \sum_{l \in L} y_{lpt} + & \forall m \in M, p \in P, t \in T \\ + & q_{mpt} = z_{mpt} + & \forall m \in M, p \in P, t \in T \\ + & x_{pt} = x_{p,t-1} + u_{pt} + & \forall p \in P, t \in T \setminus \{1\} \\ + & x_{p,1} = u_{p,1} + & \forall p \in P \\ + & q_{mpt} \geq 0 + & \forall m \in M, p \in P, t \in T \\ + & u_{pt} \in \{0,1\} + & \forall p \in P, t \in T \\ + & w_{pt} \geq 0 + & \forall p \in P, t \in T \\ + & x_{pt} \in \{0,1\} + & \forall p \in P, t \in T \\ + & y_{lpt} \geq 0 + & \forall l \in L, p \in P, t \in T \\ + & m^\text{disp}_{mpt} \geq z_{mpt} \geq 0 + & \forall m \in M, p \in P, t \in T +\end{align*}