Alinear fórmulas matemáticas

Question

Estoy escribiendo mis fórmulas y restricciones matemáticas con Overleaf. Este es mi código y también les muestro el resultado que obtuve (ver foto). Como puede ver, las fórmulas no están bien alineadas. Me gustaría mejorar el diseño alineando todas las fórmulas y etiquetándolas (con números, como se muestra en la imagen). ¡Sería extremadamente útil si alguien me puede ayudar con esto!

\documentclass{article}
\usepackage[utf8]{inputenc}
\usepackage[super]{natbib}
\usepackage{comment}
\usepackage{graphicx}
\usepackage{float}
\usepackage{hyperref}
\usepackage{amsmath}
\usepackage{amssymb}
\usepackage{amsfonts}
\usepackage{caption}
\usepackage{adjustbox}
\usepackage{lipsum}
\usepackage{lscape}
\usepackage{multicol}
\usepackage{longtable}
\captionsetup[figure]{font=small,labelfont=bf}
\captionsetup[table]{font=small,labelfont=bf}
\usepackage[justification=centering]{caption}
\usepackage{eurosym}
\usepackage{mhchem}
\usepackage{relsize}
\usepackage[table, dvipsnames]{xcolor}
\renewcommand*\descriptionlabel[1]{\hspace\leftmargin$#1$}
\usepackage[hidelinks]{hyperref}
\usepackage{enumitem}
\usepackage{glossaries}
\makeglossaries
\newcommand{\mathgl}[2]{
    \newglossaryentry{#1}{name={#1},description={#2}}
    \begin{description}[labelwidth=2cm]
      \item[\gls{#1}]#2
    \end{description}
}
\makeatletter
\newcommand*{\rom}[1]{\expandafter\@slowromancap\romannumeral #1@}
\makeatother
\def\changemargin#1#2{\list{}{\rightmargin#2\leftmargin#1}\item[]}
\let\endchangemargin=\endlist 

\begin{document}
\subsection{Stating the objective function} 
TextTextTextTextTextTextTextTextTextTextTextTextTextTextTextTextTextTextTextTextTextTextTextTextTextTextTextTextTextTextTextTextTextTextTextTextTextTextTextTextTextTextTextTextTextTextTextText

\begin{align} \min \quad BFC \cdot \bigg(\mathlarger{\mathlarger{\sum}}_{i\in I}Fc_i \cdot u_i\bigg) + BEC \cdot \bigg(\mathlarger{\mathlarger{\sum}}_{i\in I}\mathlarger{\mathlarger{\sum}}_{j \in J}\mathlarger{\mathlarger{\sum}}_{p \in P}x_i_j_p\cdot Ec_i_j_p_y\bigg) + BTC \cdot \bigg(\mathlarger{\mathlarger{\sum}}_{i\in I}\mathlarger{\mathlarger{\sum}}_{j \in J}\mathlarger{\mathlarger{\sum}}_{p \in P}x_i_j_p\cdot Tc_i_j_p\bigg) + BWC \cdot \bigg(\mathlarger{\mathlarger{\sum}}_{i\in I}\mathlarger{\mathlarger{\sum}}_{j \in J}\mathlarger{\mathlarger{\sum}}_{p \in P}x_i_j_p\cdot Wc_i_j_p\bigg) + BZC \cdot \bigg(\mathlarger{\mathlarger{\sum}}_{i\in I}\mathlarger{\mathlarger{\sum}}_{j \in J}\mathlarger{\mathlarger{\sum}}_{p \in P}x_i_j_p\cdot Z_i_j_p\bigg)\cdot Zc \label{1} \end{align} \subsection{Stating the constraints} The first constraint ensures that the demand of each customer is satisfied: \begin{align} \mathlarger{\sum}_{i\in I}x_i_j_p = D_j_p_y, \quad && \forall j \in J, p\in P, y \in Y\label{2} \end{align} \noindent The second formula makes sure that the maximum capacity of each supplier facility is not exceeded: \begin{align} \mathlarger{\sum}_{j\in J}\mathlarger{\sum}_{p\in P}x_i_j_p \leq u_i, \quad && \forall i \in I \label{3} \end{align} \noindent Contracts with specific supplier facilities may agree on minimum allocation volumes. This is ensured by the following formula: \begin{align} \mathlarger{\sum}_{j\in J}\mathlarger{\sum}_{p\in P}x_i_j_p \geq V_i, \quad && \forall i \in I \label{3} \end{align} \noindent Specific breweries desire to be supplied by at least two suppliers for some specific type of product code. This is ensured by the following two formulas: \begin{align} \mathlarger{\sum}_{i\in I}J_i_j_p \geq 2, \quad && \forall j \in J, p\in P \label{4}\\ x_i_j_p \geq b_i_j_p M_j_p \end{align} \noindentSpecific OpCos desire to be supplied by at least two suppliers for some specific type of product code. This is ensured by the following two formulas: \begin{align} \mathlarger{\sum}_{i\in I}F_i_o_p\geq 2,\quad && \forall o \in O, p\in P \label{5}\\ \mathlarger{\sum}_{i\subset I}x_i_j_p \geq F_i_o_pG_o_p,\quad && \forall i \in I, o\in O, p\in P \label{5} \end{align}

Answer 1

Una solución simple utiliza un solo alignentorno y el \intertextcomando.

Simplifiqué el preámbulo a lo que es necesario para que el código funcione. Además, no creo que realmente necesites usar un double \mathlarger, lo que hace que el número de la ecuación se coloque debajo de la ecuación, incluso cuando se usamultlined

Por cierto, no tiene que cargar amsfontscuando carga amssymb, este último lo hace por usted. Tenga en cuenta que hyperrefdebe cargarse como el último paquete, con muy pocas excepciones.

\documentclass{article}
\usepackage{mathtools}
\usepackage{amssymb}
\usepackage{relsize}
\usepackage[hidelinks]{hyperref}

\begin{document}
\setcounter{section}{4}
\setcounter{subsection}{5}

\subsection{Stating the objective function}
Text Text Text Text Text Text Text Text Text Text Text Text Text Text Text Text Text Text Text Text Text Text Text Text Text Text 
\begin{equation}
\begin{multlined}
\min \quad BFC \cdot \bigg(\mathlarger{\sum}_{i\in I}Fc_i \cdot u_i\bigg)
+
BEC \cdot \bigg(\mathop{\mathlarger{\sum}_{i\in I}\mathlarger{\sum}_{j \in J}\mathlarger{\sum}_{p \in P}x_{i j p}}\cdot Ec_{ijpy}\bigg) +{}
\\
 BTC \cdot \bigg(\mathlarger{\sum}_{i\in I}\mathlarger{\sum}_{j \in J}\mathlarger{\sum}_{p \in P}x_{ijp}\cdot Tc_{ijp}\bigg)
+
BWC \cdot \bigg(\mathlarger{\sum}_{i\in I}\mathlarger{\sum}_{j \in J}\mathlarger{\sum}_{p \in P}x_{ijp}\cdot Wc_{ijp}\bigg)
\\
+ BZC \cdot \bigg(\mathlarger{\sum}_{i\in I}\mathlarger{\sum}_{j \in J}\mathlarger{\sum}_{p \in P}x_{ijp}\cdot Z_{ijp}\bigg)\cdot Zc
\end{multlined}
\label{1}
  \end{equation}

\subsection{Stating the constraints}
The first constraint ensures that the demand of each customer is satisfied:

\begin{align} \mathlarger{\sum}_{i\in I}&x_{ijp} = D_{jpy}, \quad && \forall j \in J, p\in P, y \in Y\label{2} \\ \intertext{The second formula makes sure that the maximum capacity of each supplier facility is not exceeded:} \mathlarger{\sum}_{j\in J}\mathlarger{\sum}_{p\in P} &x_{ijp} \leq u_i, \quad && \forall i \in I \label{3} \intertext{Contracts with specific supplier facilities may agree on minimum allocation volumes. This is ensured by the following formula:} \mathlarger{\sum}_{j\in J} \mathlarger{\sum}_{p\in P} &x_{ijp}\geq V_i, \quad && \forall i \in I \label{3} \\ \intertext{Specific breweries desire to be supplied by at least two suppliers for some specific type of product code. This is ensured by the following two formulas:} \mathlarger{\sum}_{i\in I}&J_{ijp} \geq 2, \quad && \forall j \in J, p\in P \label{4}\\ &x_{ijp} \geq b_{ijp} M_{jp}\\ \intertext{Specific OpCos desire to be supplied by at least two suppliers for some specific type of product code. This is ensured by the following two formulas:} \mathlarger{\sum}_{i\in I}&F_{iop} \geq 2,\quad && \forall o \in O, p\in P \label{5}\\ \mathlarger{\sum}_{i\subset I}&x_{ijp} \geq F_{iop} G_{op},\quad && \forall i \in I, o\in O, p\in P \label{5} \end{align}

\end{document} 

Answer 2

Aquí hay un ejemplo extendido:

\documentclass[a4paper,12pt]{article}
\usepackage{mathtools}
\usepackage{lipsum}
\begin{document}
\section{Let us try}
\subsection{Stating the objective function}

%\lipsum[1]

\begin{equation}\label{1}
\begin{aligned} \min \quad BFC \bigg(\sum_{i\in I}Fc_i u_i\bigg) &+ BEC \biggl(\sum_{i\in I} \sum_{j \in J} \sum_{p \in P} x_{ijp} Ec_{ijp} y \biggr) \\ &+ BTC \biggl(\sum_{i\in I} \sum_{j \in J} \sum_{p \in P} x_{ijp} Tc_{ijp} \biggr) \\ &+ BWC \biggl(\sum_{i\in I} \sum_{j \in J} \sum_{p \in P} x_{ijp} Wc_{ijp} \biggr) \\ &+ BZC \biggl(\sum_{i\in I} \sum_{j \in J} \sum_{p \in P} x_{ijp} Z_{ijp} \biggr) Zc \end{aligned} \end{equation} \subsection{Stating the constraints} The first constraint ensures that the demand of each customer is satisfied: \begin{align}\label{2}\allowdisplaybreaks &\sum_{i\in I} x_{ijp} = D_{jpy}, \quad && \forall j \in J, p\in P, y \in Y\\ \intertext{The second formula makes sure that the maximum} &\sum_{j\in J}\sum_{p\in P} x_{ijp} \leq u_i, \quad && \forall i \in I \label{3} \intertext{Specific breweries desire to be supplied by at least two suppliers for some specific type of product code. This is ensured by the following two formulas:} &\sum_{i\in I}J_{ijp} \geq 2, \quad && \forall j \in J, p\in P \label{4}\\ &x_{ijp} \geq b_{ijp} M_{jp}\label{5} \end{align}
\end{document}

y ver si el resultado te conviene. Si es así, puedes extenderlo fácilmente.

Answer 3

Mi versión, sin \mathlargerparéntesis reducidos y algunas otras sugerencias.

Por ejemplo, BFC y los símbolos similares en la primera pantalla no significan un producto de tres cantidades, sino una sola variable, por lo que se \mathitreduce el espacio entre las letras. Contrariamente a lo que otros afirman, \cdotes necesario para evitar que los símbolos se interpreten como "una función evaluada en".

Uno debe usar \biggl(y \biggr), no solo \bigg. De todos modos, con el tamaño normal \sum, la \Bigversión parece mejor; agregue \,si el subíndice puede entrar en conflicto con el paréntesis.

Compruebe el último i\subset I, que no parece encajar.

podrías considerar

\sum_{\substack{i\in I \\ j\in J \\ p\in P}}

en lugar de la suma triple y de manera similar para las sumas dobles.

Evite las líneas en blanco antes de las pantallas. No es necesario \noindentsi no hay una línea en blanco después de la pantalla (y si tiene una, entonces \noindentestaría mal).

\documentclass{article}
\usepackage{amsmath}

\newcommand{\tvar}[1]{\mathit{#1}}

\begin{document}

\subsection{Stating the objective function} 

Text Text Text Text Text Text Text Text Text Text Text Text Text Text Text 
Text Text Text Text Text Text Text Text Text Text Text Text Text Text Text 
Text Text Text Text Text Text Text Text Text Text Text Text Text Text Text 
Text Text Text 
\begin{equation}\label{1}
\begin{split}
\min \tvar{BFC} &\cdot \Bigl(\,\sum_{i\in I} Fc_i \cdot u_i\Bigr)
+ 
\tvar{BEC} \cdot \Bigl(\,\sum_{i\in I}\sum_{j \in J}\sum_{p \in P}x_{ijp} \tvar{Ec}_{ijpy}\Bigr)
\\
{}+
\tvar{BTC} &\cdot \Bigl(\,\sum_{i\in I}\sum_{j \in J}\sum_{p \in P}x_{ijp} \tvar{Tc}_{ijp}\Bigr)
+
\tvar{BWC} \cdot \Bigl(\,\sum_{i\in I}\sum_{j \in J}\sum_{p \in P}x_{ijp} \tvar{Wc}_{ijp}\Bigr)
\\
{}+
\tvar{BZC} &\cdot \Bigl(\,\sum_{i\in I}\sum_{j \in J}\sum_{p \in P}x_{ijp} Z_{ijp}\Bigr) \tvar{Zc} 
\end{split}
\end{equation}

\subsection{Stating the constraints}
The first constraint ensures that the demand of each customer is satisfied:
\begin{equation}\label{2}
\sum_{i\in I}x_{ijp} = D_{jpy},  \quad \forall j \in J,  p\in P, y \in Y
\end{equation}
The second formula makes sure that the maximum capacity of each supplier facility 
is not exceeded:
\begin{equation}\label{3}
\sum_{j\in J}\sum_{p\in P}x_{ijp} \leq u_i,  \quad  \forall i \in I
\end{equation}
Contracts with specific supplier facilities may agree on minimum allocation volumes. 
This is ensured by the following formula:
\begin{equation}\label{4}
\sum_{j\in J}\sum_{p\in P}x_{ijp} \geq V_i,  \quad \forall i \in I
\end{equation}
Specific breweries desire to be supplied by at least two suppliers for some specific 
type of product code. This is ensured by the following two formulas:
\begin{equation}\label{5}
\sum_{i\in I}J_{ijp} \geq 2,  \quad \forall j \in J,  p\in P
x_{ijp} \geq b_{ijp} M_{jp}
\end{equation}
Specific OpCos desire to be supplied by at least two suppliers for some specific 
type of product code. This is ensured by the following two formulas:
\begin{alignat}{2} &\sum_{i\in I}F_{iop}\geq 2, &\quad& \forall o \in O, p\in P \label{6}\\ &\sum_{i\subset I}x_{ijp} \geq F_{iop}G_{op}, && \forall i \in I, o\in O, p\in P \label{7} \end{alignat}

\end{document}

Aquí está la versión con\substack

Answer 4

Para la primera ecuación, puede usar multlineel entorno (definido en el amsmathpaquete):

\documentclass{article}
\usepackage{amsmath, amssymb}
\usepackage{lipsum}

\begin{document}
\subsection{Stating the objective function}
\lipsum[11]
\begin{multline}\label{1}
\min \quad \mathrm{BFC}{\cdot}\bigg(\sum_{i\in I}Fc_i{\cdot} u_i\bigg)
+ \mathrm{BEC}{\cdot}\bigg(\sum_{i\in I}\sum_{j \in J}\sum_{p \in P}x_{ijp}{\cdot}Ec_{ijpy}\bigg)  \\
%
+ \mathrm{BTC}{\cdot}\bigg(\sum_{i\in I}\sum_{j \in J}\sum_{p \in P}x_{ijp}{\cdot}Tc_{ijp}\bigg)
+ \mathrm{BWC}{\cdot}\bigg(\sum_{i\in I}\sum_{j \in J}\sum_{p \in P}x_{ijp}{\cdot}Wc_{ijp}\bigg)   \\
%
+ \mathrm{BZC}{\cdot}\bigg(\sum_{i\in I}\sum_{j \in J}\sum_{p \in P}x_{ijp}{\cdot}Z_{ijp}\bigg){\cdot}Zc
\end{multline}
\end{document}

\subsection{Stating the constraints}
The first constraint ensures that the demand of each customer is satisfied:

\begin{align} \mathlarger{\sum}_{i\in I}x_i_j_p = D_j_p_y, \quad && \forall j \in J, p\in P, y \in Y\label{2} \end{align} \noindent The second formula makes sure that the maximum capacity of each supplier facility is not exceeded: \begin{align} \mathlarger{\sum}_{j\in J}\mathlarger{\sum}_{p\in P}x_i_j_p \leq u_i, \quad && \forall i \in I \label{3} \end{align} \noindent Contracts with specific supplier facilities may agree on minimum allocation volumes. This is ensured by the following formula: \begin{align} \mathlarger{\sum}_{j\in J}\mathlarger{\sum}_{p\in P}x_i_j_p \geq V_i, \quad && \forall i \in I \label{3} \end{align} \noindent Specific breweries desire to be supplied by at least two suppliers for some specific type of product code. This is ensured by the following two formulas: \begin{align} \mathlarger{\sum}_{i\in I}J_i_j_p \geq 2, \quad && \forall j \in J, p\in P \label{4}\\ x_i_j_p \geq b_i_j_p M_j_p \end{align} \noindentSpecific OpCos desire to be supplied by at least two suppliers for some specific type of product code. This is ensured by the following two formulas: \begin{align} \mathlarger{\sum}_{i\in I}F_i_o_p\geq 2,\quad && \forall o \in O, p\in P \label{5}\\ \mathlarger{\sum}_{i\subset I}x_i_j_p \geq F_i_o_pG_o_p,\quad && \forall i \in I, o\in O, p\in P \label{5} \end{align}
\end{document}

que producen:

Algunos comentarios:

• Aumentar el tamaño de algunos símbolos en la ecuación (en su caso \sum) no es una buena idea. Su tamaño está diseñado deliberadamente para ecuaciones atractivas, así que no destruyas los esfuerzos de los diseñadores.
• Supongo que BFC, BTC, etc son abreviaturas, que deben escribirse con fuentes upshape, es decir, deben escribirse como \mathrm{BFC}, `\mathbf{BTC}˙, etc.
• Del mismo modo c_i_j_p_yes una notación incorrecta. Debería ser o c_{ijpy}(cual es el resultado más probable deseado) o c_{i_{j_{p_{y}}}}(cual es menos probable)
• Desde el punto de vista matemático, \cdotno se necesita el uso de para la multiplicación. De todos modos, si persiste en usarlos, entonces puede reducir el espacio alrededor de ellos encerrándolos entre llaves (como se hace en MWE anterior)