amsmathequationsmath-mode
The following set of equations cannot be aligned from left to right. Since, I need to index them just with one number, I had to use split equations:
\begin{equation}
\begin{split}
X={}^ 2 \bar{x} + {}^ 1 z \\
Y={}^ 1 \bar{x} + {}^ 2 z + {}^ 2 \bar{w} \\
W= {}^ 1 y\\
Z={}^ 1 w
\end{split}
\label{eq: logical 1}
\end{equation}
Any suggestion please?
Here is a small sample of numbering equations.
\documentclass[12pt]{article}
\usepackage{amsmath}
\begin{document}
\begin{align} % numbers equations automatically
x &= (1-x) + 2x \\ % \\ ends the line
&= (x+y) - y \nonumber \\ % \nonumber removes the equation number
&= \frac{x}{2} + \frac{x}{2} % last line does not have \\
\end{align}
\begin{align*} % use of * removes all numbers in this block
x &= (2x + 5) - (x+5) \\
&= yx - (y-1) x
\end{align*}
\end{document}
This sample produces
My answer use the specific package optidef: a LaTeX library for optimization problems with the [short] option (with the short code) and without it.
I have cleaned a bit your preamble deleting the \usepackage{amsmath} and leaving \usepackage{mathtools} that is a supremum package. I have used:
\usepackage{geometry}
\usepackage{parskip}
just to have an equilibrium for the a4paper and to have not the indent space to begin of a paragraph. Using the option mini! you create the subequations and without ! you have a only numbered equation. In addition I have used other specific commands like \lvert and \rvert, typical to create \abs command.
\documentclass[12pt,twoside]{report}
\usepackage[utf8]{inputenc}
\usepackage{mathtools}
\usepackage{amssymb}
\usepackage{textcomp}
\usepackage{hyperref}
\usepackage{geometry}
\usepackage[short]{optidef}
\usepackage{parskip}
\begin{document}
Objective:
\begin{mini!}
{}{\sum_{i=1}^{N} \sum_{s=1}^{C} \sum_{r=1}^{H} \sum_{k=1}^{G} \sum_{t=1}^{T} y_{\textup{isrk}}^{t} \protect \label{eq:3.1}}{}{}
\addConstraint {\lvert p_i-\sum_{s=1}^{C} \sum_{r=1}^{H} \sum_{k=1}^{G} \sum_{t=1}^{T} v_{\textup{isrk}}^{t}\rvert}{\leq \delta,}{\quad\forall{i}\in\{{1,\ldots, N}\}}
\addConstraint { \text{left side} }{=\text{right side},}{\quad \forall{i}\in\{{1,\ldots,N}\}}
\end{mini!}
\begin{mini}
{}{\sum_{i=1}^{N} \sum_{s=1}^{C} \sum_{r=1}^{H} \sum_{k=1}^{G} \sum_{t=1}^{T} y_{\textup{isrk}}^{t} \protect \label{eq:3.2}}{}{}
\addConstraint {\lvert p_i-\sum_{s=1}^{C} \sum_{r=1}^{H} \sum_{k=1}^{G} \sum_{t=1}^{T} v_{\textup{isrk}}^{t}\rvert}{\leq \delta,}{\quad\forall{i}\in\{{1,\ldots, N}\}}
\addConstraint { \text{left side} }{=\text{right side},}{\quad \forall{i}\in\{{1,\ldots,N}\}}
\end{mini}
\end{document}
Deleting the option [short], you will have the full words (minimize and subject to):
\documentclass[12pt,twoside]{report}
\usepackage[utf8]{inputenc}
\usepackage{amssymb}
\usepackage{mathtools}
\usepackage{textcomp}
\usepackage{hyperref}
\usepackage{geometry}
\usepackage{optidef}
\usepackage{parskip}
\begin{document}
Objective:
\begin{mini!}
{}{\sum_{i=1}^{N} \sum_{s=1}^{C} \sum_{r=1}^{H} \sum_{k=1}^{G} \sum_{t=1}^{T} y_{\textup{isrk}}^{t} \protect \label{eq:3.1}}{}{}
\addConstraint {\lvert p_i-\sum_{s=1}^{C} \sum_{r=1}^{H} \sum_{k=1}^{G} \sum_{t=1}^{T} v_{\textup{isrk}}^{t}\rvert}{\leq \delta,}{\quad\forall{i}\in\{{1,\ldots, N}\}}
\addConstraint { \text{left side} }{=\text{right side},}{\quad \forall{i}\in\{{1,\ldots,N}\}}
\end{mini!}
\begin{mini}
{}{\sum_{i=1}^{N} \sum_{s=1}^{C} \sum_{r=1}^{H} \sum_{k=1}^{G} \sum_{t=1}^{T} y_{\textup{isrk}}^{t} \protect \label{eq:3.2}}{}{}
\addConstraint {\lvert p_i-\sum_{s=1}^{C} \sum_{r=1}^{H} \sum_{k=1}^{G} \sum_{t=1}^{T} v_{\textup{isrk}}^{t}\rvert}{\leq \delta,}{\quad\forall{i}\in\{{1,\ldots, N}\}}
\addConstraint { \text{left side} }{=\text{right side},}{\quad \forall{i}\in\{{1,\ldots,N}\}}
\end{mini}
\end{document}
Addendum 1: Just after the comment of nice user @Zarko I have put another row to write long condition which OP put in separate lines in equations.
\documentclass[12pt,twoside]{report}
\usepackage[utf8]{inputenc}
\usepackage{amssymb}
\usepackage{mathtools}
\usepackage{textcomp}
\usepackage{hyperref}
\usepackage{geometry}
\usepackage{optidef}
\usepackage{parskip}
\begin{document}
Objective:
\begin{mini!}
{}{\sum_{i=1}^{N} \sum_{s=1}^{C} \sum_{r=1}^{H} \sum_{k=1}^{G} \sum_{t=1}^{T} y_{isrk}^{t} \protect \label{eq:3.1}}{}{}
\addConstraint{\lvert p_i-\sum_{s=1}^{C} \sum_{r=1}^{H} \sum_{k=1}^{G} \sum_{t=1}^{T} v_{isrk}^{t}\rvert}{\leq \delta,}{\qquad\forall{i}\in\{1,\ldots, N\}}
\addConstraint{\sum_{i=1}^{N} x_{isrk}^{t}\leq \sum_{i=1}^{N}(u_{isrk}^{t}-u_{is(r+1)k}^{t}),\protect \label{eq:3.3}}{\quad}{\quad\begin{matrix}
\forall s \in \{1,\ldots,C\},\\
r \in \{1,\ldots, H-1\}, \\
k \in \{1,\ldots,G\}, \\
t \in \{1,\ldots,T\}
\end{matrix}}
\end{mini!}
\end{document}
The other equations can be added using a mechanism of the same design.
Addendum 2: Given the request of @A Azab as by comment the \addConstraint have almost 3 arguments. I have done several tests and in the first argument you can't split the equations like in your code. But in the third argument you can achieve your request with some unrefined and rough tricks.
\addConstraint{first argument}{second argument}{third argument}
See the part:
\addConstraint{
\sum_{i=1}^{N} v_{isrk}^{t} + \sum_{i=1}^{N} y_{isrk}^{t} +\sum_{i=1}^{N} x_{isrk}^{t}}{\leq 1}{\begin{matrix}
& \\[3.5em]
\hspace{-5cm} \forall i\in \{1,\ldots,N\}, s \in \{1,\ldots,C\},r \in\{1,\ldots,H\}\protect\label{eq:3.8}
\end{matrix}}
\documentclass[12pt,twoside]{report}
\usepackage[utf8]{inputenc}
\usepackage{mathtools}
\usepackage{amssymb}
\usepackage{textcomp}
\usepackage{hyperref}
\usepackage{geometry}
\usepackage{optidef}
\usepackage{parskip}
\begin{document}
Objective:
\begin{mini!}
{}{\sum_{i=1}^{N} \sum_{s=1}^{C} \sum_{r=1}^{H} \sum_{k=1}^{G} \sum_{t=1}^{T} y_{isrk}^{t} \protect \label{eq:3.1}}{}{}
\addConstraint{\lvert p_i-\sum_{s=1}^{C} \sum_{r=1}^{H} \sum_{k=1}^{G} \sum_{t=1}^{T} v_{isrk}^{t}\rvert}{\leq \delta,}{\qquad\forall{i}\in\{1,\ldots, N\}}
\addConstraint{
\sum_{i=1}^{N} v_{isrk}^{t} + \sum_{i=1}^{N} y_{isrk}^{t} +\sum_{i=1}^{N} x_{isrk}^{t}}{\leq 1}{\begin{matrix}
& \\[3.5em]
\hspace{-5cm} \forall i\in \{1,\ldots,N\}, s \in \{1,\ldots,C\},r \in\{1,\ldots,H\}\protect\label{eq:3.8}
\end{matrix}}
\end{mini!}
\end{document}
Best Answer