Label names not with leading number

I am currently working on a a documentation for some benchmark libraries for MIP solvers. This includes a description for every problem type. e.g. for binpacking I have

\section{Bin Packing Problem}\label{bpp}

\subsection{Formulation}
We are given $n$ items in an item set $I$ with weights $w_i$, with $i \in I$.
The items shall be packed into bins (also $n$ many, but we use $B$ as the set
of bins for the sake of readability) with capacity $C$ such that the number of
bins used is minimal. We use two types of variables:
\begin{itemize}
\item $x_{ij} \in \{0, 1\}$ should be $1$ iff item $i$ is packed into bin $j$.
\item $y_j \in \{0, 1\}$ should be $1$ iff bin $j$ is used.
\end{itemize}
\begin{align}
\text{minimize }      & \sum_{j \in B} y_j                                            \label{bpp:obj}\\
\text{subject to }    & \sum_{j \in B} x_{ij} = 1             & i \in I               \label{bpp:setpp}\\
& \sum_{i \in I} w_i x_{ij} \leq C y_j  & j \in B               \label{bpp:capacity}\\
& x_{ij} \in \{0, 1\}                   & i \in I, j \in B\\
& y_j \in \{0, 1\}                      & j \in B
\end{align}

As you can see the objective function and each constraint gets a label. Now, instead assume this binpacking section would be section 1. The labels are consequently named (1.1), (1.2), (1.3). But I would like them to have a name like (BPP.1), (BPP.2), (BPP.3), i.e. some common abbreviation of the underlying problem. The section itself however, should still have a number for the table of contents and other references.

Any suggestions how that might work?

You can define the style setting \theequation:

\renewcommand{\theequation}{BPP.\arabic{equation}}

This would result in labels called (BPP.1), (BPP.2), etc.

To use this in a document I would suggest a macro that sets the the style as following:

\newcounter{oldeq}
\newcommand{\setpreeqno}{% set text before equation number
\ifx\preeqno\empty% if no preeqno was given before
\def\preeqno{#1}% set to argument
\ifx\preeqno\empty\else% if an argument was given
\renewcommand{\theequation}{#1.\arabic{equation}}% set to "arg.#"
\setcounter{oldeq}{\value{equation}}% save equation counter
\fi%
\else%
\def\preeqno{#1}% set to argument
\ifx\preeqno\empty% if no argument was given
\renewcommand{\theequation}{\arabic{equation}}% reset to default arabic number
\setcounter{equation}{\value{oldeq}}% continue counting
\else%
\renewcommand{\theequation}{#1.\arabic{equation}}% set to "arg.#"
\fi%
\fi%
\ignorespaces%
}

Or in a full MWE:

\documentclass{article}
\usepackage{amsmath}

\newcounter{oldeq}
\newcommand{\setpreeqno}{% set text before equation number
\ifx\preeqno\empty% if no preeqno was given before
\def\preeqno{#1}% set to argument
\ifx\preeqno\empty\else% if an argument was given
\renewcommand{\theequation}{#1.\arabic{equation}}% set to "arg.#"
\setcounter{oldeq}{\value{equation}}% save equation counter
\fi%
\else%
\def\preeqno{#1}% set to argument
\ifx\preeqno\empty% if no argument was given
\renewcommand{\theequation}{\arabic{equation}}% reset to default arabic number
\setcounter{equation}{\value{oldeq}}% continue counting
\else%
\renewcommand{\theequation}{#1.\arabic{equation}}% set to "arg.#"
\fi%
\fi%
\ignorespaces%
}

\begin{document}
\thispagestyle{empty}
\section{Bin Packing Problem}\label{bpp}\setpreeqno{BPP}

\subsection{Formulation}
We are given $n$ items in an item set $I$ with weights $w_i$, with $i \in I$.
The items shall be packed into bins (also $n$ many, but we use $B$ as the set
of bins for the sake of readability) with capacity $C$ such that the number of
bins used is minimal. We use two types of variables:
\begin{itemize}
\item $x_{ij} \in \{0, 1\}$ should be $1$ iff item $i$ is packed into bin $j$.
\item $y_j \in \{0, 1\}$ should be $1$ iff bin $j$ is used.
\end{itemize}
\begin{align}
\text{minimize }      & \sum_{j \in B} y_j                                            \label{bpp:obj}\\
\text{subject to }    & \sum_{j \in B} x_{ij} = 1             & i \in I               \label{bpp:setpp}\\
& \sum_{i \in I} w_i x_{ij} \leq C y_j  & j \in B               \label{bpp:capacity}\\
& x_{ij} \in \{0, 1\}                   & i \in I, j \in B\\
& y_j \in \{0, 1\}                      & j \in B
\end{align}

This reference looks like \eqref{bpp:obj}.
\end{document} edit I improved the code by taking care of the global counter (inspired by @egreg's answer)

A variation upon subequations using the same infrastructure.

\documentclass{article}
\usepackage{amsmath}

\newenvironment{labeledequations}{%
\setcounter{parentequation}{\value{equation}}%
\setcounter{equation}{0}%
\def\theequation{#1.\arabic{equation}}%
\ignorespaces
}{%
\setcounter{equation}{\value{parentequation}}%
\ignorespacesafterend
}

\begin{document}

\section{Bin Packing Problem}\label{bpp}

\subsection{Formulation}
We are given $n$ items in an item set $I$ with weights $w_i$, with $i \in I$.
The items shall be packed into bins (also $n$ many, but we use $B$ as the set
of bins for the sake of readability) with capacity $C$ such that the number of
bins used is minimal. We use two types of variables:
\begin{itemize}
\item $x_{ij} \in \{0, 1\}$ should be $1$ iff item $i$ is packed into bin $j$.
\item $y_j \in \{0, 1\}$ should be $1$ iff bin $j$ is used.
\end{itemize}
\begin{labeledequations}{BPP}
\begin{align}
\text{minimize }   & \sum_{j \in B} y_j
\label{bpp:obj} \\
\text{subject to } & \sum_{j \in B} x_{ij} = 1             && i \in I
\label{bpp:setpp} \\
& \sum_{i \in I} w_i x_{ij} \leq C y_j  && j \in B
\label{bpp:capacity} \\
& x_{ij} \in \{0, 1\}                   && i \in I, j \in B
\\
& y_j \in \{0, 1\}                      && j \in B
\end{align}
\end{labeledequations}

The references to \eqref{bpp:obj} and \eqref{bpp:capacity} are correct.

\end{document} • Resetting the counter number, good idea...
– nox
Jul 16 '18 at 8:31