Table 4.

Amount of mandatory (related to intrinsic restrictions) and optional (related to real-world BPP restrictions) considered constraints depending on the number of items and bins.

	n	(5)	(9)–(15)	(16)–(18)	(19)–(22)	Quadratic	Linear
Mandatory	1	$m-|I_{\text{c}}|$	$7\left(\begin{array}{c}m\\ 2\end{array}\right)$	–	3m	–	$7\left(\begin{array}{c}m\\ 2\end{array}\right)+4m-|I_{\text{c}}|$
	$\ge 2$	$m-|I_{\text{c}}|$	$(6n+1)\left(\begin{array}{c}m\\ 2\end{array}\right)$	$2n+m-1$	$(4n-1)m$	$6n\left(\begin{array}{c}m\\ 2\end{array}\right)+n$	$\left(\begin{array}{c}m\\ 2\end{array}\right)+n(4m+1)+m-1-|I_{\text{c}}|$

	n	(23)	(24)/(25)	(26) as HC	(27)	Quadratic	Linear
Optional	1	–	–	$-p^{-}-5p^{+}$	4m	–	$-p^{-}-5p^{+}+4m$
	$\ge 2$	n	1	$-n(p^{-}+5p^{+})-\nu$	4m	$1-n(p^{-}+5p^{+})-\nu$	$n+4m$