Here's my stab at it, which goes along with what jethro and graff have already mentioned. %sets is kept as a hash for convenient deletes. By keeping track of which sets to update/delete once a resource ($next) becomes available, we only need to traverse a minimal amount of sets:
use Data::Dump qw[ pp ];
use List::Util qw[ shuffle ];
use Time::HiRes qw[ time ];

our $N //= 1e3;
our $S //= 1e4;
our $Z //= 5;

my @bools;

my %sets = map {
    my $s = $_;
    my $n = 1 + int( rand $Z );
    ++$bools[ $_ ]{ $s } for map int( rand $N ), 1 .. $n;
    $s => $n;
} 0 .. $S - 1;

my @someOrder = shuffle 0 .. $N-1;

my $start = time;
for my $next ( @someOrder ) {
    for my $s (keys %{ $bools[ $next ] }) {
        $sets{ $s } -= delete $bools[ $next ]{ $s };
        delete $sets{ $s } unless $sets{ $s };
    }
}

printf "Took %.6f\n", time() - $start;

pp \@bools;
pp \%sets;

__END__
Took 0.089563
[
  {},
  {},
  ...
]
{}

[download]

Update: FWIW, the OP code took around 20 seconds on my virtual machine running FreeBSD.

In reply to Re: Better algorithm or data structure? by repellent
in thread Better algorithm or data structure? by BrowserUk

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