This comment has nothing to do with your difficulties (except that we'll spot the source of one), just some notes on more idiomatic perl for your read loop.

First the preliminaries,

#!/usr/bin/perl
use warnings;
use strict;

our (%sender, %receiver, @p_s};
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You open a data file from a path given on the command line. There is an implicit mechanism in perl - the diamond operator with default argument - which does that, allowing you to skip opening the file. You were slurping the file, but that makes your loop run only once, with match only catching the first instance. Let's read it line by line with a while loop, and accept the default loop variable, $_, which allows us to use default match bindings and argument to chomp.

while (<>) {
    chomp;
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You're not changing notation matching (\d)-(\d) and pasting the digits back together with "-", so let's keep them together and eliminate a couple of variables.

    if (m/(\d-\d)->(\d-\d)/) {
        $sender{$1} = $2;
        $receiver{$2} = $1;
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I'll change diagnostic prints to warns, so they go over STDERR.

        warn "enter ",
            "$sender{$1}->$receiver{$2} ",
            "in dependency hashes\n";
    }
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More tricks follow with $1 and $2:     elsif (m/((\d)-\d)/) { I'm inclined towards push and shift in making a queue, but we'll stick with what you have,

        unshift @{$p_s[$2]}, $1;
        warn "unshift $1 onto process array\n";
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I'll skip the $numprocess variable entirely; you can get that from the arrays in scalar context.

    }
    else {
        warn "unmatched line: $_\n";
    }
}
# . . .
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That's your code up through the read loop.

Using the empty diamond has two effects which may not suit you. First, every file listed on the command line will be read and parsed in order. Second, if none are listed there the diamond will look at STDIN, either a pipe or the terminal. Both are useful if you design for them, otherwise they can be a source of surprise.