You need to rethink the definition of midnight. Midnight begins a day, not ends a day.

Another solution is to use Time::ParseDate. Here is some source code that I tested:

use Time::ParseDate;

use strict;

my $input = shift || "";
my $day = undef;
my $hours = undef;

if ( $input =~ m!^(\w{3})/(\d+)! ) {
    $day = $1;
    $hours = $2;
} else {
    die( "Error: use an argument of ddd/hh (e.g. Sat/36)" );
}

# set up parse string to midnight (beginning) of desired day
my $parsestring = "next $day 00:00";

my $epoch = Time::ParseDate::parsedate( $parsestring );

$epoch += ( $hours * 3600 );

print( "     Epoch: $epoch\n" );
print( "  GMT Time: " . scalar( gmtime( $epoch ) ) . "\n" );
print( "Local Time: " . scalar( localtime( $epoch ) ) . "\n" );
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When executed this outputs the following:

$ perl -w testparse.pl  Sat/36
     Epoch: 1188126000
  GMT Time: Sun Aug 26 11:00:00 2007
Local Time: Sun Aug 26 12:00:00 2007
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Last note: think carefully whether you are doing times in the local timezone or GMT/UTC. (I was running this from London, UK, in summer time hence local time being one hour ahead of GMT).