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If you have gnu awk available you could use mktime() like this:

gawk '
/PUT/||/DELETE/{
file=$5;
gsub(".*/", "", file)
stamp=$1 " " $2
gsub("[:-]", " ", stamp)
}
/PUT/ {
...

[user@host ~]$ cat test.sh
#! /usr/bin/bash

file=$1
logfile="file"

in_dt=$(grep "PUT.*$file" $logfile | cut -d' ' -f1,2)
out_dt=$(grep "DELETE.*$file" $logfile | cut -d' ' -f1,2)
...