Putting together a Theory of a program based to day of the week

I am trying to put together the theory part of a php website which integrates with mysql database which must send this data to an sqlite database on android device via push notifications. What needs to happen on the php and mysql database side is this :

"Y" amount of people work on shifts where only one person can work at any point in time. One person out of "Y" people must be at work for "x" amount of days of the week. Persons are able to swap their shifts with other persons.

The values for "Y" and "X" can be changed.

This is what i have so far( i'm trying to test it out with a specific day/month):

callout start date: 1/august/2015
run every 24 hours.
if (day=2/august/2015){
    $calloutday=Check TABLE 'Exceptions' WHERE
     day='2/august/2015';
    IF(!$calloutday){
    //follow primary programing:
    $firstcallout=Check TABLE with techs WHERE callout
        position is smallest.?
        IF($firstcallout)
        {

        }

    }
}

I am not sure how to go about this.