Employee Scheduling

Date: 09/22/98 at 18:05:26
From: Lindsay
Subject: Making a time schedule

I've figured the first part of the question, but now I have to do the 
second part. This is it:

Jill's customers at the ice cream parlor on Saturday:

  11:00am - 12:00pm   98 customers
  12:00pm - 1:00pm   120 customers
   1:00pm - 2:00pm   101 customers
   2:00pm - 3:00pm    86 customers
   3:00pm - 4:00pm    50 customers
   4:00pm - 5:00pm    42 customers
   5:00pm - 6:00pm    56 customers
   6:00pm - 7:00pm    87 customers
   7:00pm - 8:00pm   143 customers
   8:00pm - 9:00pm   132 customers
   9:00pm - 10:00pm   86 customers
  10:00pm - 11:00pm   78 customers
  
When planning each Saturday's schedule, Jill likes to follow certain 
guidelines. Using the guidelines listed below, make a time schedule 
for this Saturday, based on the number of customers Jill had last 
Saturday.

  - No person works more than 4 hours in a day.

  - No person works fewer than 2 hours in a day.

  - In addition to the servers, there is always 1 person working the 
    cash register each hour.

  - There is always 1 server for every 30 customers in the store. 
    Jill always rounds up the number of servers needed to the nearest 
    whole number. So, if there are 31 customers in an hour, 2 servers 
    should be working, and so on.  

Use fictional names or the variables for the employees (for example, 
Server A, Server B, and so on). Make your schedule easy to read. Be 
sure to show who will be the cashier each hour.

Date: 09/23/98 at 15:07:28
From: Doctor Sonya
Subject: Re: Making a time schedule

Hi Lindsay.  This looks like fun!

So what we have to do is make up a schedule for servers. Here is how I 
would go about it. First, find out how many servers (plus the cashier) 
are needed each hour. For example, for the first hour, there should be 
one cashier and four servers (98 customers need four servers. Do you 
see why?). The second hour needs one cashier and four servers as well.  
So I would make up a chart like this:

   Hour       Workers needed
     1             5
     2             5 
     3             5
     .             .
     .             . 

Once you have this list made up, start another column for workers.  
For example, if my workers are all named after letters, my third 
column might be:

   Hour   No. of Workers    Workers
     1         5            A, B, C, D, E
     2         5            A, B, C, D, E
     3         5            A, B, C, F, G  (D and E end their shifts)
     4         4            A, B, F, G (C goes off duty)  
     .         .            .

Just continue in this way, making sure that no one works more than 4 
or fewer than 2 hours. 

Once your list is all done, you'll have to put it into a schedule. 
There are a lot of ways you could do that. I would probably list the 
hours, and then who is working during them. Don't forget to delegate 
someone to the cash register each hour.

I hope this helps get you started. If you still have questions about 
how to write your schedule, don't hesitate to write us back. 

- Doctor Sonya, The Math Forum
  http://mathforum.org/dr.math/