This problem I got from someone working in a call center. The call center operation in question operates 24 hours a day, 7 days a week. Every 30 minutes, there is a projected number of agents that need to be present in order to handle calls. Here is an example of such a requirement:
The data shown is truncated. The should be 48 rows corresponding to 48 half-hour intervals in a day. The whole data can be downloaded from here.
Assuming that an agent works 9 hours per day, how do you schedule your staff in such a way that you can meet the required number of agents required per 30 minute interval using a minimum number agents.
Approach to solving this problem
Imagine for a moment that you are the manager of this call center and you want to solve this problem manually. Looking at the first row and first column of the data, you’ll see that at 12:00 am to 12:30 am on Mon you need 1 agent to be in the office. Since an agent works 9 hours per day, this agent’s duty will end at 9:00 am. If n is the total number of agents in the office at 9:00, then by the next interval, there will be agents left ( Assuming there is no new agent who comes to work).
Looking down the row under Monday, you will see that a new person is required to be in the office at 6:00 am. You then assign a new person to come to the office at this time.
Further down, another person is required at 8:30 am. However, at 9:00 am, the first person’s shift is up but the requirement is still 3 persons. So you need to assign another person to come to office a 9 am to meet the requirement. Continuing the process in this way, you can ultimately come up with a schedule of your call center agents.
You have to notice that people working at 3:30 pm will intersect the next days shift. They will leave the office at 12:30 am the next day. The same is true for all agents who come to the office between 3:30 to 12:30 pm. To make matters worse, those agents who come to work Sunday starting at 3:30 pm will have to intersect monday’s shift. This means that the one person you initially scheduled above will not be alone, but will have a companion coming from the sunday’s shift.
The big question therefore is this: Is the schedule you came up with using the manual approach the best schedule in terms of minimizing the number of staff?
We will answer this question in our next article.