Workforce Scheduling problem - Modelling to minimize resources

Question

I am working on a scheduling program for a service desk. I want to decide the number of people required to come in at each shift. The data I have is:

1. There are 4 overlapping shifts
2. Arrival pattern at the hour level
3. Each defect has a 24 hr to solved. If a defect comes in 2:00 am then I have 24 hrs from 2:00 am to solve this defect. So someone else coming in the next shift can take it over. The defects needn't be solved by the same person or within the shift he/she is working in.

I have built a simplex model where I am able to solve saying every hour how many resources are required to solve the defects within that hour. Currently my approach does not consider the following:

• Overlapping shifts are not taken into account
• 24 hour window to solve the defect is not taken into account

Can you please suggest an approach to solve this? Papers or links that solve a similar problem would also be welcome.

Answer 1

I assume that each defect requires a specified amount of labor (expressed in worker-hours) to solve, and that each worker contributes one hour of labor for each hour of their shift (no breaks). You might look at modeling demand and labor in a cumulative manner. For each hour of the time horizon, total the worker-hours required to fix all defects that must be completed on or before that hour. (This is a cumulative total, including defects that were reported more than 24 hours earlier than the target hour.) Similarly, for each hour of the time horizon calculate the total number of worker-hours applied from the start of the horizon up to that hour (where each worker contributes one hour for each hour that his/her shift overlaps the cumulative time interval). In order not to have any defects "age out", the cumulative total of worker-hours must equal or exceed the cumulative demand at each hour of the horizon.