Staff scheduling with social distancing constraints

GitHub code: https://github.com/bukhsh/os3d

It is likely that for most of us the return to work will be gradual with a degree of social distancing in effect. The government has provided advice on managing workspace during the COVID pandemic. A particular point in the advice that caught my eye was about avoiding the use of hot desks.

Hot-desking is a working arrangement where employees have no assigned desk and a single desk is shared during different time periods. This is a common practice. I thought hot desking and social distancing are conflicting objectives and if they both are pursued then we will not be able to accommodate a lot of people in our workspaces. So to investigate a bit further, I turn to something that I know: mathematical modelling.

I have written an optimisation model that maximises the occupancy of a workspace subject to a social distancing constraint. The optimisation problem is quite similar to a traditional scheduling problem, however, the social distancing constraint turned out to be a pain to implement. I am going to provide a high-level view of the mathematical model here, see the GitHub code for implementation and my lecture notes here for the formulation of selected traditional scheduling problems.

The model requires (x,y) coordinates of a seating plan as an input. The distance between the seats is calculated and the model optimises the occupancy for a given time horizon (e.g a day, a week or a month). The problem takes the form of a binary integer problem. The decision variable is defined as follows:

I have tested this model in an office space where I am based. I sit on a desk number 65 which is towards the pointy end of the building. I have placed the seating plan on a grid with an assumption that the face of TIC building is approximately 60 metres and the depth is approximately 70 metres. The distance between two adjacent seats is approximately 1.2 metres.

With 2 m social distancing, the optimal occupancy is 34% and the following figure presents a solution. The solution assigns two staff members on a desk with space for 6.

The following figure provides a relationship between social distancing and the optimal occupancy levels of the building. Note that we have 100% occupancy with the social distancing of 0.5 metres and it drops to 58% with 1 metre social distancing.

Some insights/ideas from the modelling are as follows:

  • Hot-desking: the government advice is to avoid hot-desking. However, the occupancy level improves if hot-desking is allowed. (in the case of TIC-Level 4 seating plan, only one colleague can sit in the middle on a table with six seats). Of course hot-desking would need to be accompanied by stricter cleaning regime. We’d need to balance the risk of spreading virus and benefits of increased occupancy levels by allowing hot-desking
  • Staggering work hours: this scheduling model can be used to allocate work hours to colleagues if we were to stagger work hours…or some arrangement like 2-days a week in office
  • Immunity certificates: Currently, there is no concrete evidence on herd-immunity of Covid-19. However, the government is planning to introduce immunity certificates. If a part of the workforce is immune that could be used to increase the occupancy of a building. The optimisation model can be extended to include such constraints.
  • Seating-plan optimisation: presently the model takes (x,y) coordinates of a seating-plan as given parameters. Theses can be treated as variables in the model to ask the question: for a given work-space what is a seating arrangement that maximises occupancy – I imagine it’d be a bit tricky to model all the health and safety constraints associated with changing the seating plan.
  • Use of office facilities: I am interested in an online web-based solution that provides the staff with an allocated time for using facilities. For example, when a staff member needs to use the kitchen (or rest-room) they go and log in their request, the online system allocates the facility which is least busy or a time window when they can use the facility. Similarly, when they need to enter or exit the building, a route of minimal traffic is provided by the tool. Such a solution would need a live feed of sensor-data. This is something which is doable but needs time and effort.

If you are interested in collaborating on any of the above ideas then feel free to get in touch. Thanks for reading this blog and good luck with returning to the new normal.

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