I was talking to a friend of mine who had just returned from a trip to Las Vegas. He was there to attend a wedding. While he was describing the various organisational aspects from the wedding planner, I immediately had the thought that this is very much like an optimisation problem. In fact, it seemed to be like a scheduling problem. The many different moving parts to this problem made me very interested. So, I will describe how to optimise a wedding in Las Vegas.

## Setting the scene

First of all, I would like to say that I am not actually optimising a wedding, but optimising the wedding venue. This blog will focus on the operations of the wedding venue and how they process all the weddings throughout the day. Also, just to be clear I am not talking about a wedding with Elvis as the celebrant. I am talking about a wedding venue at Las Vegas that manages all of the event planning. This wedding venue could be anywhere in the world, it is just that I heard about this venue. That said, there is a particular excessiveness that is really characteristic of Las Vegas.

The wedding venue of focus has a number of wedding lengths, for example, 30 minutes, 1 hour and 1.5 hours. We could even think of this as each wedding slot lasting 30 minutes and it is possible to book 1, 2 or 3 slots. Throughout the whole day, the wedding venue is in use. So it could be assumed that every available wedding “slot” has been booked. We likely need to relax the assumption, as it is unlikely that all slots are booked throughout the whole day.

The venue also has a garden for photos (they supply a photographer) and drivers are provided to pick up the wedding party (the bride and groom have different pick-up locations).

## Where is the optimisation problem?

It may not be totally clear where optimisation could be used in this setting. If you don’t see it, that is ok. It is a little subtle and in reality it may not be necessary. For other unnecessary uses of optimisation please have a look at my blog on optimising a football team.

There are in fact two different optimisation problem.

### Online scheduling

The first is in the booking stage. The complicating aspect here is that weddings can last 30 minutes, 1 hour or 1.5 hours. So, when making bookings the planner must decide where it is possible to schedule each of the different length weddings. This type of problem is called an *online* job shop scheduling problem. The **online** part of this problem means that the all of the input data is not known in advance, but revealed over time. For the wedding venue problem, the job shop scheduling problem can be described as follows:

- The set of jobs are the weddings to be held at this venue.
- The cost of the weddings increase non-linearly with the duration, i.e. a 1 hour wedding is more expensive than two 30 minute weddings.

- The set of periods when to scheduling the jobs are the “slots” during the day when the wedding venue is open

This problem is a little different to job shop scheduling, because it is not possible to change the order of the jobs or move them forward or back in time. So, the typical objective of make span (the time from the start of the first job until the end of the last job) does not apply. It is really about finding a feasible schedule that maximises the profit from the weddings.

Not knowing all the data in advance really complicates the job. Online optimisation techniques are required.

### Staff scheduling

The second optimisation problem is related to the many moving parts to the wedding venue operations. The part that first piqued my interest was that there are three rooms of the wedding venue and the goal is to make sure these are all occupied at all times. If all weddings were 30 minutes, you could simply schedule each “wedding” to pass through the reception area to the chapel to the garden for photos, spending just 30 minutes in each. The staff scheduling for this is fairly simple, you just need:

- three photographers (one for each room),
- four drivers (one for the bride and one for the groom, then double this so a driver is delivering one wedding while another is picking up), and
- one celebrant.

There are also many other jobs, such as cleaners and receptionist for the venue. But for this example, lets just keep it to photographers, drivers and celebrants.

Now, we are in a situation where there are different length weddings: 30 minutes, 1 hour and 1.5 hours. So we don’t have full utilisation of the rooms. Also, if we want to reduce costs, we don’t want to employ photographers, drivers and celebrants to work when there are no weddings. So we need to start to look at optimisation techniques.

#### Staff scheduling constraints

In this optimisation problem you have the following constraints:

- For each wedding there must be one celebrant, a driver for each the bride and groom and a photographer.
- Pick up and delivery of the bride and groom is scheduled to take 30 minutes (including leaving the venue, picking up the passengers and delivering them to the venue).
- Each staff shift must be three hours long.
- You can’t split shifts (i.e. work from 9:00 to 11:00 then 14:00 to 16:00).
- In a 24 hour operation, there must be an adequate amount of rest between shifts
- A shift can be at most 8 hours long.
- Each shift over 6 hours requires a lunch break.

The objective of this problem is to minimise the staff costs. This should translate into a minimal number of working staff. Also, staff can have different wages, so this will be taken into account when minimising the total cost.

Many of these constraints are related to classical staff scheduling problems. It is just an application to the wedding venue setting. Optimisation here would also be useful in the case that the wedding venue is not fully booked. You can manage the staff shifts so that you only have people working when there are weddings being performed.

## Optimisation in Las Vegas

Las Vegas is known for many things, many of these can be viewed from a mathematical perspective. There are many more optimisation problems that exist in this city. It is just a matter of keeping an eye out for them.

Next time you see a high throughput wedding venue, think of the optimisation that has gone to make that place highly efficient.