It is indeed amazing in how many situations mathematics can be applied. In this blog, we explore something we have not explored before in our blogs and that is operations management – with specific reference to point-of-sale (POS). For the layperson it is indeed interesting that for so many business, strategic or operational problems, there is a neat mathematical solution.

Here’s a mundane problem that almost anybody who has ever been into a retail store is aware of: How many POS (check-out counters) are optimal in a store?

On the one hand, having many POS terminals takes up valuable retail space and requires expensive resources to operate the terminals. On the other hand, having too few terminals causes long queues and sometimes annoyed customers detracting from the shopping experience (and the brand!).

The push and pull nature of this conundrum, means that it is well primed for an operations research/mathematical optimisation solution, particularly in the branch of mathematics known as queuing theory.

Traditional mathematical solutions to queuing problems

A few more traditional mathematical solutions exist to calculate a queuing problem. Amongst these, we have Little’s Law and the Sakasegawa Formula.

Little’s Law looks at the following:

• Average queue length
• Average arrival time
• Average waiting time (output)

The characteristic that is difficult to calculate in Little’s Law is average queue length. Here  Sakasegawa’s Formula can help as it looks at a few other variables namely:

• = Line Length (average)
• = Utilisation (arrival rate/service capacity)
• M = Number of channels

Although these equations are useful for simple indicative calculations, today’s leading retailers are looking to bring more sophistication into their queuing calculations.

Analytical smarts

These days, advanced retailers are utilising optimisation models (prescriptive analytics) which take into account several data, including (but not limited to) one or more of the following:

1. Foot-traffic in the store and arrival rate,
2. Square meterage of the store,
3. Variety of basket sizes (items, value, type),
4. Average check-out time,
5. Type of check-outs (account payments, returns processing, purchasing of airtime/electricity, RICA-ing, etc.), and
6. Centralised check out/de-centralised check out (number of check-out areas).

The optimisation model is trained on known data. Sensitivity models are built, and the final model solution allows for the input of some of the data (above) and then an output in terms of the number of POS required (and sometimes also the types of POS).

Different types of point-of-sale

Traditionally there was only one type of POS. These days however, stores offer a variety including the following:

1. Standard POS check-out – this is where a client will pay for their goods. They may have other options such as paying their accounts, buying airtime and making returns.
2. Self-service check-out – whilst not yet popular in SA, these are found across Europe and the US, allowing the customer to check out without the requirement of check-out staff.
3. Online click-and-collect terminals – here the customer purchases online and picks it up at the store. This terminal helps the staff prepare the item(s) for the customer’s imminent arrival.
4. Online purchase processing – for some retailers the stock used for online purchases are managed at some key stores. Managing online orders and packaging them for couriers requires multiple “point of sale” systems.
5. Mobile POS – many stores have the ability to have staff walk around in-store with a mobile POS, thus enabling contingency when there are very long queues.

The different types of POS are used within the model too.

Optimal resources and rostering of tasks

Linked to a POS-model should be an optimal resourcing model/rostering of tasks. These models ensure that each store is correctly staffed with both permanent and contract staff. The skills of the staff are also key. Can check-out staff pack shelves? Can customer service staff also conduct POS duties? What POS tasks are reserved for senior staff?

How do you determine how many POS terminals you need in a retail store? Prescriptive analytics can show you the way. To find out more about how Principa’s advanced analytics capabilities can improve your operational management challenges, please get in touch.

Author

Thomas has 18 years of experience in data science focusing on the EMEA region. His experience traverses multiple industries and disciplines covering analytics, consulting and software solutions for companies ranging from large banks and retailers to telcos and manufacturing operations. A large part of his experience comes from working with credit providers helping them harness the predictive power of data through the use of machine learning and decision tech. Thomas holds an MA in Mathematics from Edinburgh University.