*The ‘probability of sale arbitrage’ model that revolutionizes P & L *

When talking to fashion company managers and executives, one of their biggest concerns is stock transfers. Are they throwing good money after bad by transferring unsold stock?

In the back of their mind is that pervasive worry about expense and making the wrong call:

“Should I just leave the stock in situ and go through the usual round of markdowns, or take a risk and spend money transferring to other branches in the hope of full price sales?”

Well, the first thing to say is that this line of reasoning is completely flawed.

Ultimately, stock transfer is about something that C executives deal with successfully every day – finding ways to increase return on investment. And we can tell you that stock transfers are the undiscovered gem of ROI.

It’s all about identifying imbalances in the probability of sales.

In simple terms, when you move stock from a place with (for example) a 20-30% probability of selling to one with a 60-70% probability, you KILL it. Wherever you have such imbalances in probability of sale, the ROI is enormous. In fact, you want to spend the MAXIMUM amount in order to move as much stuff as you possibly can.

Yes, that’s right.

When you have the right model to follow, the more store-to-store transhipments you make, the happier you make your shareholders.

Of course, you don’t just want to know which garments will sell better elsewhere, but also the optimal numbers that need to remain in place. We don’t want to increase the sale of full price items by creating stock outs at ‘exporting’ stores. A retail store is a consumer ecosystem where reducing choice, or perception of choice, can lead to customers taking their business elsewhere.

So, we’re looking to optimize transhipments between stores to hit the sweet spot of optimal full price sales without stock outs.

Here’s how the Evo Replenishment tool does it, in a process similar to the more straightforward restocking of inventory.

**3 steps to optimal store-to-store transfers**

1. The system collects data for sales, inventory stock, weather and competition, together with the business rules decided by headquarters and logistical constraints for shipments between stores.

2. The system processes data, estimating, for example, the impact of stock-outs and promotions, in order to get the future potential of sales for article, size and store.

By comparing the sales potential with the stock, the system calculates the orders for the missing pieces, but also the release of excess pieces in the shops, caused by lack of customer demand.

3. The optimization algorithm allocates the goods by moving them to the point of sales with the greatest potential, minimizing logistics costs between the shops and the number of packages to be packed, respecting the constraints specified by the head office.

The output is a list of transhipments to be made between pairs of shops, by item and size.

** Transhipment parameters**

Three main parameters are able to regulate transhipments between stores: the maximum number of packages per store, the minimum number of pieces per pack and minimum value of each package. The first one imposes a ceiling on the number of packages that each store can send to potential recipients, so as to limit the shipments and therefore the workload of the shops.

In this graphic, for example, this number is set to 3.

The second and the third parameters ensure that each package sent has a minimum number of pieces and / or a minimum value so as to make shipping worthwhile even when set against the logistical costs. In these figures, for example, each package must contain at least 7 pieces with a minimum value based on the list price of the items equal to €150.

The choice of these parameters allows us to check the number of transhipments carried out. As transhipments entail costs for the company, both in terms of logistics and in terms of extra work for the shop staff, we have to ask the question:

*Does the added value obtained from transhipments justify the shipping costs?*

**Increased sell-throughs of transfers**

To answer this question, let's start from the benefits of transhipments in terms of sell-through. This graph is a comparison, taken from historical customer analysis, between the sell-through of the goods handled and the baseline sell-through

In particular, the sell-through of the transhipped goods is calculated as the percentage of the items handled sold in the recipient stores within 30 days of arrival. The baseline sell-through is the percentage of inventory of the same items, always sold within 30 days in stores where no movement has occurred.

**Costs and benefits analysis of transhipments**

From the comparison of the two quantities, a picture emerges of how the transhipments contribute to increase the sell-through of the articles by more than 30 percentage points at full price, that is before the start of the sales. It is precisely this increase in sell-through which justifies the shipping costs of transhipments, as is shown in the detailed 'costs and benefits' below.

Note also there is the cost of the store managers’ input in the process. Again, this cost needs to be judged on ROI as our research has shown time and time again the experience and intuition of store managers adds value to machine-generated suggestions.

By analyzing the impact of transhipments on each managed item, we assume an average selling price of the articles (ASP, or average selling price) of €100, net of any discounts. By subtracting the average cost of the item, we obtain an average net margin of €55 per item.

As we have seen, transhipments increase the probability of selling each item by about 32%. The net benefit from the transhipment of each item will therefore be given by the product between the two values, in this case equal to €17.53.

As for the costs, the shipping of each item is estimated by dividing the shipping cost of each pack, equal to €7 in our example, by the average number of items per package, estimated at 10 pieces.

We add the package preparation cost, which requires extra work for store managers: assuming about 1 hour of work to prepare a package with 10 pieces, and an hourly cost for the company of €20, the cost of picking & packing per item is around €2.

In addition, imagining that in about an hour of work a shopkeeper is able to rework 20 options, always at an hourly cost of €20, we get an additional cost of €1 per item, taking into account the time spent by the stores to view and edit the proposal for re-allocation and transhipments.

**The low percentage impact of transhipment costs**

So we can see that the total costs for the transfer of a moving item are given by the sum of the 3 costs just analyzed, for a total of €3.74.

The net margin for each item moved is equal to €13.80, which corresponds to about 80% of the benefit obtainable from the transhipment. In other words, the costs of transhipment have only a 20% impact on the benefit obtained through the movements.

The extra margin is strictly related to the average margin per item, and therefore to the average selling price of the items.

**Finding the threshold for a profitable average selling price**

Once we have our model in place, we can establish a level at which transfers are profitable and create forecasts showing the margins available at different average selling prices.

The graph below shows a simulation of the incremental margin trend as the average selling price of the items changes.

The higher the price of the articles, the greater is the margin obtainable from the transhipments, and therefore it is more viable to move the items.

Conversely, if the price is too low, transhipments may not be viable. The threshold value highlighted by this simulation is about €20, so any price higher than that is sufficient to justify the transhipment of goods between stores.

Obviously, to limit delivery costs, it is also necessary to adjust the number of pieces shipped within each package. As the price goes up, the optimal minimum number of pieces per package drops, and even shipments of a few items at a time are viable.

The business rules and the automatic optimization allow you to easily control the delivery costs when the average selling price changes, enabling adaptation of the algorithm from time to time depending on the context.

**Conclusion**

As we pointed out at the beginning of this post, far from being an expensive worry, stock transfers can actually be a source of increased margins and greater profitability.

Once you identify imbalances in the probability of sales and set your transhipment parameters you will never look back.

Happy shipping!

*Want to find out more about Evo Replenish? It's just one of many solutions we offer to our retail clients.*

### About the writers

Elena Marocco joined Evo Pricing as Data Scientist in 2016 after a very successful internship experience.

A brilliant, cum-laude graduate in Mathematics at the University of Turin, she defended an MSc with an innovative solution for Fashion Inventory Management.

She is excited about the world of Probability, Statistics and, more generally, in discovering useful Maths that can have a significant impact through real life applications.

Martin Luxton is a writer and content strategist who specializes in explaining how technology affects business and everyday life.

Big Data and Predictive Analytics are here to stay and we have only just begun tapping into their enormous potential