The practice of cross docking is another error that follows logically from a mistaken assumption. I have already shown why MIN/MAX and __EOQ__are wrong. The basic assumption is that "reducing logistics costs increases profits", and the problem is precisely how costs are calculated. I won't go into that now; another time I will show how cost accounting gives the wrong information for decision making. And decisions are what determine profits, or so we hope (otherwise we would have to recognize the irrelevance of any method and, worse, the irrelevance of managers).

But let's focus on this mistake today. I will demonstrate why cross docking always reduces profits.

Why do we have inventories?

I am going to repeat myself a little, because it is good to go to the basis of everything in order to understand what to do and, certainly, what not to do.

Inventories are necessary because the customer has no tolerance for waiting once he has expressed his need. It is obvious that it is not possible to maintain inventory of custom-made products, and in that case customers do expect a lead time. But products that are consumed on a regular basis, by a large number of customers, and that do not change their specifications frequently, represent very low risk if they are manufactured in advance. Therefore, if you don't have it in stock, you are very likely to lose the sale.

The answer to the question was obvious: we have inventory to make sales (which cannot be made without inventory).

## How much inventory do we require at each node of the chain?

I hope not to bore you with this platitudes.

The minimum inventory is required to meet the maximum expected demand before the next replenishment.

This means that the inventory level of a SKU in a store will depend on the maximum expected sales level within a replenishment time, the replenishment time being the number of days between one order and another plus the time it takes for delivery (transit). In the article about MIN/MAX ya demostré que si permitimos un tiempo variable, el inventario siempre está equivocado.

Let's assume now that you have listened to me and in the stores you have daily replenishment frequency and it takes one day to transit. In other words, you need inventory to satisfy the maximum level of sales that can occur in a two-day period.

## What is the fundamental difference between a distribution center and a store?

Of course, the formula also applies to the distribution center (DC). But the sales level of the distribution center is the sum of the sales of all the stores. In other words, the CEDI does not have independent sales, but its sales level will be a combination of what happens in the stores.

Having established that, let's see what "maximum sales level" means at each node, in a store and in the DC.

When we look at the actual sales for the last 30 days of any SKU in a store, we see a lot of variability. We can see several days of zero units and days of 5 units, 1 or 10. When we look at the sales of that same SKU in another store on the same days, we see that they also have a lot of variability, but where the first store sold zero, the second store sold 5, and so we see that the combination of both stores have sales with less variability overall.

If we combine the sales of many stores, the variability of their total sales is much smaller than the variability of each individual store. This is known as statistical aggregation (in general, the variability is reduced by the square root of the number of aggregation points).

As a result, the "maximum sales level" of the distribution center will be much lower than the sum of the "maximum sales levels" of each store added together. We have just discovered why it is convenient to have a distribution center! The DC inventory that is sufficient for daily sales is much less than if we had the inventories in the stores.

## Great, good theory, and what does it have to do with cross docking?

It should also be taken into account that suppliers are not very fond of making daily deliveries to the chain. Therefore, orders to external suppliers have a different replenishment time, several times longer than one day. Being very conservative, let's assume that we place weekly orders with external suppliers.

If instead of dispatching to DC we were to ask them to dispatch to each store, the total inventory of all the stores added together would be very large. So large that there is not enough space and, quite possibly, not enough working capital. That leads to reduced quantities ordered and we start to cause stock-outs or out-of-stocks. But this is exactly what causes us to lose sales, and we want inventory to make sales.

That is why if we ask for weekly dispatch to DC, it is because we store the product there and react daily to fluctuating demand, reducing inventory and also eliminating out-of-stocks in the stores, which is where sales are made.

Wait a minute: if I receive orders on a weekly basis, but I make daily dispatches, the receiving operation and the dispatching operation are, by system construction, decoupled.

If I force the coupling of the two, I must ship to the stores what I receive weekly, but then now I can't take advantage of statistical aggregation either, the main reason for DC!

Cross docking is precisely the coupling of receiving and shipping. See how in this article about __cross docking__ system is described as one that reduces storage at the DC to less than 24 hours.

In other words, cross docking is a practice that destroys the value of aggregation and generates excess inventories and out-of-stocks at the points of sale.

## Let's put some numbers

In a retail chain, the gross margin on each product can be 30% or more. The higher it is, the greater the effect.

The effect of out-of-stocks on sales is asymmetric, as we know from the Pareto principle. The 80/20, remember? That is, if we go from zero out-of-stocks to 5% out-of-stocks (which is extremely conservative), the sales we will lose are 15% or more. I have already told the real experience of a manufacturer that by reducing 5% out-of-stocks increased sales by 40%. Let's calculate with 15%.

If our chain, with no out-of-stocks, sells 100, the total margin will be 30. If it has a 10% profit on sales, that gives 10, so we know that our total operating expense is 20.

By reducing sales by 15%, we will have a total margin of 85 x 30% = 25.5, i.e., profits reduced to 5.5. To compensate for this loss of 4.5, the total expense would have to be reduced by more than 4.5, which represents ~ 23%.

Unless the savings from cross docking exceed 23% of the total expense (which includes all salaries, leases, energy, etc.), this is very bad business.

Cross docking goes against the primary objective of the system, which is to facilitate flow.

## Why hasn't anyone noticed this and continue doing cross docking?

The description I made of the system, with weekly supply frequency to the DC and daily distribution to the stores is the practice proposed by Goldratt. But this is not done either, and most companies do not know how to take advantage of their DC other than to save transportation costs, in addition to saving the chaos of receiving many different trucks at each store.

As the practice today is wrong, cross docking effectively improves the current operation. Remember Drucker: "Doing the right things wrong is much better than doing the wrong things right.

In these circumstances, where the prevailing practice is to misuse DC, one can indeed say that cross docking has the benefits listed in the article already cited.

But the article also says that implementing cross docking requires investment and commitment from the teams. In other words, if you have already implemented it, it may be more difficult to get out of this permanent situation of out-of-stocks in stores and excess inventory.

I'm going to make a speculation as to why someone came up with cross docking. I guess it was mimicking the hub or hub system of passenger flights, where it is much more efficient for the airline to make a stopover than to make direct flights between all its destinations. In effect, if I have multiple destinations and they can all also be origins, but every day there is a different amount of passengers wanting to go from one place to another, the most efficient thing to do is to bring the passengers to a hub, where all the passengers going to a destination from various origins are put together in a few flights. This is again statistical aggregation.

That flight system would be more efficient if passengers agreed to wait a week in a hotel at the hub, but I'm afraid I wouldn't do that. That's why the hub is not a DC that accumulates inventory. But products do not complain and in that case we can apply what I explained in previous paragraphs.

## Conclusions

Again, a reality check helps you understand: go into a store with a shopping list (including products from that store, of course) and see how many times you find everything. If cross docking served any purpose, you would find what you need more times and not see so much inventory piling up, to the point where several of those products expire or become obsolete.

Many of the industry's "best practices" such as academic program content are wrong. Going back to basics allows us to better understand our business. Cross docking promises to reduce costs, but let me ask you a question: what is your company in business for, to make money or to save money? The good news is that doing the right thing is simpler and much more profitable.