# Bootstrapping Reaction Time analysis (BRT)

Many trading companies provide a wide range of products to their customers. These goods must satisfy both ongoing and suddenly emerging customer needs. Let’s take the case of a stationery retailer. To optimize sales, a stationer must have an adequate range of pens available that will suit every taste. Offerings will include inexpensive pens that school children and students would use (we will refer to this as group one) as well as a variety of luxury pens (which we will refer to as group two).

Demand for inexpensive pens (group one) is fairly constant, though subject to seasonality. Demand for luxury items in group two – because of their high price and relatively small customer base – is inconsistent and therefore hard to predict. However, a stationer who wants to stay in business and be profitable must be able to cater to all types customers. To do so, it needs to keep a reserve of both groups of products.

It may be possible to use classical tools to forecast sales for the first group. There is, however, a problem forecasting sales for the second group. The difficulty here is that we cannot use methods of calculation that involve a common average for any given period of time for the purpose because the sales of the luxury items are irregular. They are not quantitatively consistent. A stationer may sell no luxury pens during one three week period, but then sell five units in a two day period. Because the luxury products generate a higher profit margin than the inexpensive items, the stationer is especially interested in selling them and must have sufficient stock in its warehouse to do so, both in terms of earnings and as an extension of the assortment database.

As an example, presume that sales for the luxury pens are properly described in the following table:

For the purpose of this analysis, we will also presume that system response time is four days. This means that in four days after an order is placed, it will be received from a warehouse and available for sale. Our starting balance, for the sake of demonstration, is one item.

The table above indicates that over a 31 day period, the stationer sells 30 luxury pens. The stationer’s goal is to determine whether to buy more product from its suppliers now, and if so, how much.

To find out, the average daily consumption of the product per day must be determined and interpolated into the future. If you multiply response time by average consumption, the result is future sales for the response time. You then subtract the current balance in stock (1 piece).

If we performed a simple, classic calculation, this is what we would do. To calculate the average sales per day we take the number of days in the analysis (31 days) and divide it by the total number of sales for this time period. Thirty pens were sold in 31 days; 30/31 = 0.97 pieces per day.

So, if Vc is the Average daily volume of sales, and tS is response time we can determine system response time (St) easily.

The amount of product a company will sell over our time period is calculated here:

St = Vc * tS = 0.97 * 4 = 3.9 pieces.

With 1 piece in stock, we can assume that we probably need to order 3 pcs (3.9 – 1 = 2.9).

The above analysis, based on calculating average daily sales, obviously does not answer these questions.

### To solve the problem of analyzing irregular and sparse demand, we suggest using the Bootstrapping Reaction Time (BRT) method.

The word “bootstrapping” comes from a saying “to pull one’ self over a fence by one’s bootstraps,” with the goal of making previously unseen, yet the necessary information, show itself.

In our first analysis, we multiplied average daily sales by response period to obtain a daily sales forecast. The goal, however is not to determine daily sales; rather, it is to bootstrap and find the most probable sales within the response period.

It is best to analyze the data so that it can answer the following question: “What forecast option is the most appropriate for us, based on the available data?” To find the answer, begin by creating a table of all possible outcomes of the data we have. First, split the data by response periods: the first response time is days 1 through 4; the second is days 2 through 5, the third is days 3 through 6. In total there are 28 possible outcomes:

The “C” column shows how much product is sold for a selected period of time (4 days).

What do we do with this data next? Our results presented a scatter of between 0 and 11 pieces. We need to decide which of these values is most suitable as a basis for determining how much stock to keep on hand. To determine this parameter, simply form a histogram (a table that summarizes frequency) like this:

Now that we have this data, we can move even further in our sales analysis. Begin by asking the following question: “To how many customers is your company ready to ensure unconditional availability of the product?” “Unconditional availability” is defined by more than a one month analysis It includes the largest number of an item ever sold on one day. For the stationer in our case, that number is 100; 100 pens were sold in one transaction.

That means that we need 100 pieces of the product available every day. Knowing this is good because it ensures the ability to provide a high level of service to our customers. At the same time, it is undesirable because it requires a large outlay of money and usurps a lot of space at the warehouse.

There are choices to be made here. You can maintain a high level of availability, thus satisfying more customers by holding more product in stock, or you can decide on a low level of service. You will have fewer customers satisfied, but will save on money outlay because you have not overstocked.

To obtain meaningful and valuable results, it is necessary to decide how many customers out of 100 you are interested in serving unconditionally. This is a managerial decision, and when carrying out an analysis of product turnover, the person responsible for sales (or stocks) must consciously and independently determine what raw data to include.

The popular level is anywhere from 80 out of 100 to 91 out of 100. For our example, we will use 80 because we consciously choose to reject the remaining customers; meeting their demands simply involves keeping too much extra product around.

What is the next step? We need to go back to our histogram and find the maximum value of sales. We want the total frequency of the demand for smaller sales figures to be as close to the selected level of availability as possible. In other words, we must logically choose the possible maximum demand which will occur in 80 out of 100 of our customers for the selected response time.

For our sample, this value is equal to eight pieces, (because it covers demand in 21 of the 28 possible outcomes). If we had chosen the level of availability to be 70 out of 100, the value would be five pieces and cover 20 out of 28 possible outcomes. Management can interpret the value of the eight pieces that we found as follows: When serving 8 out of 10 customers, a maximum of eight units of the product will be sold in any given four-day period. I therefore recommend that we add 7 pieces to our stock (remember, we already have one).

Here you can clearly see that using the BRT (Bootstrapping Reaction Time) method provides significantly different values than those obtained the “old-fashioned way.” It provides more accurate and reasonable analytics for regular (but sometimes) rare sales and is recommend for products that must be available to your steady customers.

### Mycroft Assistant allows you to modify individual settings for use with the BRT method, and therefore caters to all your specific products or product groups. It provides tools that accurately enable you to predict future product consumption.

Know more:

— Demand forecasting – information about it you can find HERE

— Sales analysis – information about it you can find HERE ;

— Planning – information about it you can find HERE and HERE ;

If you want to get started with the Mycroft Assistant – where we have implemented everything necessary for you to work effectively, simply sign up HERE and follow the provided instructions.