Negotiation and agreement generally require models of the peers who are involved in the negotiation. One typical area where negotiation takes place is in selling and retailing, which is also known as Customer Relationship Management (CRM). Customers and products are usually modelled using previous retailing experiences with similar or dissimilar customers and products. Machine learning is typically used to construct these models, which can be used to design mailing campaigns, to recommend new products, to do cross-selling, etc. Many CRM problems can already be solved through rankers, recommender systems, etc., provided that there are good models of customer and product behaviours available. A related but more general problem is when models are used to negotiate with one or more features of the product (or, less frequently, the customer) such as prices, bonuses, warranties, etc. Additionally, if it is possible to make several bids until an agreement is reached, methods must be devised so that the maximum pro t is obtained by the seller. In this work, we present a taxonomy of CRM problems, from which we distinguish those that have already been solved and those whose solutions are still pending. Then, we extend classical purchase probability rankings to the notion of pro t probability curves (price-dependent distributions), and we propose a simple negotiation solution for these cases.
The evolution of small-sized retailing to mass Customer Relationship
Management (CRM) has usually implied greater automation of the selling process, the
selection of products, customer prescriptions, cross-selling, up-selling, market
segmentation, etc. Techniques such as mailing campaign design, recommender
systems, and others (e.g. data-mining and machine learning [
Consider, for instance, a classical mailing campaign design or market
targeting problem. Given n equal products and m customers, the subset of customers
to whom a product must be o ered (customer prescription) must be devised.
In order to do this, machine learning is usually employed to learn probabilisitc
models, which assess the probability of buying for each customer, from which
a ranking of customers is performed. If the campaign has both xed and
variable costs, there are simple techniques (e.g. pro t lifts) to calculate the subset
of customers that maximises the expected pro t [
A very di erent type of problem, however, is when product or customer buying expectations can be in uenced by changing one or more features of the product or the customer, such as prices, bonuses, warranties, etc. For instance, the probability of a customer buying a product changes dramatically if the price is modi ed. And it is frequent to adjust prices (or, in a subtler way, to o er discounts) to those customers who are less eager to buy a product. Setting di erent prices for various customers can allow us to maximise pro t.
In this scenario, we need to move from probabilistic models (where, given a product and a customer, we have a probability of buying) to pro t probability curves or price-dependent distributions (where, given a product and customer, we see the evolution of the probability of buying according to a certain feature (e.g. price)). This more complex scenario has not been addressed to date.
Additionally, negotiating with price or other negotiable features normally
implies that counter-o ers from both buyer and seller are allowed up to a
maximum number of bids or until an agreement is reached. In other words an o er
can be made to a customer at a given price, and if the customer does not buy
the product, a lower price (a special discount o er for that particular customer)
can be o ered. This is the beginning of a negotiation process between the seller
and the buyer that we have already studied in [
However, in general, the case when a negotiation can take place, in parallel, for several products and customers must also be solved. In this case, not only must the pro t probability curves for each pair of product and customer be derived, but is also necessary to analyse how to combine these curves to develop new optimal negotiation strategies in these much more complex scenarios.
This work attempts to address this problem. We place ourselves on the side of the seller. Since the main overall objective is to sell as much as possible with the highest possible net price. Therefore, agreements are considered to be optimal when they are optimal for the seller. Nonetheless, the techniques that we discuss in this paper can also be used when both buyer and seller model each other, or when a buyer wants to negotiate with several sellers.
The paper is organised as follows. In Section 2, we devise a taxonomy of CRM prescription problems, from which we distinguish those that have been solved in the past and those which we propose a solution. In Section 3, we present a detailed description of a speci c scenario with one kind of product, a negotiable price, and M customers, and explain how it is possible to solve other kinds of CRM prescription problems using the same strategy. In Section 4, we present our conclusions and future work. 2
There are a great variety of di erent CRM prescription problems that can be de ned only by taking into account the cardinality of the di erent kinds of products and customers (1 1; N 1; 1 M; N M ) and the presence or absence of negotiation. As we have stated in the introduction, if a feature is negotiable, then we can introduce some kind of negotiation into the CRM process; however, if it is non-negotiable ( xed), then we are dealing with a traditional CRM prescription problem. Focusing on the seller, in this paper, when we refer to the price of a product we mean the net price that the seller obtains for the product, e.g., if a customer buys a product for 3 euros, the net price is 3 euros since xed and variable costs are not included (except if mailing is involved).
In any of these situations, data-mining techniques can help the seller by modelling customer behaviour in order to make good decisions. In this context, that means obtaining as much pro t as possible. 2.1
Case 1 in Table 1 (one kind of product, xed net price, and one customer) is trivial. In this scenario, the seller o ers the product to the customer at a xed price and the customer may or not buy the product. The seller cannot do anything more because s/he does not have more products to sell. S/he cannot negotiate the price of the product with the customer, and s/he does not have any more customers for the product.
Case 2 in Table 1 (one kind of product, xed net price, and M customers) is the typical case of a mailing campaign design. The objective is to obtain a customer ranking to determine the set of customers to whom the mailing campaign should be directed in order to obtain the maximum pro t. Data-mining can help in this situation by learning a probabilistic estimation model from previous customer data that includes information about similar products that have been sold to them. This model will obtain the buying probability for each customer, so by putting them in order of decreasing buying probability, the most desirable customers will be at the top of the ranking. Using a simple formula for marketing costs, we can establish a threshold/cut-o in this ranking. The customers above the threshold will be o ered the product. This is usually plotted using the so-called lift charts.
Case 3 in Table 1 (N kind of products, xed net price, and one customer) is symmetric to case 2. Instead of N customers and one product, in this case, there are N di erent products and only one customer. The objective is to obtain a product ranking for the customer. Similarly, data-mining can help to learn a probabilistic estimation model from previous product data that have been sold to similar customers. This model will predict the buying probability for each product, so by putting them in order of decreasing buying probability, the most desirable products for the customer will be at the top of the ranking. This case overlaps to a great extent with recommender systems.
Case 4 in Table 1 (N kinds of products, xed net price, and M customers) is
studied in [
In the above four cases, we have assumed that the net price of the product is xed. When this is not the case, the objective of the sellers changes. They do not have to sell the product, but they have to sell it at the maximum price, which the seller and the buyer can negotiate. Figure 1 (Left) shows how the behaviour of a customer can be approximated. The customer buys the product if the price is less than or equal to the maximum price that s/he could pay for it. Figure 1 (Right) shows the expected pro t for each price (the expected pro t is equal to the buying probability multiplied by the price). In this case, it is clear that the maximum expected pro t is obtained when the seller sells the product at the maximum price that the customer can pay.
We will show later, that the seller does not know this real model and tries to learn the most accurate model from previous data by using data-mining techniques.
In [
There are some details that should be taken into account from our work in [
The cases 6, 7 and 8 in Table 1 have not yet been studied. However, they can be understood as an extension of case 5 combined with the rankings of customers and products that are used in the approaches proposed in Table 1 for the cases 2 and 3.
In case 6 in Table 1 (one kind of product, a negotiable price, and M customers), there is a curve for each customer, that is similar to the curve in case 5 (Figure 4, Left). If the seller can only make one o er to the customers, the seller will o er the product at the price that gives the maximum expected pro t (in relation to all the expected pro t curves) to the customer whose curve achieves the maximum. However, if the seller can make several o ers, the seller will distribute the o ers along the curves following a negotiation strategy. In this case, the seller not only changes the price of the product, but the seller can also change the customer that s/he is negotiating with, depending on the price of the product (that is, by selecting the customer in each bid who gives the greatest expected pro t at this price). Therefore, these curves can be seen as an evolution of the customer ranking for each price.
Case 7 in Table 1 (N kind of products, a negotiable price, and one customer) is symmetric to case 6. Instead of one curve for each customer, there is one curve for each product that was learned from the previous customer data. In this case, the curves represent a ranking of products for that customer. The learned datamining models will help the seller to make the best decision about which product the seller o ers to the customer and at what price. Figure 4 is an example of this case since the curves would represent three di erent products to be o ered to one customer.
Case 8 in Table 1 (N kind of products, a negotiable price, and M customers) is the most complex of all. There is one data-mining model for each product and customer (i.e., N M curves). The objective is to o er the products to the customer at the best price in order to obtain the maximum pro t. Multiple scenarios can be proposed for this situation: each customer can buy only one product; each customer can buy several products; if the customer buys something, it will be more di cult to buy another product; there is limited stock; etc.
To solve cases 6, 7 and 8, we propose extending the classical concept of ranking customers or products to pro t probability curves in order to obtain a ranking of customers or products for each price (similar to cases 2 and 3). For example, Figure 4 shows that, for a price of 300,000 euros the most desirable customer is the one represented by the solid line, the second most desirable one is the customer represented by the dotted line, and the least desirable customer is the one represented by the dashed line. The situation changes for a price of 200,000 euros; at that point the most desirable customer is the one represented by the dashed line, the second most desirable one is the customer represented by the solid line, and the least desirable customer is the one represented by the dotted line. Therefore, an important property of these probabilistic buying models is that there is a change in the ranking at the point where two curves cross.
Scenario with Negotiable Price and several Customers To study case 6 in more depth, we start with the simplest situation with two customers, and we explain the negotiation strategy that the seller will follow by means of an example.
In Figure 5, there are two curves representing the buying model of two different customers. The buying model of the rst customer follows a normal distribution with 1 = 400 and 1 = 100, and it is represented by a dashed line. The buying model of the second customer follows a normal distribution with 2 = 300 and 2 = 200, and it is represented by a dotted line. These are the models; however, the real situation is that the maximum buying price for customer 1 is 100 euros and 150 euros for customer 2.
We assume a simple negotiation process for this example. The negotiation
strategy that we describe is similar to the Best Local Expected Pro t (BLEP)
strategy explained in [
The strategy consists of o ering the product at the price that obtains the maximum expected pro t for the customer whose curve reaches the maximum. If the customer accepts the o er, the process is nished. If the customer does not accept the o er, his/her curve is normalised taking into account the following: the probabilities of buying that are less than or equal to the probability of buying at this price will be set to 0; and the probabilities greater than the probability of buying at this price will be normalised between 0 and 1. This process is repeated with each customer until one of them accepts an o er1. The trace of the negotiation process is described in Table 2 (Left) and shown graphically in Figures 6 and 7. In each iteration, the maximum of the functions is calculated (the envelope curve). The envelope curve is represented by a solid line in Figures 6 and 7.
Note that as Table 2 (Left) shows, the third o er is greater than the second one. This is because there is more that one customer in the negotiation process and the o er is made at the price that maximises the expected pro t at each iteration. Therefore, it is easy to propose an improvement for this negotiation strategy with a limited number of o ers, which is similar to BLEP with n bids. This improvement is a pre-process that consists of calculating the n points and ordering them by the price before starting the negotiation. Following the example shown in Table 2 (Left), if there are only 4 bids no one will buy the product. However, with our improvement (the pre-process) customer 2 will buy the product at a price of 150 euros as shown in Table 2 (Right).
This negotiation scenario suggests that other negotiation strategies can be
proposed for application to problems of this type in order to obtain the maximum
pro t. One problem with the BLEP strategy is that it is very conservative. It
might be interesting to implement more aggressive strategies that make o ers
at higher prices (graphically, more to the right). A negotiation strategy that
attempts to do this is one of the strategies proposed in [
In case 6, we have presented an example with two customers and one product, but it would be the same for more than two customers. In the end, there would be one curve for each customer, and the same negotiation strategies could be applied.
Case 7 (N kind of products, a negotiable price, and one customer) is the same as case 6, but the curves represent the buying model of each product for each customer, and a ranking of products will be obtained for each price.
Case 8 (N kind of products, a negotiable price, and M customers) can be studied using the same concept of expected pro t curves, but there will be N M curves. The use of simulation or some kind of evolutionary computation will be necessary to obtain a good solution because case 8 is similar to case 4 where the best point in each curve does not give the best global solution. For each of the N kind of products, there will be M curves that belong to the buying model of each customer. Figure 8 presents a simple example with two products and two customers, where a customer can only buy a maximum of one product. In this example, customer 1 (dashed line) has the maximum expected pro t for both products, corresponding to 80 euros for product 1 and 112 euros for product 2. The best local decision would be to o er product 2 to customer 1; however, customer 2 (dotted line) has the maximum expected pro t of 27 euros 1 More stop conditions are possible (e.g. limited number of o ers (BLEP with n bids), minimum selling price, etc.) for product 1 and 52 euros for product 2. Thus, for a better global solution, it would be better to o er product 2 to customer 2 and product 1 to the customer 1 since the overall pro t would be greater. 4
In this paper, we have devised a taxonomy of CRM prescription problems, where automated learning can help a seller to make a good decision about which product should be o ered to which customer and at what price in order to obtain as much overall pro t as possible.
Some of these problems have already been studied, and we have explained the approaches proposed to solve them. In the cases that have not yet been studied (negotiable price, several products and/or several customers), we have proposed a solution based on the extension of rankings to expected pro t curves, in which there is a ranking of customers and/or products for each price of the product.
As future work, we plan to study the performance of the proposed methods with experiments applying the negotiation strategies described in Section 3 and other suitable negotiation strategies to cases 6, 7 and 8 shown in Table 1.