WO2001011522A2 - Method for optimizing net present value of a cross-selling marketing campaign - Google Patents

Method for optimizing net present value of a cross-selling marketing campaign Download PDF

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Publication number
WO2001011522A2
WO2001011522A2 PCT/US2000/021453 US0021453W WO0111522A2 WO 2001011522 A2 WO2001011522 A2 WO 2001011522A2 US 0021453 W US0021453 W US 0021453W WO 0111522 A2 WO0111522 A2 WO 0111522A2
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cross
optimizing
customer
linear
problem
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PCT/US2000/021453
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French (fr)
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WO2001011522A8 (en
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Yuri Galperin
Vladimir Fishman
Leonid Gibiansky
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Marketswitch Corporation
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Publication of WO2001011522A8 publication Critical patent/WO2001011522A8/en

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    • GPHYSICS
    • G06COMPUTING; CALCULATING; COUNTING
    • G06QDATA PROCESSING SYSTEMS OR METHODS, SPECIALLY ADAPTED FOR ADMINISTRATIVE, COMMERCIAL, FINANCIAL, MANAGERIAL, SUPERVISORY OR FORECASTING PURPOSES; SYSTEMS OR METHODS SPECIALLY ADAPTED FOR ADMINISTRATIVE, COMMERCIAL, FINANCIAL, MANAGERIAL, SUPERVISORY OR FORECASTING PURPOSES, NOT OTHERWISE PROVIDED FOR
    • G06Q30/00Commerce, e.g. shopping or e-commerce
    • G06Q30/02Marketing, e.g. market research and analysis, surveying, promotions, advertising, buyer profiling, customer management or rewards; Price estimation or determination

Abstract

The present invention applies a novel iterative algorithm to the problem of multidimensional optimization by supplying a strict, nonlinear mathematical solution to what has traditionally been treated as a linear multidimensional problem. The process consists of randomly selecting a statistically significant sample of a prospect list, calculating the value of the utility function for each pair of an offer and selected prospects, reducing the original linear multidimensional problem to a non-linear problem with a feasible number of dimensions, solving the non-linear problem for the selected sample numerically with the desired tolerance using an iterative algorithm, and using the results to calculate an optimal set of offers in one pass for the full prospect list.

Description

TITLE: Method for Optimizing Net Present Value of a Cross- Selling Marketing

Campaign

FIELD OF THE INVENTION

This invention relates generally to the development of a method to optimize the effects of cross-selling marketing campaigns. More specifically, this invention is an improvement on the application of classical methods of discrete linear programming to the problem of multidimensional optimization.

BACKGROUND OF THE INVENTION

Businesses typically have a number of promotions to offer to a large list of prospective customers. Each promotion may have an eligibility condition, a response model, and a profitability model associated with it.

Some promotions may be combined into Peer Groups (i.e., groups of mutually exclusive offers, such as a credit card with different interest rates). A constraint may be placed on the maximum number of offers that goes to any customer; in addition, there may be business requirements such as minimal number of sales, minimal NPV (Net Present Value) per customer, maximal budget, etc. These requirements may apply to any individual promotion, a peer group, or a campaign as a whole.

The goal of cross-selling marketing optimization is to determine what offers to send to which customers to maximize a utility function of the campaign (total NPV, total number of sales etc.), while satisfying all the business requirements and constraints.

The present state of the art lets marketers process one offer at a time. A response and/or profitability model is applied and customers are rank-ordered based on propensity to respond to the offer. After this ordering, a certain percentage from the top of the list is selected to receive the offer. The same process is applied to all available offers separately.

As a result, the best, most responsive and valuable customers are saturated with offers and the middle segment of the customer list is ignored. The overall efficiency of the campaign therefore degrades.

Another significant drawback of this approach is the inability to satisfy various real- life constraints and business goals.

Most sophisticated marketers have tried to consolidate models built for different offers. However, these attempts have not been based on any solid scientific method, but rather have utilized an ad hoc approach. Because of this, only the most-simple constraints have been able to be satisfied and the solutions have been sub-optimal with respect to a utility function. In fact, these marketers haven't even been able to estimate how far off they are from the true optimum.

What would therefore be useful is a process that provides a mathematically optimal offer allocation, i.e., one that selects an optimal set of offers for each customer that maximizes the utility function and satisfies all business goals and constraints. SUMMARY OF THE INVENTION

The present invention represents the application of a novel iterative algorithm to the problem of multidimensional optimization. The present invention supplies a strict, nonlinear mathematical solution to what has traditionally been treated as a linear multidimensional problem.

The problem in its original form is a problem of discrete linear programming. However, due to a huge number of dimensions (in a typical business case N = O(108 ), M = O(102)), the application of classical methods of discrete linear programming is not feasible.

The process of the present invention consists of randomly selecting a statistically significant sample of a prospect list, calculating the value of the utility function for each pair of an offer and selected prospects, reducing the original linear multidimensional problem to a non-linear problem with a feasible number of dimensions, solving the nonlinear problem for the selected sample numerically with the desired tolerance using an iterative algorithm, and using the results to calculate an optimal set of offers in one pass for the full prospect list.

It is an object of the present invention to increase the efficiency of a cross-selling marketing campaign. It is an object of the present invention to increase the efficiency of cross-selling campaigns that include a large number of offers.

It is an object of the present invention to provide optimization of cross-selling campaigns wherein groups of offers can be mutually exclusive.

It is an object of the present invention to increase the efficiency of cross-selling campaigns that are targeted to large number of prospective customers.

It is an object of the present invention to increase the efficiency of cross-selling campaigns by selecting an individual, optimal set of offers for each customer.

It is an object of the present invention to constrain of maximum number of offers sent to a customer within cross-selling campaigns.

It is an object of the present invention to satisfy business goals, like minimum number of sales and budget constraints, while optimizing cross-selling campaigns as applied to individual offers, groups of offers or the entire campaign.

It is an object of the present invention to maximize a user-chosen utility function, like total NPV or number of sales, within a cross-selling campaign.

It is an object of the present invention to mathematically maximize the utility function and satisfy all constraints within a cross-selling campaign.

It is an object of the present invention to allow interactive changes in goals or constraints of cross-selling campaigns and quickly view the results.

It is an object of the present invention to provide final scoring for cross-selling campaigns in a single pass so as to scalable and efficient enough to process a list of 100 million customers overnight.

It is yet another object of the invention to provide true "one-to-one" marketing in cross-selling campaigns.

BRIEF DESCRIPTION OF THE DRAWINGS

Figure 1 is a flow chart of the basic process of the present invention.

Figure 2 is a more detailed data flow of a marketing optimization process of the present invention.

Figure 3 is a flow chart of the single pass process of the present invention. Figure 4 is a flow chart of the novel iterative algorithm of the present invention.

DETAILED DESCRIPTION OF THE INVENTION

The present invention represents the application of a novel iterative algorithm to the problem of multidimensional optimization of cross-selling campaigns by supplying a strict, nonlinear mathematical solution to the traditional linear multidimensional problem desired to be solved when offering a large number of promotions M to a very large set of prospective customers N.

The process of the present invention, as shown in figure 1, consists of randomly selecting a statistically significant sample 10 of a prospect list, calculating the value of the utility function 20 for each pair of an offer 30 and selected prospects 10, reducing the original linear multidimensional problem to a non-linear problem 40 with a feasible number of dimensions, solving the non-linear problem 50 for the selected sample numerically with the desired tolerance using an iterative algorithm, and using the results to calculate an optimal set of offers 60 in one pass for the full prospect list.

Let A=(a1J), be a solicitation matrix, where a, = 1, if offer j goes to a customer i = 0, otherwise; R = (r,.) , be a response matrix, where r.j - is a probability for a customer i respond to a promotion j;

P = (p ), be a profitability matrix, where p, - is a profitability of a customer i, if he/she responds to a promotion j. Total NPV of the campaign, NPV = NPV( A, R, P), is a linear function of a,-, r1J5 p,_ and other economic parameters of the campaign.

Eligibility conditions, peer group logic, and maximal number of offers per customer constraint can be expressed by a set of inequalities Clk

Clk( A) <= 0, i = l, 2, ..., N, k = 1, 2, ..., K where C, are linear functions, and N is of the order of number of customers in the prospect list, K is number of restrictions. These customer-level restrictions are applied for each individual. Economic goals are expressed by a set of inequalities G for each promotion and the whole campaign:

GJ;1( A, R, P) <= 0, j = l, 2, ..., M, 1 = 1, 2, ..., L.

GO I( A, R, P) <= 0, 1 = 1, 2 Lo where G, are linear functions, and M is of the order of number of promotions in the campaign, L. is total number of restrictions. These main restrictions are applied for a promotion or the campaign, and G is a sum over all eligible customers.

It is desired to then find a solicitation matrix A that maximizes NPV(A,*) under the condition that all constraints C and G are satisfied.

The solution presented by the inventors uses the following steps, as shown in figure 2. A first step is to create a campaign or project by selecting a set 202 of targeting optimizer (TO) projects from a modeling database 200. Each TO project contains promotion and offer economics, and eligibility information for a selected pool of prospects. Each TO project includes substitute offer groups 206, model calibration 204, and eligibility information that is combined with the prospect input to create an eligibility matrix 214.

For prospect input, one selects, randomly, a statistically significant sample or testing DCP (derived customer pool) 212 of a prospect list from a customer database 210. Matrices P and R are then calculated for selected prospects at 224. The next steps, to reduce the original linear multidimensional problem to a non-linear problem with a feasible number of dimensions and solve the non-linear problem for the selected sample numerically with the desired tolerance using a novel iterative algorithm (described below) is done by the optimization engine 240.

Input data reports 230 record the matrices and offers used. Using this input data, campaign level constraints 242, and offer level constraints 244, the optimization engine 240 produces a solicitation matrix 250. This is used to calculate report data 252 for optimization reports 254 that are tested at 260 to see if the selected constraints 242 and 244 satisfied the desired offer solicitation schema 256. If satisfied, a final report 260 is generated. If the offer solicitation schema 256 are not satisfied, campaign level constraints 242 and offer level constraints 244 are adjusted to produce another iteration.

The optimization engine 240 calculates the vector of parameters L of the ANPV (adjusted NP V) functions

AΝPV.(L, r., Pl), where j = 1, 2, ..., # of promotions; r, = (r,_) - vector of propensities to respond of a customer i to promotions 1, 2, ...

Pi = (Pij) _ vector of profitability of a customer i for promotions 1, 2, ...

It then calculates the optimal solicitation matrix 250 in a single pass through the full prospect list. To accomplish that, as shown in figure 3:

1. Read the next customer record 31 ;

2. Calculate vectors r, and p, 32;

3. Calculate anp v_ = (ANPV.(L, r„ p,), j = 1, 2, ..., # of promotions) 33;

4. Based on the values of anp v, and eligibility conditions, calculate solicitation vector a, = ( a, , j=l , 2, ..., ..., # of promotions ), which defines the optimal set of promotions that goes to a customer i at 34; and

5. Repeat the previous four steps until the end of the customer list at 35. To calculate matrices P and R for selected prospects at 224 and reduce the original linear multidimensional problem to a non-linear problem with a feasible number of dimensions described above, the present invention needs to solve the high dimensional conditional extremum problem with a large number of restrictions. The present invention uses the Lagrange multiplier technique to take into account only the main restrictions. They can be of an equality or inequality type. This low-dimensional nonlinear problem is solved by a gradient type iterative process.

At each iterative step, the optimization of ANPV.(L, r„ p,) under customer-level restrictions (high dimensional linear problem) is made directly, record by record. It is equivalent to the following min-max problem:

Min,{Lb>o,Lc}

Figure imgf000008_0001
ANPV(L, r„ p.) , where ANPV(L, r„ Pl) = ANPV(L, r„ p,)0 + L„ Gb( A, R, P) + Lc Gc( A, R, P)

Here, summation over all the inequalities is assumed.

The algorithm, as shown in figure 4, consists of following steps:

1. Prepare data 41.

2. Calculate initial value of the functional and gradients 42.

3. Set a value for initial algorithm steps 43; for each Lagrange multiplier, the step should be set equal to the initial value of the functional divided by the square of the gradient.

4. Make a step along the gradient 44.

5. Update the step 45, if needed.

6. Calculate new value of the functional 46, taking customer level restrictions into account.

7. Check convergence 47.

8. If not converged at 48, go to step 4.

9. Output the results 49 upon adequate convergence.

It is important to underscore that the above algorithm is not a heuristic, but delivers a strict mathematical solution for the multidimensional optimization problem formulated above. Tests performed by inventors on a variety of real business cases show that the iterative procedure in Step 4 above typically converges with the tolerance of 0.1% in less then 30 iterations. That allows a user to work with the cross-selling optimizer of the present invention interactively and perform real-time analysis of the financial outcome of marketing activities.

A novel feature of the algorithm used by the present invention, the one-pass scoring, enables rollout scoring of a 100M record database overnight.

The present invention operates on a computer system and is used for targeted marketing purposes. Using the present invention in conjunction with a neural network, the present invention provides a user with data indicating the individuals or classes or individuals who are most likely to respond to direct marketing.

Claims

We Claim:
1. A method for optimizing a cross-selling marketing campaign, comprising: randomly selecting a statistically significant sample of a prospect list; calculating a value of a utility function for each pair of an offer and selected prospects; reducing an original linear multidimensional problem of optimizing said utility function to a non-linear problem with a feasible number of dimensions; solving said non-linear problem for the selected sample numerically with a desired tolerance using an iterative algorithm to produce results; and using said results to calculate an optimal set of offers in one pass for said prospect list.
2. The method for optimizing a cross-selling marketing campaign of claim 1 , wherein said utility function is a net present value (NPV).
3. The method for optimizing a cross-selling marketing campaign of claim 2, wherein said NPV is a linear function of at least a solicitation, response, and profitability.
4. The method for optimizing a cross-selling marketing campaign of claim 3, wherein customer level constraints of eligibility conditions, peer group logic, and maximal number of offers per customer can be expressed by a set of inequalities Clk CΛ( A) <= 0, i = l, 2, ..., N, k = 1, 2, ..., K where C, are linear functions, N is of the order of number of customers in the prospect list, and K is number of restrictions.
5. The method for optimizing a cross-selling marketing campaign of claim 4, wherein campaign level constraints of economic goals are expressed by a set of inequalities G for each promotion and the whole campaign:
G.,( A, R, P) <= 0, j = l, 2, ..., M, 1 = 1, 2, ..., L.
GOJ( A, R, P) <= 0, 1 = 1, 2, ..., L0 where G. are linear functions, M is of the order of number of promotions in the campaign, L. is total number of restrictions, and G is a sum over all eligible customers.
6. The method for optimizing a cross-selling marketing campaign of claim 5, wherein said results are a solicitation matrix A that maximizes NPV(A,*) under a condition that all constraints C and G are satisfied.
7. The method for optimizing a cross-selling marketing campaign of claim 6, wherein said solicitation matrix A is determined by letting A=(a1J), where a,j = 1, if offer j goes to a customer i
= 0, otherwise; R = (r,.) , be a response matrix, where ry - is a probability for a customer i respond to a promotion j; P = (py), be a profitability matrix, where p,j — is a profitability of a customer i, if he/she responds to a promotion j; and a total NPV of the campaign, NPV = NPV( A, R, P), is a linear function of a,., ry,
P.r
8. The method for optimizing a cross-selling marketing campaign of claim 7, wherein an optimization engine calculates the vector of parameters L of the ANPV (adjusted
NPV) functions ANPV.(L, r„ p,), where j = the number of promotions; r, = (r ) - vector of propensities to respond of a customer i to promotions 1, 2, ...j; and p. = (py) - vector of profitability of a customer i for promotions 1, 2, ...j.
9. The method for optimizing a cross-selling marketing campaign of claim 8, wherein the optimal solicitation matrix is calculated in a single pass through the prospect list by: reading in customer record i; calculating vectors r, and p, ; calculating anp v, = ANPV.(L, r„ p,); using values of anpvt and eligibility conditions to calculate solicitation vector a, = ( a,. ), which defines the optimal set of promotions that goes to a customer i; and repeating the previous four steps until reaching the end of the prospect list.
10. The method for optimizing a cross-selling marketing campaign of claim 9, wherein r„ p, are calculated and the linear multi-dimensional problem of optimizing said utility function is reduced to a non-linear problem with a feasible number of dimensions by using a Lagrange multiplier technique to take into account only main restrictions to produce a low-dimensional non-linear problem by a gradient-type iterative process comprising: making directly, at each iterative step, an optimization of ANPV.(L, r„ p,) under customer-level restrictions equivalent to the following min-max problem:
Min,{Lb>0)Lc} Max.{C<=0) ANPV(L, r„ p.) , where ANPV(L, r„ p.) = ANPV(L, r„ p,)0 + L, Gb( A, R, P) + Lc Gc( A, R, P) and iteratively solving this by: calculating an initial value of the functional and gradients; setting a value for initial algorithm steps, wherein for each Lagrange multiplier, the step is set equal to the initial value of the functional divided by the square of the gradient; making a step along the gradient; updating the step if needed; calculating a new value of the functional taking customer level restrictions into account; checking for convergence; making another step along the gradient if not converged; and outputting results upon convergence.
PCT/US2000/021453 1999-08-06 2000-08-05 Method for optimizing net present value of a cross-selling marketing campaign WO2001011522A2 (en)

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US7634431B2 (en) 2006-03-08 2009-12-15 Sas Institute Inc. Systems and methods for costing reciprocal relationships
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US7499868B2 (en) 1999-08-06 2009-03-03 Marketswitch Corporation Method for optimizing net present value of a cross-selling marketing campaign
US6993493B1 (en) * 1999-08-06 2006-01-31 Marketswitch Corporation Method for optimizing net present value of a cross-selling marketing campaign
US8015045B2 (en) 1999-08-06 2011-09-06 Experian Information Solutions, Inc. Method for optimizing net present value of a cross-selling marketing campaign
US8285577B1 (en) 1999-08-06 2012-10-09 Experian Information Solutions, Inc. Method for optimizing net present value of a cross-selling marketing campaign
US7904327B2 (en) 2002-04-30 2011-03-08 Sas Institute Inc. Marketing optimization system
US8065262B2 (en) 2003-10-17 2011-11-22 Sas Institute Inc. Computer-implemented multidimensional database processing method and system
US7689528B2 (en) 2004-07-09 2010-03-30 Fair Isaac Corporation Method and apparatus for a scalable algorithm for decision optimization
US8732004B1 (en) 2004-09-22 2014-05-20 Experian Information Solutions, Inc. Automated analysis of data to generate prospect notifications based on trigger events
US7624054B2 (en) 2005-08-25 2009-11-24 Sas Institute Inc. Financial risk mitigation optimization systems and methods
US7634431B2 (en) 2006-03-08 2009-12-15 Sas Institute Inc. Systems and methods for costing reciprocal relationships
US7813948B2 (en) 2006-08-25 2010-10-12 Sas Institute Inc. Computer-implemented systems and methods for reducing cost flow models
US10121194B1 (en) 2006-10-05 2018-11-06 Experian Information Solutions, Inc. System and method for generating a finance attribute from tradeline data
US8027871B2 (en) 2006-11-03 2011-09-27 Experian Marketing Solutions, Inc. Systems and methods for scoring sales leads
US9508092B1 (en) 2007-01-31 2016-11-29 Experian Information Solutions, Inc. Systems and methods for providing a direct marketing campaign planning environment
US9916596B1 (en) 2007-01-31 2018-03-13 Experian Information Solutions, Inc. Systems and methods for providing a direct marketing campaign planning environment
US10078868B1 (en) 2007-01-31 2018-09-18 Experian Information Solutions, Inc. System and method for providing an aggregation tool
US8024241B2 (en) 2007-07-13 2011-09-20 Sas Institute Inc. Computer-implemented systems and methods for cost flow analysis
US7996331B1 (en) 2007-08-31 2011-08-09 Sas Institute Inc. Computer-implemented systems and methods for performing pricing analysis
US8050959B1 (en) 2007-10-09 2011-11-01 Sas Institute Inc. System and method for modeling consortium data
US7930200B1 (en) 2007-11-02 2011-04-19 Sas Institute Inc. Computer-implemented systems and methods for cross-price analysis
US8533322B2 (en) 2007-11-19 2013-09-10 Experian Marketing Solutions, Inc. Service for associating network users with profiles
US9058340B1 (en) 2007-11-19 2015-06-16 Experian Marketing Solutions, Inc. Service for associating network users with profiles
US8200518B2 (en) 2008-02-25 2012-06-12 Sas Institute Inc. Computer-implemented systems and methods for partial contribution computation in ABC/M models
US8296182B2 (en) 2008-08-20 2012-10-23 Sas Institute Inc. Computer-implemented marketing optimization systems and methods
US9152727B1 (en) 2010-08-23 2015-10-06 Experian Marketing Solutions, Inc. Systems and methods for processing consumer information for targeted marketing applications
US10255598B1 (en) 2012-12-06 2019-04-09 Consumerinfo.Com, Inc. Credit card account data extraction
US10102536B1 (en) 2013-11-15 2018-10-16 Experian Information Solutions, Inc. Micro-geographic aggregation system
US10262362B1 (en) 2014-02-14 2019-04-16 Experian Information Solutions, Inc. Automatic generation of code for attributes
US10019508B1 (en) 2014-05-07 2018-07-10 Consumerinfo.Com, Inc. Keeping up with the joneses
US10242019B1 (en) 2014-12-19 2019-03-26 Experian Information Solutions, Inc. User behavior segmentation using latent topic detection
US9767309B1 (en) 2015-11-23 2017-09-19 Experian Information Solutions, Inc. Access control system for implementing access restrictions of regulated database records while identifying and providing indicators of regulated database records matching validation criteria
US10019593B1 (en) 2015-11-23 2018-07-10 Experian Information Solutions, Inc. Access control system for implementing access restrictions of regulated database records while identifying and providing indicators of regulated database records matching validation criteria

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AU769761B2 (en) 2004-02-05
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CA2381349A1 (en) 2001-02-15
WO2001011522A8 (en) 2001-12-27

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