974 KiB
Promoting financial products to bank customers¶
In 2016, a retail bank sold several products (mortgage account, savings account, and pension account) to its customers. It kept a record of all historical data, and this data is available for analysis and reuse. Following a merger in 2017, the bank has new customers and wants to start some marketing campaigns.
The budget for the campaigns is limited. The bank wants to contact a customer and propose only one product.
The marketing department needs to decide:
- Who should be contacted?
- Which product should be proposed? Proposing too many products is counter productive, so only one product per customer contact.
- How will a customer be contacted? There are different ways, with different costs and efficiency.
- How can they optimally use the limited budget?
- Will such campaigns be profitable?
Predictive and prescriptive workflow¶
From the historical data, we can train a machine learning product-based classifier on customer profile (age, income, account level, ...) to predict whether a customer would subscribe to a mortgage, savings, or pension account.
- We can apply this predictive model to the new customers data to predict for each new customer what they will buy.
- On this new data, we decide which offers are proposed. Which product is offered to which customer through which channel:
- a. with a greedy algorithm that reproduces what a human being would do
- b. using an optimization model wih IBM Decision Optimization.
- The solutions can be displayed, compared, and analyzed.
Table of contents:
This notebook requires a mathematical background.
If you're new to optimization, following the online free Decision Optimization tutorials (here and here) might help you get a better understanding of Mathematical Optimization.
This notebook is part of Prescriptive Analytics for Python
It requires either an installation of CPLEX Optimizers or it can be run on IBM Watson Studio Cloud (Sign up for a free IBM Cloud account and you can start using Watson Studio Cloud right away).
The purpose of this Notebook is not to provide a perfect machine learning model nor a perfect optimization model. The purpose is to show how easy it is to mix machine learning and CPLEX data transformations by doing a forecast, then getting fast and reliable decisions on this new data.
This notebook takes some time to run because multiple optimization models are solved and compared in the part dedicated to what-if analysis. The time it takes depends on your subscription type, which determines what optimization service configuration is used.
How decision optimization can help¶
Prescriptive analytics (decision optimization) technology recommends actions that are based on desired outcomes. It takes into account specific scenarios, resources, and knowledge of past and current events. With this insight, your organization can make better decisions and have greater control of business outcomes.
Prescriptive analytics is the next step on the path to insight-based actions. It creates value through synergy with predictive analytics, which analyzes data to predict future outcomes.
Prescriptive analytics takes that prediction to the next level by suggesting the optimal way to handle that future situation. Organizations gain a strong competitive advantage by acting quickly in dynamic conditions and making superior decisions in uncertain environments.
With prescriptive analytics, you can:
- Automate complex decisions and trade-offs to better manage your limited resources.
- Take advantage of a future opportunity or mitigate a future risk.
- Proactively update recommendations based on changing events.
- Meet operational goals, increase customer loyalty, prevent threats and fraud, and optimize business processes.
import pandas as pd
import matplotlib.pyplot as plt
from matplotlib.colors import ListedColormap
%matplotlib inline
known_behaviors = pd.read_csv("https://raw.githubusercontent.com/vberaudi/utwt/master/known_behaviors2.csv")
known_behaviors.head()
Check the 2016 customers¶
a = known_behaviors[known_behaviors.Mortgage == 1]
b = known_behaviors[known_behaviors.Pension == 1]
c = known_behaviors[known_behaviors.Savings == 1]
print("Number of clients: %d" %len(known_behaviors))
print("Number of clients predicted to buy mortgage accounts: %d" %len(a))
print("Number of clients predicted to buy pension accounts: %d" %len(b))
print("Number of clients predicted to buy savings accounts: %d" %len(c))
known_behaviors["nb_products"] = known_behaviors.Mortgage + known_behaviors.Pension + known_behaviors.Savings
abc = known_behaviors[known_behaviors.nb_products > 1]
print("We have %d clients who bought several products" %len(abc))
abc = known_behaviors[known_behaviors.nb_products == 3]
print("We have %d clients who bought all the products" %len(abc))
products = ["Savings", "Mortgage", "Pension"]
Do some visual analysis of the historical data¶
It's possible to use pandas plotting capabilities, but it would require a new version of it. This Notebook relies on matplotlib as it is present everywhere.
def plot_cloud_points(df):
figure = plt.figure(figsize=(20, 5))
my_cm = ListedColormap(['#bb0000', '#00FF00'])
axes = {p : ('age', 'income') if p != "Mortgage"else ('members_in_household', 'loan_accounts') for p in products}
for product in products:
ax = plt.subplot(1, len(products), products.index(product)+1)
ax.set_title(product)
axe = axes[product]
plt.xlabel(axe[0])
plt.ylabel(axe[1])
ax.scatter(df[axe[0]], df[axe[1]], c=df[product], cmap=my_cm, alpha=0.5)
In the following visualization, you can see the behavior of the 2016 customers for the three products. The green color indicates that a customer bought a product; red indicates a customer did not buy a product. The depth of the color indicates the number of purchases or non-purchases.
plot_cloud_points(known_behaviors)
Understanding the 2016 customers¶
We can see that:
- The greater a customer's income, the more likely it is s/he will buy a savings account.
- The older a customer is, the more likely it is s/he will buy a pension account.
- There is a correlation between the number of people in a customer's household, the number of loan accounts held by the customer, and the likelihood a customer buys a mortgage account. To see the correlation, look at the upper right and lower left corners of the mortgage chart.
known_behaviors.columns
Let's use the following columns as machine-learning features:
cols = ['age', 'income', 'members_in_household', 'loan_accounts']
X = known_behaviors[cols]
ys = [known_behaviors[p] for p in products]
X.head()
We use a standard basic support gradient boosting algorithm to predict whether a customer might by product A, B, or C.
from sklearn import svm
from sklearn import ensemble
classifiers = []
for i,p in enumerate(products):
clf = ensemble.GradientBoostingClassifier()
clf.fit(X, ys[i])
classifiers.append(clf)
unknown_behaviors = pd.read_csv("https://raw.githubusercontent.com/vberaudi/utwt/master/unknown_behaviors.csv")
for c in unknown_behaviors.columns:
assert c in known_behaviors.columns
to_predict = unknown_behaviors[cols]
print("Number of new customers: %d" %len(unknown_behaviors))
Predict behaviors of the new customers¶
import warnings
warnings.filterwarnings('ignore')
predicted = [classifiers[i].predict(to_predict) for i in range(len(products))]
for i,p in enumerate(products):
to_predict[p] = predicted[i]
to_predict["id"] = unknown_behaviors["customer_id"]
Package new data with predictions for optimization¶
offers = to_predict
offers.head()
Do some visual analysis of the predicted data¶
plot_cloud_points(offers)
The predicted data has the same semantic as the base data, with even more clear frontiers:
- for savings, there is a clear frontier at $50K revenue.
- for pension, there is a clear frontier at 55 years old customers.
The training data contains customers who bought more than one product, let's see our prediction
a = offers[offers.Mortgage == 1]
b = offers[offers.Pension == 1]
c = offers[offers.Savings == 1]
print("Number of new customers: %d" %len(offers))
print("Number of customers predicted to buy mortgages: %d" %len(a))
print("Number of customers predicted to buy pensions: %d" %len(b))
print("Number of customers predicted to buy savings: %d" %len(c))
to_predict["nb_products"] = to_predict.Mortgage + to_predict.Pension + to_predict.Savings
abc = to_predict[to_predict.nb_products > 1]
print("We predicted that %d clients would buy more than one product" %len(abc))
abc = to_predict[to_predict.nb_products == 3]
print("We predicted that %d clients would buy all three products" %len(abc))
Remarks on the prediction¶
The goal is to contact the customers to sell them only one product, so we cannot select all of them.
This increases the complexity of the problem: we need to determine the best contact channel, but also need to select which product will be sold to a given customer.
It may be hard to compute this. In order to check, we will use two techniques:
- a greedy algorithm
- CPLEX, the IBM leading optimization solver.
offers.reset_index(inplace=True)
Get business decisions on the 2017 data¶
Assign campaigns to customers¶
- We have predicted who will buy what in the list of new customers.
- However, we do not have the budget to contact all of them. We have various contact channels with different costs and effectiveness.
- Furthermore, if we contact somebody, we don't want to frustrate them by proposing multiple products; we want to propose only one product per customer.
Some input data for optimization¶
# How much revenue is earned when selling each product
productValue = [200, 300, 400]
value_per_product = {products[i] : productValue[i] for i in range(len(products))}
# Total available budget
availableBudget = 25000
# For each channel, cost of making a marketing action and success factor
channels = pd.DataFrame(data=[("gift", 20.0, 0.20),
("newsletter", 15.0, 0.05),
("seminar", 23.0, 0.30)], columns=["name", "cost", "factor"])
offersR = range(0, len(offers))
productsR = range(0, len(products))
channelsR = range(0, len(channels))
Using a greedy algorithm¶
- We create a custom algorithm that ensures 10% of offers are made per channel by choosing the most promising per channel. The algorithm then continues to add offers until the budget is reached.
gsol = pd.DataFrame()
gsol['id'] = offers['id']
budget = 0
revenue = 0
for product in products:
gsol[product] = 0
noffers = len(offers)
# ensure the 10% per channel by choosing the most promising per channel
for c in channelsR: #, channel in channels.iterrows():
i = 0;
while (i< ( noffers // 10 ) ):
# find a possible offer in this channel for a customer not yet done
added = False
for o in offersR:
already = False
for product in products:
if gsol.get_value(index=o, col=product) == 1:
already = True
break
if already:
continue
possible = False
possibleProduct = None
for product in products:
if offers.get_value(index=o, col=product) == 1:
possible = True
possibleProduct = product
break
if not possible:
continue
#print "Assigning customer ", offers.get_value(index=o, col="id"), " with product ", product, " and channel ", channel['name']
gsol.set_value(index=o, col=possibleProduct, value=1)
i = i+1
added = True
budget = budget + channels.get_value(index=c, col="cost")
revenue = revenue + channels.get_value(index=c, col="factor")*value_per_product[product]
break
if not added:
print("NOT FEASIBLE")
break
# add more to complete budget
while (True):
added = False
for c, channel in channels.iterrows():
if (budget + channel.cost > availableBudget):
continue
# find a possible offer in this channel for a customer not yet done
for o in offersR:
already = False
for product in products:
if gsol.get_value(index=o, col=product) == 1:
already = True
break
if already:
continue
possible = False
possibleProduct = None
for product in products:
if offers.get_value(index=o, col=product) == 1:
possible = True
possibleProduct = product
break
if not possible:
continue
#print "Assigning customer ", offers.get_value(index=o, col="id"), " with product ", product, " and channel ", channel['name']
gsol.set_value(index=o, col=possibleProduct, value=1)
i = i+1
added = True
budget = budget + channel.cost
revenue = revenue + channel.factor*value_per_product[product]
break
if not added:
print("FINISH BUDGET")
break
print(gsol.head())
a = gsol[gsol.Mortgage == 1]
b = gsol[gsol.Pension == 1]
c = gsol[gsol.Savings == 1]
abc = gsol[(gsol.Mortgage == 1) | (gsol.Pension == 1) | (gsol.Savings == 1)]
print("Number of clients: %d" %len(abc))
print("Numbers of Mortgage offers: %d" %len(a))
print("Numbers of Pension offers: %d" %len(b))
print("Numbers of Savings offers: %d" %len(c))
print("Total Budget Spent: %d" %budget)
print("Total revenue: %d" %revenue)
comp1_df = pd.DataFrame(data=[["Greedy", revenue, len(abc), len(a), len(b), len(c), budget]], columns=["Algorithm","Revenue","Number of clients","Mortgage offers","Pension offers","Savings offers","Budget Spent"])
The greedy algorithm only gives a revenue of \$50.8K.
Using IBM Decision Optimization CPLEX Modeling for Python¶
Let's create the optimization model to select the best ways to contact customers and stay within the limited budget.
import sys
import docplex.mp
Set up the prescriptive model¶
There are two ways to solve the model:
- Subscribe to our private cloud offer or Decision Optimization on Cloud solve service here.
- Use a local solver, a licensed installation of CPLEX Optimization Studio. Note that this model is too big to solve using the Community Edition, so if url and key are None, the script will fail.
url = None
key = None
docplex solve methods take various arguments: you can pass the api and key at each function call or you can put them at model declaration with a context.
from docplex.mp.context import Context
context = Context.make_default_context()
context.solver.docloud.url = url
context.solver.docloud.key = key
context.solver.agent = 'docloud'
from docplex.mp.model import Model
mdl = Model(name="marketing_campaign", checker='on', context=context)
Define the decision variables¶
- The integer decision variables
channelVars, represent whether or not a customer will be made an offer for a particular product via a particular channel. - The integer decision variable
totaloffersrepresents the total number of offers made. - The continuous variable
budgetSpentrepresents the total cost of the offers made.
channelVars = mdl.binary_var_cube(offersR, productsR, channelsR)
Set up the constraints¶
- Offer only one product per customer.
- Compute the budget and set a maximum on it.
- Compute the number of offers to be made.
- Ensure at least 10% of offers are made via each channel.
# At most 1 product is offered to each customer
mdl.add_constraints( mdl.sum(channelVars[o,p,c] for p in productsR for c in channelsR) <=1
for o in offersR)
# Do not exceed the budget
mdl.add_constraint( mdl.sum(channelVars[o,p,c]*channels.get_value(index=c, col="cost")
for o in offersR
for p in productsR
for c in channelsR) <= availableBudget, "budget")
# At least 10% offers per channel
for c in channelsR:
mdl.add_constraint(mdl.sum(channelVars[o,p,c] for p in productsR for o in offersR) >= len(offers) // 10)
mdl.print_information()
Express the objective¶
We want to maximize expected revenue, so we take into account the predicted behavior of each customer for each product.
obj = 0
for c in channelsR:
for p in productsR:
product=products[p]
coef = channels.get_value(index=c, col="factor") * value_per_product[product]
obj += mdl.sum(channelVars[o,p,c] * coef* offers.get_value(index=o, col=product) for o in offersR)
mdl.maximize(obj)
Solve with the Decision Optimization solve service¶
mdl.parameters.timelimit = 30
s = mdl.solve()
assert s, "No Solution !!!"
print(mdl.get_solve_status())
print(mdl.get_solve_details())
Analyze the solution¶
totaloffers = mdl.sum(channelVars[o,p,c]
for o in offersR
for p in productsR
for c in channelsR)
mdl.add_kpi(totaloffers, "nb_offers")
budgetSpent = mdl.sum(channelVars[o,p,c]*channels.get_value(index=c, col="cost")
for o in offersR
for p in productsR
for c in channelsR)
mdl.add_kpi(budgetSpent, "budgetSpent")
for c in channelsR:
channel = channels.get_value(index=c, col="name")
kpi = mdl.sum(channelVars[o,p,c] for p in productsR for o in offersR)
mdl.add_kpi(kpi, channel)
for p in productsR:
product = products[p]
kpi = mdl.sum(channelVars[o,p,c] for c in channelsR for o in offersR)
mdl.add_kpi(kpi, product)
mdl.report()
comp2_df = pd.DataFrame(data=[["CPLEX", mdl.objective_value, mdl.kpi_value_by_name('nb_offers'), mdl.kpi_value_by_name('Mortgage'), mdl.kpi_value_by_name('Pension'), mdl.kpi_value_by_name('Savings'), mdl.kpi_value_by_name('budgetSpent')]], columns=["Algorithm","Revenue","Number of clients","Mortgage offers","Pension offers","Savings offers","Budget Spent"])
comp_df = comp1_df.append(comp2_df, ignore_index=True)
comp_df
comp_df.set_index("Algorithm", inplace=True)
my_plot = comp_df['Revenue'].plot(kind='bar')
With the mathematical optimization, we made a better selection of customers.
What if our budget is increased?¶
If our manager is prepared to increase the allocated budget, they might want to know whether the additional budget campaigns would bring more revenue.
#get the hand on the budget constraint
ct = mdl.get_constraint_by_name("budget")
The following cell takes a relatively long term to run because the jobs are run sequentially. The standard subscriptions to DOcplexcloud solve service only allow one job at a time, but you can buy special subscriptions with parallel solves. If you have such a subscription, modify the following cell to benefit from it.
res = []
for i in range(20):
ct.rhs = availableBudget+1000*i
s = mdl.solve()
assert s, "No Solution !!!"
res.append((availableBudget+1000*i, mdl.objective_value, mdl.kpi_value_by_name("nb_offers"), mdl.kpi_value_by_name("budgetSpent")))
mdl.report()
pd.DataFrame(res, columns=["budget", "revenue", "nb_offers", "budgetSpent"])
Due to the business constraints, we can address a maximum of 1680 customers with a \$35615 budget. Any funds available above that amount won't be spent. The expected revenue is \$87.1K.
Dealing with infeasibility¶
What about a context where we are in tight financial conditions, and our budget is very low? We need to determine the minimum amount of budget needed to adress 1/20 of our customers.
ct.rhs = 0
s = mdl.solve()
if not s:
#rename the constraint with a "low" prefix to automatically put a low priority on it.
ct.name = "low_budget"
#setting all bool vars to 0 is an easy relaxation, so let's refuse it and force to offer something to 1/3 of the clients
mdl.add_constraint(totaloffers >= len(offers)//20, ctname="high")
# solve has failed, we try relaxation, based on constraint names
# constraints are prioritized according to their names
# if a name contains "low", it has priority LOW
# if a ct name contains "medium" it has priority MEDIUM
# same for HIGH
# if a constraint has no name or does not match any, it is not relaxable.
from docplex.mp.relaxer import Relaxer
relaxer = Relaxer(prioritizer='match', verbose=True)
relaxed_sol = relaxer.relax(mdl)
relaxed_ok = relaxed_sol is not None
assert relaxed_ok, "relaxation failed"
relaxer.print_information()
mdl.report()
print(mdl.get_solve_status())
print(mdl.get_solve_details())
We need a minimum of 15950\$ to be able to start a marketing campaign. With this minimal budget, we will be able to adress 825 possible clients.
Conclusion¶
Algorithm comparison¶
Here are the results of the 2 algorithms:
| Algorithm | Revenue | Number of clients | Mortgage offers | Pension offers | Savings offers | Budget Spent |
|---|---|---|---|---|---|---|
| Greedy | 50800 | 1123 | 299 | 111 | 713 | 21700 |
| CPLEX | 72600 | 1218 | 381 | 117 | 691 | 25000 |
- As you can see, with Decision Optimization, we can safely do this marketing campaign to contact 1218 customers out of the 2756 customers.
- This will lead to a \$91.5K revenue, significantly greater than the \$49.5K revenue given by a greedy algorithm.
- With a greedy algorithm, we will:
- be unable to focus on the correct customers (it will select fewer of them),
- spend less of the available budget for a smaller revenue.
- focus on selling savings accounts that have the biggest revenue
Marketing campaign analysis¶
We need a minimum of \$16K to be able to start a valid campaign and we expect it will generate \$47.5K.
Due to the business constraints, we will be able to address 1680 customers maximum using a budget of \$36K. Any money above that amount won't be spent. The expected revenue is \$87K.
| Scenario | Budget | Revenue | Number of clients | Mortgage offers | Pension offers | Savings offers |
|---|---|---|---|---|---|---|
| Standard | 25000 | 72600 | 1218 | 381 | 117 | 691 |
| Minimum | 16000 | 47500 | 825 | 374 | 142 | 309 |
| Maximum | 35500 | 87000 | 1680 | 406 | 155 | 1119 |
Summary¶
This Notebook presented how to set up and use IBM Decision Optimization CPLEX Modeling for Python to formulate a Mathematical Programming model and solve it using IBM Decision Optimization on Cloud.
References¶
- CPLEX Modeling for Python documentation
- Decision Optimization on Cloud
- Need help with DOcplex or to report a bug? Please go here.
- Contact us at dofeedback@wwpdl.vnet.ibm.com.
Copyright © 2017 IBM. Sample Materials.