Leveraging operations research to optimise the distribution of banking advisors

10 min readApr 21, 2022

Context

Retail banking physical networks are reducing their presence on the territory to cope with the drifting costs of their activity and the decline in customers’ visits to bank branches due to the digitalization of customer experience. Therefore, banking institutions must close their branches and pool spaces to accommodate different customers, especially those targeted at mass-market customers.

Furthermore, the banking relationships are undergoing a profound transformation: on the one hand, customers want to have digitized processes; on the other hand, they are seeking advice, particularly for the most critical moments in their lives (e.g., real estate purchases) or because their needs require expertise (e.g., tax exemption).

The location of branches, but most importantly of banking advisors, is thus a key stake for banks to capture customers with the highest potential and support them. We’ve observed this challenging context with many clients, raising our interest in applying modern numerical methods to help banking networks staff their branches better positioned for customer acquisition.

The use case developed here falls within the scope of a customer acquisition objective, aiming to optimize the presence of advisors in areas to be developed, and can be adapted to all types of customers. In our study, the customer base considered is limited to business customers with a turnover of fewer than 3 million euros. In this scope, we show that market exposure for the advisors can be increased by up to 60%!

Several approaches, from heuristic analysis based on business rules to AI-based methods, can be considered to tackle this kind of problem. However, from a mathematical point of view, the presented problem translates very well into a constrained resource allocation problem. This challenge is often solved using mixed-integer linear programming (MILP) methods. This respect aligns with the questions addressed by the Optiwise Operations Research (OR) laboratory of Sia Partners. MILP methods provide optimal solutions within reasonable computation times (due to the relatively low dimensionality of the use case considered). This does not apply to heuristic methods that do not guarantee the solution’s optimality.

Modeling

Decision variables and mapping of the state-space

Operations Research (OR) systems provide decision-making for the end-users. The first question that we need to ask ourselves is what kind of decision the algorithm will raise. In this case, the ambition is to relocate banking advisors. We illustrate the associated determination in the figure below. For each advisor and branch: “should advisor A be placed in branch B?”.

The output of the model will be an assignment matrix between advisors and branches. Once this is out of the way, the next question is: how to evaluate these decisions?

The model’s output will be an assignment matrix between advisors and branches. Once this is out of the way, the next question is: how do we evaluate these decisions?

Parameters — evaluating supply and demand

We’re evaluating the new business that an advisor can bring in when placed in different branches. Three main classes of parameters are needed:

Segmentation of the territory (i.e., catchment area for each branch)
Expected demand for banking advice
Usual supply by each advisor when placed in a branch

The parameters considered in our study are the following:

Location of the branch;
Number of advisors per branch;
Performance of each advisor;
Location of competitors;
Economic attractiveness of the area.

Location of the branches and expected demand for banking services (blue: low, red: high). Advisors should be placed in the branches in order to maximise the captured demand.

The data used to assess these parameters is two-fold:

“External” data, collected for the most part in open data, which allows quantifying the demand in the various areas under consideration;
“Internal” data, specific to the bank of interest, allows the available offer to be quantified. In this case, the internal data was generated with the help of business experts.

The quantification of the demand for a given area is obtained through various external indicators:

Demographic indicators, i.e., population density, number of inhabitants, and standard of living, were obtained via INSEE using a 200m by 200m grid covering the whole of France [1];
Macroeconomic factors, i.e., the rate of business creation per town obtained via the Observatoire des Territoires [2], the rate of business closures [3], and the unemployment rate [4] obtained at the departmental level via INSEE;
Competition indicators: the location of bank branches of the leading French banks obtained using our DeepReview product [5] as well as the CIC (Crédit Industriel et Commercial) [6] and data.gouv [7] websites;
Indicators characterizing the potential prospects of the bank branches: location and general information on the companies listed in the SIRENE register available via data.gouv [8].

The internal data is of two kinds:

Information relating to the branches of interest: location and minimum staff;
Information about the advisors to be placed: score, quota, actual presence in the branch, and branch of reference.

Setting up a cost function

The objective of the proposed model is to maximize the presence in areas with a high potential and/or to be developed for a corporate customer base with a turnover of fewer than 3 million euros. In other terms, an objective function related to the imbalance between supply and demand must be minimized.

The quantification of the different areas’ potential is carried out through a demand function which associates to each site a score calculated as the product of a potential score (which quantifies the attractiveness of the area), a target segment rate (which quantifies the interest for the bank) and a presence rate of the competition. Here we aim at matching this demand with an offer. The offer, here, depends on the distribution of the various advisors in the branches and is calculated as the sum of the presence rate of the advisors in these branches multiplied by their score (which depends on their commercial productivity and their potential).

The following diagram illustrates the global architecture of the tool:

Business Constraints

The scenarios for relocating advisors can be compared with the initial ones to select the most profitable cases for the bank. We carry out the maximization task in compliance with several constraints:

Each branch must keep a minimum number of staff for normal operations;
The relocation of advisors must not impact them by more than 30 km.

Build and run

The mathematical formalization of a linear programming problem consists of three elements:

The decision variables represent the quantities on which one can act and whose optimal values one seeks to determine;
The cost function, which is the quantity to be minimized;
The constraints are to be respected.

In our case, the decision variables are binary variables indicating whether an advisor should be located in a specific branch or not; the cost function is the sum over all areas of the gaps between the demand in an area and the offer that an advisors distribution generates in the said area. The constraints are the same as the ones aforementioned:

Each branch must keep a minimum number of staff for normal operations;
The relocation of advisors must not impact them by more than 30 km.

Once the problem has been appropriately defined, we apply a Mixed Integer Programming solving algorithm such as Branch & Bound to determine the optimal distribution. The combination of decision variables minimizes the cost function while satisfying the constraints.

The implementation of the modeling of the problem and its resolution was carried out in Python, using the pulp library amongst others, which allows to build the model in a few minutes (depending on the size) and solve it in under a minute.

Results

Examining the performance of the model

The decisions that the model aims to support are the reassignments (temporary or permanent) of the various specialized advisors to the sectors with the highest potential.

To measure the performance of the model, we monitor the following indicators:

The number of new customer contacts in total and by branch, sector, advisor, or customer category;
The equipment rate (i.e., the number of products or services subscribed to) per new client, branch, sector, or advisor;
Outstanding flows entrusted by customer (declarative), branch, sector, or advisor;
Average net banking income (NBI) per new customer, branch, sector, or advisor.

These indicators can be estimated either directly from the output of the decision by the model or require to be confronted to reality.

Results in the Paris Area

The model was tested on three French regions with different levels of urbanization, and resulted in performance improvements of up to 60%. We show below the results obtained for the Paris area. The first picture illustrates the initial distribution with a total of 34 advisors distributed in three main branches from the 49 considered:

In such a configuration, the gap between the total demand and offer in the sector reaches 78 points.

The picture below shows the optimal distribution found by our model:

Although many branches remain without advisors (predictable since there are more branches than advisors in our use case), most of them are allocated between one and three advisors, reducing the gap between the total demand and offering to 32 points, i.e., improving the performance by almost 60%.

Conclusion

This article illustrates how we leverage Operations Research to efficiently allocate advisors to a set of branches mapping the territory. We focused on an illustration using a French bank. This approach can easily be generalized to various sectors, and several alternative methods exist and have been experimented with by Sia Partners’ OR lab.

Beyond optimizing the distribution of a bank’s advisors in its branches by reducing the gap between the demand and the offer in each area, the solution we developed can be a real game-changer in the retail banking industry and generate value in various ways:

By improving the quality of the bank’s offer, each advisor’s specific set of skills and matching it with customers’ needs. This enables better customer satisfaction thanks to more appropriate banking advice depending on the population and improved geographic proximity;
By increasing the digitalization of the bank, integrating the model into one of Sia Partners’ optimization-oriented platforms and allowing banks to easily manage the advisors’ distribution, leading the way to banking 4.0.

The ways to make use of this tool are indeed two-fold:

In a short term fashion, it can be used to design high impact punctual operations and deploy, on a specific day or for a short period, the advisors into the optimal branches;
In a long-term fashion, it can be leveraged to achieve a fully automated and efficient distribution planner, one of the pillars of the bank of tomorrow and adequate response to retail banking’s transformation.

Going further

Coupling of OR algorithms

This use case is a first step in developing intelligent networks. In this case, we only considered fixed advisors. However, advisors must sometimes leave the branch to go and meet clients. In this context, this optimization module can be supplemented with a routing algorithm to design efficient driving patterns to maximize the advisors’ efficiency.

Alternate takes on supply and demand balancing

This use case is a simple occurrence of a vast category of problems aiming at balancing demand and offer. For example, Sia Partners has addressed such topics in very different contexts: optimal placement of EV charging stations, cyber-security, water production, etc. While the principle remains the same — minimization of the net imbalance — the MILP technique presented in the article isn’t always the safest bet:

The size of the problem is a big differentiator between use cases. More prominent use cases might be too much to handle for LP techniques and require meta-heuristics to reduce optimality. On the other hand, more minor instances or instances where many decisions have the same effect (e.g., EV charging) can provide good results from simple heuristics, reducing complexity at implementation and runtime
The need for a linear formulation can straight-out ban some use cases from LP approaches. In most cases, it is possible to find a way to linearize a problem, often at the cost of drifting from a fair model of reality. A careful examination of the tradeoff between efficiency gains and coherence must be undertaken.

References

Data sources:

[1] Demographic data: “Revenus, pauvreté et niveau de vie en 2015 — Données carroyées”, https://www.insee.fr/fr/statistiques/4176290?sommaire=4176305#consulter

[2] Rate of business creation per town: “Taux de création d’entreprises par secteurs d’activité”, https://www.observatoire-des-territoires.gouv.fr/taux-de-creation-dentreprises-par-secteurs-dactivite

[3] Rate of business closures: “Défaillances d’entreprises”, https://www.insee.fr/fr/statistiques/series/102773703

[4] Unemployment rate: “Taux de chômage localisés au 4ᵉ trimestre 2021”, https://www.insee.fr/fr/statistiques/2012804#tableau-TCRD_025_tab1_departements

[5] DeepReview, https://www.heka.ai/en/our-solutions/deep-review

[6] CIC branches: “Agences et distributeurs”, https://www.cic.fr/fr/banques/particuliers/agences-et-distributeurs/ExportPoiFormat.aspx

[7] Crédit Coopératif branches: “Centres d’affaires Crédit Coopératif”, https://www.data.gouv.fr/fr/datasets/centres-daffaires-credit-cooperatif/

[8] SIRENE register: “Base Sirene des entreprises et de leurs établissements (SIREN, SIRET)”, https://www.data.gouv.fr/fr/datasets/base-sirene-des-entreprises-et-de-leurs-etablissements-siren-siret/