## Mathematical Optimisation In Five Phases

For businesses wishing to improve their credit decisions, the adoption of Mathematical Optimisation is an important consideration. Mathematical optimisation is more than a straight data-driven strategy design as it incorporates prescriptive analytics.

## What is Mathematical Optimisation?

Mathematical optimisation broadly consists of three features: 1) The main objective is to minimise or maximise the outcome of a function by 2) exploring different values for a collection of variables within the function 3) in an environment with specific constraints. In other words, mathematical optimisation will enable you to identify what you need to change to get the best outcome for a specific scenario.

Read more about what mathematical optimisation is, examples and impact it can have on your business in these blogs “What Is Mathematical Optimisation And How Does It Benefit Business?“ and “Everything You Ever Wanted To Know About Mathematical Optimisation”.

We will now explore the 5 key phases of building an optimisation strategy.

### 1.      Objective and constraints

• Brief explanation: Define a clear objective/goal. Identify constraints and factors that can influence your objective. The objective/goal then needs to be translated into a formula, which will consist of the components identified, often called the decision model. All possible constraints should also be listed; which include business rules, policy/government regulation, data, implementation, software etc.
• Example: You want to optimise profit by assigning the best credit limit to an account. Maximising profit will be the objective, with different limits as actions and the components that form part of the decision model will typically include risk, spend and interest for example. Constraints in this scenario might be a policy bad rate limit, a fixed credit appetite amount that can’t be exceeded or maximum limits per account etc.
• Dependencies: Skills and experience. You need a team that knows the business and has a good understanding of the environment to assess the requirements; which include defining the objectives, listing the constraints, identify the data required.
• Your problem has more than one possible action.
• You have the skills and resources to define the objective, identify the constraints to your objective and how it will affect possible actions, as well as the capability to build and execute the optimisation strategy.
• You have sufficient data available (objective and performance points), this depends on the objective but usually at least 12-24 months performance for each observation group is required (where the observation groups need to represent the population).
• Data is available on account-level, and the decision model can be applied on account-level.
• The key components of the decision model can be modelled (the effect of different actions can be modelled).
• You have data-driven strategies in place and have performed tests in the past to obtain different actions for the same groups of people. You will be able to ascertain the sensitivity of your customer on certain actions (interactions between customer behaviour and reactions to treatments).
• You’re aware of all restrictions for implementing the strategy.

### 2.      Component models

• Brief explanation: These are the components in the decision model; it is data-driven predictive models, usually split between sensitive and insensitive models. You will thus create action-effect models to determine the effect an action will have on key components in the decision model. You can conduct inference about the magnitude of the differences in actions across subsets of the population and apply cross-validation to determine the predictive power.
• Examples: Predicting bad debt, sales and interest on a credit limit for different limit scenarios.
• Dependencies: Data quality, skills & resources. There needs to be sufficient data to design data-driven predictive models, skills and resources to develop the models.
• You have the necessary skills and modelling software,
• You can predict component models based on actions,
• Accuracy of component models are acceptable,
• You can cater to the sensitivity of the relationship between characteristics and actions.

### 3.      Optimisation

• Brief explanation: After the component models are developed, the sensitivity of the relationship between characteristics and actions will be catered for, and optimisation can be done by the interaction of the different models in a cohesive mathematical framework. Different scenarios can be applied, and the trade-off between decisions can be determined and quantified. An efficient frontier will be created to decide which strategy should be produced and implemented (an efficient frontier is a set of optimal outcomes for a defined set of values of a specific attribute).
• Example: The trade-off between profit and risk can be explored in the efficient frontier as well as how certain constraints have an impact on the profit. In the graph below, for example, you can increase profit while maintaining the same risk when implementing the “new strategy”:

• Dependencies: Analytical skills and optimisation software.
• You have suitable software for optimisation.
• The trade-off between different decisions can be quantified.
• The chosen new strategies can be deployed and tracked appropriately in the current environment.

### 4.      Deployment

• Brief explanation: Depending on the business environment, the strategies can be deployed either on an individual level or a segmented/tree-based level. The segmented level approach is more simplistic and easier to deploy, but it requires customers to be grouped which reduces the effectiveness of the action, and it takes significant time to develop a tree-based strategy from the individual level strategy.
• Dependencies: Deployment software
• You have strategy deployment software.
• You’re able to deploy a complex strategy utilising either decision trees, scorecards or other calculations.
• You’re able to run a randomised champion/challenger testing within the environment.

### 5.      Tracking

• Brief explanation: Tracking the optimisation strategy against the hold-out sample to calculate the true quantifiable impact of the strategy.
• Dependencies: Skills, data and software. The new strategy and hold-out sample (old/current strategy for comparison) need to be implemented properly with no bias; the data needs to be stored and tracked against the predefined KPI’s.