## Everything You Ever Wanted To Know About Mathematical Optimisation

Today we explore some of the frequently asked questions around mathematical optimisation.  For the most part, the questions are answered in the context of credit risk.  However mathematical optimisation and operations research, in general, have many applications.

## What exactly is “Optimisation”?

“Optimisation” is an advanced mathematical technique used to find certain best values to improve a business problem.  It is used in various industries to solve a variety of business challenges.  In credit, visionary lenders are adopting optimisation to make better credit decisions.

### In the credit space it has been used for (amongst other things):

• setting optimal loan amounts to offer (term credit products)
• deposit amounts to request (secured lending)
• credit limits and overdrafts to set (revolving)
• credit limit decreases and limit increase offers (revolving)
• authorisation strategies (revolving)
• pricing of loans
• customised discounts to offer (cards and retail)
• vouchers to offer (retail marketing)
• calculating collection settlement amounts

For example, we may need to find the best individual credit limits to offer each of our customers. The goal will be to boost the profitability of the business while reducing bad debt, adhering to lending legislation, reducing attrition, increasing spend and not over-indebting customers to the point where they can’t pay.  Essentially Optimisation is a big mathematics problem.

## How is this different from using a scorecard?

Scorecard strategies tend to be a lot less complex than Optimisation. The following table gives the decisioning evolution of organisations from traditionalists to visionaries.

Optimisation typically uses a variety of models with the strategy design – this may include multiple scorecards, affordability models, action-effect models, local constraints (e.g. credit limits cannot exceed \$25,000), and global constraint conditions (e.g. the sum of all limit increases must be less than \$100,000,000).

Traditionally, scorecards and analytical strategy design tools use historic data to predict likely behaviour, but inherently assume the observations will be treated as it were in the past. Optimisation analyses all the potential relationships that exist between the profile characteristics and the potential terms of business (strategy treatments) in order to build an optimised strategy that maximises the business objective (e.g. profit) within the client’s portfolio constraints. Action effect modelling is used to determine the impact of decisions at an account level.

## What type of business problems can optimisation solve?

Optimisation has been proven to provide significant lift when applied throughout the credit lifecycle. At any point where a decision is taken, optimisation can assist in making the best decision.

The scope for optimisation within non-traditional “non-credit” areas is very wide. Optimisation can also contribute significantly to making operational processes more efficient. Some industries and applications are noted below:

• Logistics – finding the optimal flying/shipping routes for passengers, freight
• Machine processing – e.g. optimise the use of machines (e.g. printers, generators), to schedule maintenance, and to improve output
• Working schedules – used in factories, call-centres and hospitals, for example
• Viability models – determining viability models of mines, machines
• Pricing models – used in the airline industry to price tickets
• Floor planning – determining the optimal floor plan in a factory, parking lot, office space

## How do I know if my business is ready for optimisation?

The readiness for optimisation in a business area comes down to a variety of key factors.

• The availability of rich data (in credit this would be a minimum of one year’s worth of account-level data)
• Preferably a history of using models to make decisions
• Pull-and-push: a business area that needs to push one/many thing(s) while restricting another/others (e.g. grow sales while restricting bad debt)
• A team that is in agreement on what the constraints are (for example what is the maximum bad-debt acceptable for the company, what is the maximum limit amount allowed, what is the total capital available for lending over the next year)
• A single driver for the problem (usually profit)
• A minimum of one year’s account-level data
• The ability to implement an automated and optimised decision strategy (for example through Principa’s DecisionSmart)
• The ability to run randomised tests (champion/challenger)
• Requires an organisational commitment to implement a test, if successful

## What sort of results have Principa witnessed after the implementation of an optimisation  strategy in the credit space?

A recent optimisation challenger strategy increased revenue by 15% and reduced delinquency by 10% (actual ROI of above 7).

• Another Principa Optimisation challenger developed in account management has increased profit per up to date account by 4% and reduced delinquency by 5% (ROI of 13.7)
• A Principa Optimisation challenger developed for new business limit setting has increased profit by 10% and reduced delinquency by 3%

## What is needed to implement an optimisation strategy?

A few things need to be in place in order for an optimisation strategy to be feasible.  If not possible then “principals of optimisation” could also be adopted.

1. Sufficient data – the organisation will need rich data and a sufficient number of accounts on which to model.
2. A clear objective – what are you looking to achieve? Maximise profit, minimise risk, minimise the number of staff are all examples of popular optimisation problems in this space. Furthermore, the limitations and constraints of the business should be understood (e.g. it is bank policy not to breech a bad rate of 15%, there is only a maximum of \$10,000,000 allocated for credit limit allocations, each account may have a maximum credit limit of \$10,000, customer cannot breach government prescribed affordability/debt-burden-ratio thresholds).
3. Analytics – the organisation/vendor will need to be able to build a variety of data-driven models. The organisation will also need to be able to model the optimisation problem utilising suitable software.  Examples of this software include FICO’s Model Builder and Decision Optimizer, SAS, and R.
4. Deployment – the organisation will need to be able to deploy a strategy in their environment using their own (or a vendor’s) business rules management system. The system should be able to deploy complex strategies utilising decision trees, scorecards and calculations.  It should also be able to run a randomised champion/challenger testing within the environment.  If a complex decisioning environment already exists (e.g. with multiple tests running for other purposes) it should be assessed whether an optimisation strategy can be deployed without upsetting the other tests.
5. Monitoring – the organisation will need to be able to monitor the optimisation strategy to determine how well it is doing when compared to the hold-out sample.

Do you have a business problem that you think Mathematical Optimisation might be able to solve, then why not contact us to see how Principa might help?