Business rules can be mathematically modeled (if and when known) and included in the optimization model as constraints, but those constraints could lead into infeasibility. For this reason, incorporating certain rules as a post-processing step will give businesses a better view of what can be achieved with predictive analytics. Therefore, a business rule framework should be designed to modify model recommendations in post-processing for business reasonable and implementable solution.
Using a constant elasticity model for demand as an example, the optimal price, which is a function of the marginal cost (c) and associated elasticity (r) of the segment is given by:
To estimate margin uplift, baseline margin is calculated first as the product of the baseline demand at baseline price and marginal cost as:
For the optimal price recommendation, the optimal margin M* is:
Therefore, the margin uplift is the optimal margin minus baseline margin:
Often, it is not practical for the business to embrace elasticity values and optimal price points as they are. The business may require rules such as specific price ending value, minimum and maximum price levels, price gap between segments at the same location, price gap between same segments in certain proximity, price position as compared to competition in the same geographic location, etc. Therefore, it is important to aggregate segment attributes and elasticity values to build a business rules matrix, where each combination will be assigned a price change.
Margin uplift calculation for each possible price point can determine the “implementable optimal” price for that segment. For segments at the same location (for instance, adult vs. child haircut at a salon) a rule dictating a maximum price difference allowed between two services could employ an enumeration approach for all feasible price point pairs to find the best combination.
The implementation of business rules may also require additional optimization/heuristic models. For example, if a business rule states that “the price variation between two locations with a certain proximity (in terms of distance) could at most be $x”, then the network optimization problem could have many location pairs within the specified distance. Each location in this network may have different price decrease/increase recommendations as per the business rules framework. Therefore, the “implementable optimal” price points have to be determined by using margin uplift calculation within an algorithm.
For a successful implementation of predictive analytics, the collaboration of business rules and science is the secret. Integrating business rules with mathematical optimality provides an edge over the competition.