# Setting Optimal Prices with Portfolio-Level Rules

Price optimization involves managing the inevitable tradeoffs among price, profitability, and sales volume to set a price that maximizes revenue and profitability. Set a price too low to boost sales and your profitability can suffer; conversely, a too-high price can boost item profitability but reduce overall sales.

Analysts rely on economic models to estimate and predict the performance of business decisions – but these models vary based on industry type and pricing schemes. Each industry – for example, retail, financial services, or utilities – dictates a unique set of dependent variables (e.g., final sales volume), input variables (e.g., price), and market influences (e.g., macroeconomic forecasting). In addition, the use of nonlinear models – for example, calculating unit sales based on exponential terms of price and market indices such as treasury bills – creates complex equations that must be optimized efficiently to calculate an optimal price.

Within price optimization, an opportunity curve defines the set of scenarios that optimizes two conflicting key performance indicators (KPIs) – for example, profit and sales volume. Each scenario on the opportunity curve represents a different set of optimal prices in the portfolio of price segments, as well as a different pricing strategy. An increase in price would increase per-unit profit, but probably also reduce overall sales volume. To attract more customers, you might need to lower the price. But by how much?

That’s where the opportunity curve is most useful. It shows optimal KPI balance given constraints such as these:

- Cell-level rules: Minimum and maximum pricing bounds for each segment.
- Event-level movement rules: Overall movement boundaries for all price segments at event level when compared to current values. This helps temper price changes across time periods.
- Price segment-level movement rules (can be applied to other groups as well): Rules defined to limit price changes on a set of price segments, for example grandfathered accounts.
- Associated segment rules: Rules dictating linkages between price segments. For example, prices for customers with high credit scores should be better than prices for those with low credit scores.
- Associated variable rules: Rules that dictate linkages between multiple variables of a single price segment. For example, the introductory price of a price segment should be better than the final price.
- Portfolio-level rules: Event-level KPI-based rules – the focus of this article.

This article explains the impact of using portfolio-level rules (PLRs), which are event-level rules, optimized as one, that place overall restrictions on all price segments. With PLRs in place, we can no longer solve each price segment individually, but instead must focus on determining the optimal balance among multiple segments. Because PLRs impose a constraint on overall KPI, they increase the complexity of the underlying optimization problem. They also provide the ability to set rules at the event level based on a company’s long-term strategies. For example, a bank may wish to improve net interest income across all product types. Along with the two (possibly conflicting) KPIs selected for optimization of each event, it is possible to set bounds on other KPIs in order to meet the strategic goals of the organization. Portfolio-level rules are illustrated in the following examples:**Overall PLRs**In overall PLRs, customers set rules that restrict event-level KPI values.

- Primary KPIs: Volume <= constant, or Profit >= current profit
- Secondary KPIs: RAROC <= constant, or Net Interest Margin >= 2.3

No PLRs |
Overall PLR: Profit >= Current Profit |

The charts above show the effect of a simple overall rule ensuring that the current profit level is maintained throughout each optimization scenario.

Suppose the bank then defines a subset PLR. This selective rule requires the volume of a pricing segment (in this example, only the Relationship Money Markets) be greater than a specific value. When you overlay the new subset PLR opportunity curve on top of the original curve based on the high price elasticity and profitability of the Relationship Money Market segments, you find that a change in price affects only a part of the opportunity curve.

**Subset PLRs**

In subset PLRs, customers set rules on subsets of price segments.

- Volume (CDs, long-term > 3yrs) >= current volume (CDs, >3 yrs)
- Volume (high-risk, high-balance tier) <= constant

In contrast to business rules that create only bounds and linear constraints – cell rules and movement rules set bounds on optimization variables, while associated segment and associated variable rules create linear constraints on variables – PLRs’ addition of nonlinear constraints to an optimization model dramatically increases the complexity of the underlying optimization problems – and of the representative equations.

Model development services from SAP Performance and Insight Optimization help businesses accurately forecast demand for even the most complex financial services and retail pricing segments. The resulting models allow organizations to assess price sensitivity along with effects of cannibalization, seasonality, and competitor pricing on demand. And because they use a company’s actual business rules and strategies to determine an optimal price set, they help the organization improve overall financial performance.

For more information on SAP Services, please visit www.sap.com/services.