The Science of Pricing: How Smarter Algorithms Can Help Firms Price Multiple Products

Why It Matters

Companies often sell many products at once, from airline tickets and hotel rooms to online retail bundles. Setting the right price for each product is complex because customers compare options and respond differently to price changes.

Key Takeaways

• New algorithms can help firms better predict how customers choose between multiple products.
• Improved demand estimation allows companies to set more effective prices across product lines.
• The approach offers stronger mathematical guarantees, giving firms more reliable pricing insights.
  

The Challenge of Pricing Multiple Products

Pricing a single product is difficult enough. But most businesses must price many products simultaneously. Airlines, for example, sell tickets across different routes and seating classes. Online retailers offer hundreds or thousands of items that compete with one another for customer attention.

Customers rarely make decisions in isolation. Instead, they compare alternatives before deciding what to buy. Moreover, customers differ widely in their preferences, willingness to pay, and sensitivity to product attributes. If one product becomes more expensive, some customers may switch to a cheaper substitute, while others may remain loyal depending on their individual preferences. These heterogeneous substitution behaviours make it challenging for companies to predict demand and set optimal prices.

To tackle this problem, researchers often rely on models that estimate how consumers choose among products. One widely used framework is the mixed multinomial logit model, which captures how different customers value different product attributes. However, estimating these models accurately from data can be difficult, especially when firms manage many products and large datasets.

A New Way to Learn Customer Preferences

The study introduces a new algorithm that can learn these complex customer preferences more efficiently and reliably. Instead of relying on traditional estimation methods, the approach uses advanced statistical techniques to recover customer choice patterns from observed purchase data.

The key advantage lies in its ability to identify the underlying preference structure across different types of customers. In real markets, consumers rarely behave the same way, some prioritise price, others value quality or convenience. The algorithm separates these patterns and estimates how each group responds to changes in product attributes or prices.

Importantly, the researchers provide provable guarantees about the algorithm’s performance. This means the method comes with mathematical assurances about how accurately it can recover customer preferences under certain conditions. For companies relying on data-driven pricing strategies, such guarantees increase confidence in the results.

From Demand Estimation to Better Pricing

Once companies understand how customers choose between products, they can design more effective pricing strategies. The research shows how the new algorithm can be applied to multiproduct pricing, where firms optimise prices across several products simultaneously.

By improving demand estimation, the algorithm allows companies to anticipate these shifts more accurately. This leads to more informed pricing decisions that balance profitability with customer demand.

The research also demonstrates how the method performs well with large datasets and complex product offerings, conditions that increasingly characterise modern digital marketplaces.

Business Implications

For businesses operating in competitive markets, better pricing decisions can significantly improve revenue and profitability.

First, companies should invest in advanced data analytics that capture how customers compare products rather than viewing demand for each item separately.

Second, firms can use improved demand models to design coordinated pricing strategies across product portfolios. This approach is particularly relevant for sectors such as airlines, hospitality, e-commerce and subscription services.

Third, the research highlights the growing importance of data-driven pricing tools. As companies collect more detailed purchasing data, algorithms that can extract meaningful insights from this information will become essential for maintaining competitive advantage.

Ultimately, smarter pricing requires more than intuition. It requires tools that can uncover how customers truly make choices, and translate those insights into practical pricing strategies.

Authors and sources

Authors: Yiqun Hu (AWS AI Labs), Limeng Liu (Nanyang Technological University), David Simchi-Levi (Massachusetts Institute of Technology), Zhenzhen Yan (Nanyang Technological University)

Original article: Management Science

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