Dynamic Pricing models: Types, algorithms, and best practices

What Are Dynamic Pricing Models? 

Dynamic pricing models are pricing strategies that allow businesses to adjust their prices in real-time based on current market conditions and demand. These models use algorithms and data to continuously monitor and analyze factors such as supply and demand, competitor prices, customer behavior, and external events to determine the optimal price for a product or service. 

The goal of dynamic pricing is to maximize profit by setting prices that are high enough to cover costs when demand is high and low enough to stimulate demand when it is low.

This is part of a series of articles about machine learning for business.

Benefits of Dynamic Pricing Models 

Dynamic pricing is gaining popularity as businesses look for a competitive edge to increase their profits and respond to competition. Dynamic pricing models offer several benefits to businesses:

• They can increase profitability by helping companies set prices that maximize revenue and profits. By analyzing market demand and competitors’ prices in real-time, businesses can set prices that are high enough to make a profit, but low enough to remain competitive.
• Dynamic pricing models can drive sales increases. By adjusting prices in response to changes in market demand, businesses can attract more customers and increase sales. For example, during peak periods when demand is high, prices can be raised to reflect this, while during slow periods prices can be lowered to boost sales. They can improve customer satisfaction by providing consumers with prices that are more in line with their perceived value of a product or service. This can lead to increased customer loyalty and repeat business.
• Dynamic pricing allows businesses to respond to changes in the market quickly and effectively. For example, if a competitor lowers prices, businesses can respond by lowering their own prices to remain competitive.
• A dynamic pricing model can reduce costs. By automating pricing decisions, businesses can save time and resources that would otherwise be spent manually adjusting prices. This can free up resources that can be used to pursue other strategic initiatives.

Types of Dynamic Pricing 

Time-Based Pricing

Time-based dynamic pricing adjusts prices based on the time of day or the day of the week. This model takes into account the variation in demand for a product or service at different times and adjusts prices accordingly.

Some real-world examples of time-based dynamic pricing include:

• Airline tickets: Airlines often use dynamic pricing to adjust ticket prices based on the time of day, the day of the week, and the proximity to the departure date. Prices tend to be highest for flights during peak travel times (e.g., weekends, holidays) and lower for off-peak times.
• Hotel rooms: Hotels use time-based dynamic pricing to adjust room rates based on the time of day, the day of the week, and the proximity to the check-in date. Prices are typically higher for weekends and holidays and lower during the weekdays.
• Energy consumption: In the energy industry, dynamic pricing is used to adjust the price of electricity based on the time of day. Energy consumption is usually higher during the day, so prices are often higher during those hours. At night, when energy consumption is lower, prices are typically lower as well.

Segmented Pricing

Segmented pricing involves dividing a market into different segments and charging different prices to each segment based on their willingness to pay. This approach recognizes that different customers value a product or service differently and are willing to pay different prices.

Pricing differences may take into account location, demographics, and product versions.  For example, movie theaters use segmented pricing to target different customer segments based on age, time of day, and day of the week. They may offer discounted prices for children and senior citizens, while charging higher prices for adults during peak periods. Likewise, e-books are usually cheaper than physical paperback copies of books, which are cheaper than hardback editions.

Personalized Pricing 

Personalized pricing adjusts prices for each individual customer based on factors such as past purchases, demographic information, and location. For example, an online retailer may offer different prices for customers based on their purchase history and preferences. This type of pricing can be effective in retaining customers and increasing revenue.

Auction-Based Pricing 

Auction-based pricing determines prices through a bidding process. This model is commonly used in e-commerce and online auction sites. Buyers place bids on products or services, and the highest bidder wins. This type of pricing allows businesses to take advantage of market demand and can result in higher prices for in-demand products or services.

How Does a Dynamic Pricing Algorithm Work? 

A dynamic pricing algorithm is a mathematical model that helps businesses determine the optimal price for a product or service. The following formula represents the basic idea behind a dynamic pricing algorithm to identify the optimal price for a product or service based on the customer group or other factors.

P* = argmax p * d(p)

        P

In this formula:

• p is the price of the product or service.
• d(p) is the demand for the product or service at price p. It represents the number of units that will be sold at a given price.
• argmax is the symbol for the argument that maximizes the value of a function. In this case, it represents the price that will maximize the product of the price and the demand (p * d(p)).

The dynamic pricing algorithm calculates the price that will maximize the revenue by analyzing the demand for the product or service at different prices. The algorithm uses demand data to calculate d(p) at different prices, and then selects the price that will result in the highest revenue.

For example, if demand is high at a low price and decreases as the price increases, the dynamic pricing algorithm will set a lower price to maximize revenue. Conversely, if demand is low at a low price but increases as the price increases, the dynamic pricing algorithm will set a higher price to maximize revenue.

Like all algorithms, the accuracy of the results depends on the input data. The more diverse and accurate the data, the better the pricing model’s performance. Most pricing algorithms use historical data from product sales to estimate demand, however, models may also incorporate real-time data and other external factors to make pricing decisions. Typically, a machine learning engine works in two stages to calculate the effect of each price change and optimize prices accordingly.

Common Dynamic Pricing Algorithms 

There are several mathematical models that can be used in dynamic pricing.

Bayesian Model

This model uses Bayesian inference to estimate the probabilities of different demand scenarios given the available data. The model uses these probabilities to determine the price that will maximize revenue based on the expected demand at different prices. The Bayesian model is most useful for dealing with uncertain demand and for making pricing decisions in real-time.

Reinforcement Learning (RL)

Reinforcement learning is a type of machine learning that focuses on learning from experience. In dynamic pricing, RL algorithms can be used to determine the optimal pricing strategy based on the relationship between price and demand. RL algorithms work by defining a reward function that represents the expected reward (e.g., revenue) for a given price, and then adjusting the price over time to maximize the reward. RL algorithms are particularly useful for handling complex pricing environments with multiple factors affecting demand.

Decision Trees

This algorithm builds a tree-like model to represent the relationships between prices and demand, and then uses this model to make pricing decisions. The decision tree algorithm splits the data into segments based on the price and demand characteristics, and then applies different pricing strategies to each segment. 

5 Best Practices for Dynamic Pricing

Establish Business Goals

The first step in implementing dynamic pricing is to clearly define the business goals for the pricing strategy. This may include increasing revenue, improving profit margins, or capturing a greater share of the market. Understanding the business goals will help guide the choice of pricing method and metrics of success.

Establish Metrics to Measure Success 

Once the business goals have been defined, it is important to outline the metrics that will be used to measure success. This may include revenue, profit margins, market share, or customer satisfaction. These metrics will be used to evaluate the effectiveness of the dynamic pricing strategy and make adjustments as needed. 

Select the Pricing Method

There are several different pricing methods that can be used in dynamic pricing. The choice of pricing method will depend on the business goals and the characteristics of the market and product. Here are brief explanations and examples of three common methods:

• Cost-plus pricing: Calculate production costs and add a markup percentage. Straightforward but doesn’t consider customer willingness to pay or competitor pricing. Example: Product costs $50, desired markup 30%, selling price = $65.
• Value-based pricing: Determine price based on the perceived value to customers. Requires deep understanding of the target market but can lead to higher profit margins. Example: Software company sets price at $99/month based on customers’ perceived value of time-saving benefits.
• Market-oriented pricing: Takes into account competitor pricing and market conditions. Requires continuous monitoring and may involve price matching or undercutting. Example: An online retailer prices a product at $145, slightly lower than competitors’ $150 price point.

Collect Sufficient Data

Dynamic pricing requires access to data on demand, cost, and competitor pricing. This data can be collected through various means, including surveys, transaction data, and market research. It is important to have access to accurate and timely data to make informed pricing decisions. You should also include internal data on production costs, revenues, and profit margins.

Implement Price-Point Determination

Take advantage of software that uses algorithms such as Bayesian models, reinforcement learning, or decision trees to determine the optimal price based on demand and cost data. Automated price-point determination systems can help ensure that prices are adjusted in real-time to respond to changing market conditions.

Dynamic Pricing Models Management with aporia

Dynamic pricing models can be incredibly effective in optimizing pricing strategies for businesses, but they also come with some risks. One of the biggest risks is that these models can be complex and difficult to manage in production, and even small changes can have significant impacts on pricing outcomes. Additionally, without proper monitoring and observability, it can be challenging to diagnose issues with dynamic pricing models and make necessary improvements. 

aporia solves these issues by providing a comprehensive observability platform that enables businesses to monitor and diagnose issues with their dynamic pricing models in real-time. By using aporia, businesses can ensure that their dynamic pricing models are performing optimally, with any issues quickly identified and addressed before they can negatively impact pricing outcomes. 

The aporia platform supports any use case and fits naturally into your existing ML stack alongside your favorite ML tools and frameworks. aporia empowers organizations with key features and tools to ensure high model performance: 

Production Visibility

• Single pane of glass visibility into all production models. Custom dashboards that can be understood and accessed by all relevant stakeholders.
• Track model performance and health in one place. 
• A centralized hub for all your models in production.
• Custom metrics and widgets to ensure you’re getting the insights that matter to you.

ML Monitoring

• Start monitoring in minutes.
• Instant alerts and advanced workflows trigger. 
• Custom monitors to detect data drift, model degradation, performance, etc.
• Track relevant custom metrics to ensure your model is drift-free and performance is driving value. 
• Choose from our automated monitors or get hands-on with our code-based monitor options. 

Explainable AI

• Get human readable insight into your model predictions. 
• Simulate ‘What if?’ situations. Play with different features and find how they impact predictions.
• Gain valuable insights to optimize model performance.
• Communicate predictions to relevant stakeholders and customers.

Root Cause Investigation

• Slice and dice model performance, data segments, data stats, or distribution.
• Identify and debug issues.
• Explore and understand connections in your data.

To get a hands-on feel for aporia’s ML observability platform, we recommend: 

• Get a private tour of the platform and see aporia in action