## How to Build a Dynamic Pricing Model | by Etienne Yuan

DS in the Real WorldThe following is known to be true in business: High Price, Low Volumes. High Volumes, Low Price. Or is it? Photo by Benjamin Sharpe on UnsplashIn this article, I share with you my experience in building a dynamic pricing system for a long-distance train company, and how we increased the number of seats sold without changing our timetables, nor lowering our average price per seat, by applying very basic principles of implementation also applies to any business in which the service it sells shares some characteristics with train seats, that is to say:The cost of selling one additional unit, or marginal cost, is close to a unit available is not sold by the time the service is rendered, (e. g. A train leaves the station), then it cannot be kept in stock, and its potential value is lost would be the case of hotel rooms, airlines, long-haul bus tickets, cinema, theater, concerts, zoos, cruises, sporting events, order to build the model, we first need to answer the following questions:How much of a good or service do customers buy? How much do customers pay? When do customers buy? Let’s start by taking a look at a typical demand function:The demand function is the mathematical expression of the relationship between the price of a good or service, and the quantity of said good or service that you can sell at a given price. As stated, for normal goods, the higher the price, the lower the quantity of goods sold. This results in a downward sloping demand function. As you move to the right in the horizontal axis and you increase the quantity or volume of product you want to sell, then you need to lower the price you charge in order to achieve that quantity of goods, how much of a good or service customers want to buy will depend on the price. Other things remaining equal, as you lower the price, more customers will be willing to pay for the graph above can also tell us how much we can charge, given a determined number of units you want to simplify, let’s assume that a customer can only buy one unit of the service (in this case a train ticket). Then if you price the ticket at €9, then there are 30 people willing to buy a ticket. If you price it at €3, then there are 90 people willing to buy a ticket (30 willing to buy at €9 plus the 60 additional customers willing to buy at €3) a firm can only charge one and the same price to all customers, and because revenue equals price times quantity, then if the firm charges 6 Euros per ticket, then it will sell 60 tickets, for a total of €360 in metimes though, firms have the ability to charge different prices to different customers. Economists call this ability price discrimination, and what this enables the firm to do is to increase revenue by capturing more of the value under the demand curve the example above, if our train company can charge different prices for adult and children passengers, then they could potentially increase revenues from a maximum of €360 they could reach with a single price, to €440 (40 tickets at €8 per adult, plus 20 tickets at €6 per child) area under the demand curve represents the value that a particular good or service is delivering to the customer. So, if you could charge not only two different prices to two different types of customers, but several different prices to several different types of customers, then you could capture most of the area under the demand curve and substantially increase revenue, purely from your pricing strategy, without having to incur the cost of increasing departures, changing seating arrangements, increased advertising, or offering additional services on we have established that there is very little additional cost to selling a seat on a train that is going to depart with that seat empty anyway, and that the value of a seat unsold is lost forever, it will make sense to sell any empty seats at any price above zero, as long as you have empty seats only we knew a way to segment customers by their price all procrastinate, and so do consumers, too. People will usually postpone purchase decisions for as much as they can. In the case of train tickets, we discovered that this behavior created a pattern with very sporadic purchases of tickets for train departures taking place still far into the future. Then, purchases become more frequent about one month prior to departure, accelerating one week prior to departure, and with a peak of tickets bought one day prior to we plot the percentage of tickets remaining to be sold on the horizontal axis, and the number of days left before a train’s departure on the vertical, then we get a downward sloping function. As the time to departure gets closer, ticket sales accelerate, and so the number of tickets remaining to be sold decreases also found out that the later a passenger bought a ticket, the less price-sensitive he or she was. Thus, we found the variable that allowed us to price discriminate:, we need to find the particular price we need to charge at a particular time, given that we have a particular number of tickets left to sell. As luck would have it, we have two equations sharing two variables that can be solved simultaneously:The Price Demand Function: P = g(Q)where Price (P) is a function (g) of Quantity (Q) the Number of Tickets left: Q = h(T)where Quantity (Q) is a function (h) of Time (T) gives us a new function, where Price is a function of Time. P = f(T) = g(h(T))Shown graphically in the top right quadrant in the figure above. This function tells us what price per ticket to charge at any particular time, given how many tickets we have left to this function, we can also calculate the expected price P at any given value of time T and quantity Q to populate a matrix, and show this function in tabular metimes things don’t happen as expected, if for example, contrary to what our functions predicted, we sell more or fewer at any given time (T) and price (P), the quantity of goods sold was higher than expected, then it means that more people were willing to buy a ticket at the prevailing time and can represent this variance as an upwards shift in the demand the demand function shifts upwards in the top left quadrant in the image above. Then, in order to have tickets left to sell for later, when we can charge higher prices, the price needs to go up already now. This results in a similar parallel upward shift in the curve representing Price as a function of Time in the top right quadrant. Both illustrated in milarly, if we sell fewer tickets than expected, then it means that at a given Time and Price, the quantity sold was lower than expected. This results in the downward shifted curves in green. In order to fill the train, the price needs to go as time progresses, we find further discrepancies between the number of tickets we expected to sell, versus the actual number of tickets sold, we can think of them as further shifts in the demand agine that we consistently find that we are selling more tickets than expected. These can be viewed as consecutive upward shifts in the price demand function for tickets, and the matching parallel upward shifts in the price/time function, as can be seen in the upward shifting red curves in the image lculating all the values that these upward and downward shifted demand functions give us all the Prices P, given combinations of Times T and Quantities Q needed to fill the full Price Matrix for our hypothetical train departure, showing us the prices that we needed to charge at any given combination of Time to Departure and Seats left to Sell that would maximize revenue for that implementation, we had to make some policy decisions to simplify the transition to the new that pricing different travel segments in a train network was a rather complex exercise, we did not modify the existing pricing model too extensively, but ended up implementing the price matrix on top of the existing model, as a percentage of listed now had two pricing classes (not to be confused with carriage classes): The new, dynamically priced discounted tickets, which were non-refundable; and the full-price, which remained available for purchase as a fully-refundable ticket at the same fixed full-price all the of the first decisions that needed to be done was to allocate seats per departure into these two ticket classes, which was initially done manually but was later automated, using historical data as a simplify marketing communications, we decided not to charge more than the listed full price ticket, effectively capping the maximum price we could charge, even if the train was going to be very full. In the same vein, we also decided never to charge less than 20% of the full price also had to cluster our different departures, and implement different matrices for the different clusters. An example of one of the matrices we implemented can be seen introduction of this pricing system allowed us to retire an older, much more complicated one that relied on many more variables, requiring lots of manual input, and an expensive software licensing fee. Replacing it with a simpler, more robust and cheaper one that required fewer, in fact, only two inputs: (1) Time to Departure and (2) Quantity of Seats onomists usually say that all information is ultimately distilled into the price. And in this case, it worked out precisely like that. We actually made more accurate predictions with fewer inputs, so the model required lower maintenance. Simplicity is cheaper to also retired several complicated discounted ticket classes. This single, time-dependent pricing, allowed us to replace them while simultaneously capturing a broader price range, not only in lower price points, if you bought your tickets earlier, but also in the higher price points, by introducing more nuanced pricing that hugged the demand function closer as time to departure approached. Effectively, it significantly improved our ability to we went live with these price matrices, we saw a 5% increase in the number of tickets sold. Not only from additional sales from the discounted tickets, but interestingly, also from increased full-priced tickets, because the system allowed us to more accurately predict the number of full-price tickets we could the near-zero marginal cost of the additional tickets sold, all the associated increase in revenue went directly to the bottom-line, as no additional variable costs had to be incurred after the matrices were implemented in our ticketing system, resulting in a pure increase of profit margin.

## Leadership Guide to Machine Learning Pricing Algorithms ⚙️

Machine learning pricing algorithms are not just profit maximising pricing tools, but, rather a movement that is redefining price and revenue management. It’s also a pricing language that’s transforming profitable revenue growth in your market and industry.

We’ve been hearing a lot about algorithms in the press recently, but are price algorithms like ‘dynamic pricing algorithm python’ really as good as vendors say or are they all just sales hype?

In this article, we will demystify algorithmic pricing. Also, explain the pros and cons of price algorithms like dynamic price algorithms python. In addition, we will share some of the known risks pricing teams have dealt with when they’ve installed a new price system.

Introducing algorithmic pricing…

A pricing algorithm is a quantum leap from fixed pricing, mark up to mark down and simplistic cost-plus calculations. A sophisticated price algorithm is a customised heuristic, integrated within a pricing system. Furthermore, it enables a pricing team to implement and adjust differentiated price strategies across many different products and customer segments.

The beauty of pricing algorithms like dynamic pricing algorithms python is that they enable pricing teams to find out almost instantly if a price action or strategy is working or not. A pricing algorithm works away in the background predicting changes to implement optimal prices. What’s more, there’s no excel spreadsheet involved or time wasted updating and reviewing prices manually.

All price reviews are automated to a specification. Leaving the pricing team much more time to identify and capture new revenue and share-of-wallet opportunities.

What is a Dynamic Pricing Algorithm?

If you are new to algorithmic pricing, a dynamic pricing algorithm is a customised heuristic operating typically within a high power pricing system. The algorithm is like the pricing blueprint or pricing logic in code. The pricing system is the price data technology running the pricing logic and queries really, really quickly.

Essentially, the pricing system churns through tons of price volume data, sales transactions, orders, promotions and special offers. While the price algorithm is the set of rules that guides the automation and calculates the optimal price changes across the product portfolio and different customer segments.

How did businesses set and manage price before machine learning pricing algorithms?

Before algorithmic pricing, B2C and B2B companies basically did margin targeting using cost-based pricing. Unfortunately, margin-based pricing or cost-based pricing leaves ALL businesses vulnerable to revenue loss, lost profit and customer flight.

Cost-based pricing is like a really rudimentary price algorithm. Basic price algorithms like cost-plus pricing put businesses at risk because they either push up prices too high – leading to volume loss – and or set prices too low – leading to revenue loss.

So in a way, algorithmic pricing has always been around. The main difference now is that they are much more sophisticated than they used to be.

Case study: Amazon book pricing algorithm

Amazon’s pricing algorithm is an excellent example of dynamic pricing algorithms for e-commerce (the opposite of a basic cost-plus algorithm). Amazon is one of the first to implement sophisticated algorithmic pricing. Its strategy is not just using internal inputs to adjust prices, but also external inputs as well derived from an open algorithmic marketplace.

To get this data, Amazon provides outside sellers with an API (Amazon Marketplace Web Service). Their API basically enables Amazon to collect and monitor real-time data updates on consumer buying patterns. It also churns through data relating to competitive price responses, new product pricing opportunities, tactical discounting levels and recommended inventory and pricing levels.

In essence, Amazon’s API enables them to build and inform a sophisticated dynamic pricing system, which is capable of sourcing data and informing price decisions in near real-time.

After refining their API technology over the past few years, Amazon is now in a great position to capitalise on their business, pricing and distribution model. The data collected from the website, for example, feeds into their price optimisation algorithms prices every 15 minutes. This is essential for Amazon because around 18% of the revenues come from third-party seller services. Including commissions, fulfilment, and shipping fees. What’s more, 3, 000 sellers join the marketplace every single day. Which means their dynamic pricing algorithm helps them forge a better e-commerce capability to not only set prices but also manage the marketplace and arbitrate sellers. ;

How do pricing teams benefit from machine learning pricing algorithms?

Dynamic price algorithms are growing in popularity with both B2C and B2B businesses across many industries (banking, insurance, FMCG, retail). Many of the best pricing teams are using price algorithms to set and manage price.

Key advantages of price algorithms are:

1. They can (if designed correctly) help pricing teams to pick up on loss-making price actions and course-correct almost in real-time to avoid substantial volume and margin losses.

2. They help pricing teams to find previously unrealised revenue and margin opportunities much faster while generating incremental EBIT growth safely.

3. They generate useful output via data visualisation tools and dashboards. But of course, only when all the key data inputs have been defined in the back-end pricing system, and the algorithm has been customised for the business, industry and market.

Functionality to look for in AI pricing programs

Not all price algorithms are the same. In fact, each business should have its own price algorithm. Here are a few popular types of pricing algorithms businesses use to set and manage prices and revenues:

Policy-driven streamline – this is a price algorithm developed from fairly rudimentary business goals and pricing policies (input data). The danger here is that the price review process is very inward-looking and not an accurate view of the market at all.

Advanced segmentation – this is a price algorithm that sets and manages price reviews using a range of internal and or external factors or pricing rules (like in the Amazon example above). For example, in retail businesses, prices fluctuate during the course of a day or are adjusted to different customer groups or segments using tactical discounting.

Micro-segmentation – is a useful aspect of algorithmic pricing because it enables the price system to account for all the price variations across many different customer and price groups. Consequently, it also takes into account price sensitivity, awareness and willingness of the customer to pay, wait or accept a substitute.

Standout Capabilities of Machine Learning Pricing Algorithms

The hallmarks of a good price algorithm are:

Dynamic pricing – It sets prices based on the business’ and competitor’s price, trends and volume/demand drivers and any supply-side elasticities.

Personalised pricing – It can be programmed to set prices and discount levels based on differences in consumer attributes, preferences, value drivers, price sensitivities, and buying behaviours.

Differentiated pricing strategies – It can be adjusted to good, better, best pricing principles. Also, it uses price tiers and versioning to influence shoppers to first engage with your basic reference products and then upgrade to more premium product types.

Efficiency guarantees – It can set prices based on product placement, branding and price positioning, time of launch date in the market.

Advanced internal indicators – It does lots of statistical analyses of transactional data, inventory, catalogue data to inform product cost position at any one time. These are internal indicators of the price which the programmer may choose to incorporate in the algorithm.

Integration with merchandising and inventory management – It can also perform deep-dive analyses on stock levels and selling frequency to keep track of inventory and avoid under-stocking and overstocking. These are again internal indicators. The programmer may want to account for supply-side elasticities and maximise inventory at the best price.

A checklist to assess machine learning pricing algorithms

If you are considering buying new pricing technology and want to understand the backend price algorithm a system uses, or want to create your own algorithm, you should have a few resources at hand first. We recommend the following:

1. You need to have expertise and insight on the business operations, market, customer base, product portfolio to construct the right pricing algorithm – out of the box solutions don’t work and create serious delay and issues with zero margin gains.

2. Buying a pricing system does not mean it is already equipped with a price algorithm right for your business. Therefore, we highly recommend that you meet the programmer or implementation consultant to see how much they really know about pricing and the challenges you face in your industry. And, preferably before you buy the new system.

3. Pricing algorithms are created by people (usually IT programmers who have ample IT programming and system knowledge but limited pricing expertise or industry knowledge). The sales consultant may not want you to look behind the scenes, however, it’s worthwhile knowing how much the programmer understands about your business and pricing before they work on your algorithm.

look behind the scenes

4. Vendors of price algorithms and the system typically have one basic algorithm which they partly adjust based on the requirements you give them. Meaning, if you or your team are looking to them for pricing expertise, they are in fact, looking to you and don’t have the expertise you really need.

5. The system automates the algorithm even if the algorithm is good or bad. Before you roll it out in the market, make sure you’ve tested and tested, and pilot tested the algorithm.

6. All systems even AI systems have limitations and are prone to change.

7. The pricing team needs to constantly run experiments, price trials and test to work out and adjust input parameters, bandwidths, price floors & ceiling, and price ladders.

8. You cannot run the same price algorithm forever. Pricing is a system, not an event. This is why you need a pricing team.

Implications

How do you know a good machine learning pricing algorithms from a bad one?

The price-setting process you choose to automate is effectively your price algorithm. In other words, a price algorithm is only as good as:

1. The quality of the input variables you feed into the system

2. Your price data strategy

3. Your price architecture and design

4. The expertise of the person creating the algorithm

5. The calibre of your pricing team and their ability to read the output of the algorithm

The challenge here then is to construct the right pricing algorithm. Also, to find the right AI software system to run it. Not an easy thing to do at all.

The trap many businesses fall into, unfortunately, is automating a rudimentary cost-based algorithm or price volume algorithm. Still, to this day, very few businesses or software providers have nailed the perfect price value profit equation. Many are dressing up basic price algorithms with fancy IT systems. Which only really serves to automate the same old mistakes, but much faster.

Conclusion

The pressure is now on for pricing and revenue management functions. That is, to understand and learn how to inform and use pricing algorithms to drive profitability. Or else face many years managing overly complex pricing systems that are out of whack with the market. And ultimately leaking hard-earned margin on a daily basis.

If you already bought or are considering to buy an AI-driven pricing system or looking to introduce algorithmic pricing to your business, remember all IT systems have limitations. You need to know what these limitations are to manage them appropriately.

It takes years for AI-driven price algorithms to learn your market and understand what price actions work or not. This is why you need a world-class pricing team monitoring and guiding the system and auditing the price algorithm.

A pricing team should always lead a pricing system, not the other way around.

A customised price algorithm is not a black box solution.

Click here to access your free pdf guide on driving pricing strategy in your business.

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## Dynamic Pricing Algorithms in 2021 | State of Repricing Technologies

Price management is a significant problem faced by many companies, including retailers, because errors in price tracking can lead to improper results, leading to lost profits. Traditional price management techniques are prone to errors, preventing companies from achieving optimal pricing.

Dynamic pricing algorithms help businesses make informed pricing decisions. It allows eCommerce companies to change prices frequently and gather real-time feedback data. As a result, the company can respond to demand changes effectively, automate price management and reduce the risk of forecasting errors.

Besides, you can use these pricing algorithms to optimize demand, supply, subsidiary products, and competitive prices. The purpose is to make informed decisions, stay flexible, and adjust prices according to your business needs. In today’s article, we will discuss dynamic pricing algorithms. Read on!

How do dynamic algorithms work?

Dynamic algorithms use artificial intelligence (A. I. ) and machine learning (ML) technologies for price management, ensuring scalability and allowing companies to make informed decisions. In addition, these algorithms enable companies to achieve portfolio-level pricing by considering implicit and explicit dependencies.

Besides, these algorithms help retailers bring flexibility in their pricing operations, allowing them to set prices for different shopper groups. Depending on your needs, you may consider factors like market trends, customer behavior, buying patterns, and demand fluctuations to set an optimal value.

Dynamic algorithms focus on a core estimation, a dependency between price and demand. And they consider a wide range of other pricing and non-pricing factors to extend the formula. These factors are:

Procurement expensesDemand cannibalizationCompetitor pricesProducts Promo activities Inventory costs

The pricing algorithm processes relevant data points, leading to precise and accurate results. Depending on the retailer’s needs, most pricing algorithms also focus on sales data. The algorithm uses this historical sales data to estimate the demand function.

Typical pricing algorithms workflow

Pricing algorithms allow companies to update prices more frequently and make informed decisions through automation technologies. The purpose is to develop pricing strategies that can react to competitors’ price changes. A typical pricing algorithm has four stages:

Stage 1: The algorithm processes the historical sales data, pricing points, and product demand. Stage 2: The algorithm uses identified dependencies to build the demand function and streamline the pricing strategy. Stage 3: The cutting-edge algorithmic processes and mathematical models use a wide range of pricing and non-pricing factors to yield correct estimations and optimal prices. Stage 4: The algorithm applies the recommended prices and reruns the loop for the latest repricing results.

Bear in mind that this four-stage workflow is a basic pattern/general phase, meaning the algorithm must align with the retailer’s specific cases, targets, and constraints. Some companies develop dynamic algorithms based on cutting-edge neural networks that can process millions of repricing situations to generate accurate results.

Creating a forecasting algorithm for price tracking or price management is complicated because the model may not align with every case. Therefore, it is crucial to use a software system with dynamic algorithms that align with your business goals and needs.

Factors to consider when choosing a dynamic pricing algorithm

A typical dynamic algorithm uses historical data for price tracking and management. It means they use passive strategies to learn the demand function. If your products have a long life cycle, you may not face any issues. However, if you have products with a short life cycle, you will face a wide range of difficulties. The same is true for new products and an unstable demand function.

Remember, this can lead to inaccuracies in pricing strategies, leading to substantial financial risk for your company. The primary problem faced by most retailers revolves around exploration and exploitation because they fail to find optimal prices.

For instance, this is often due to a limited time, preventing retailers from testing pricing techniques and gathering the demand points. So, it is crucial to choose the correct pricing algorithm or system to ensure it aligns with your specific strategy.

Common factors, such as overall market strategy, business goals, and company maturity levels play a crucial role in choosing a dynamic algorithm or model. Here are a few essential goals to consider when choosing a pricing algorithm.

Maximum revenue

Suppose you want to increase your revenue by selling your products with unknown demand functions. In that case, you need a dynamic algorithm that builds a demand function by considering factors like sales history for similar products. That way, the algorithm performs essential calculations to generate prices, leading to maximum revenue.

Increased gross profit

Depending on your goal, if you want to avoid dropping marginality and increase gross profit, you need a dynamic algorithm designed to balance these two metrics (gross profit and marginality) to generate a price.

Improved customer experience

Dynamic algorithms can help avoid inconsistent customer experience. So, if your goal is to improve customer experience and satisfaction without any complications, you should aim for an algorithm that focuses on satisfying a specific service level.

Zero or minimized cannibalization

As a retailer, your goal is to minimize cannibalization between your products. In that case, the dynamic algorithm you use must generate prices for your new products without risking the Key Value Items (K. V. s) sales.

Moreover, if you wish to use a pricing algorithm for your business operations, make sure you have clear and S. M. A. R. T goals of your company or retail shop position. That way, you can streamline the pricing strategies and help your managers to avoid time-consuming work.

Final words

Dynamic pricing algorithms use cutting-edge machine learning and artificial intelligence technologies for price management. The purpose is to increase your products’ prices and capitalize on demand. Using these algorithms enables you to stay competitive in retail or any other market.

We recommend using dynamic algorithms to analyze and streamline the demand curve for your customers, leading to an accurate display of the demand curve with the min/max price customers want to pay for your products. In addition, you can gather more data on your customers, analyze behavior patterns and purchasing attitudes using a dynamic algorithm.

pricing strategies

## Frequently Asked Questions about dynamic pricing algorithm python

### What is dynamic pricing algorithm?

Dynamic pricing algorithms help businesses make informed pricing decisions. It allows eCommerce companies to change prices frequently and gather real-time feedback data. As a result, the company can respond to demand changes effectively, automate price management and reduce the risk of forecasting errors.Jun 17, 2021

### How do you calculate dynamic pricing?

A successful dynamic pricing setup relies on 5 core steps:Define your commercial objective.Build a pricing strategy.Choose your pricing method.Establish pricing rules.Implement, test, and evaluate the strategy.May 8, 2018

### What is a dynamic pricing model?

Dynamic pricing is a pricing strategy that applies variable prices instead of fixed prices. Instead of deciding on a set price for a season, retailers can update their prices multiple times per day to capitalize on the ever-changing market.