The Pricing Problem

How can we know if we have set the optimal price for a product to achieve our business objectives and generate the most value for our company?

In 1960, Edmund Jerome MacCarthy introduced the concept of the 4Ps of the marketing mix as the fundamental pillars of any marketing strategy: Product, Price, Place& Promotion, and over time three other factors were added to the mix, People, Process & Presence, until getting the 7Ps we know today.

These pillars refer to the fundamental aspects of the main objective of marketing, which can be defined as “offering the right product or service, at the right time, in the right place and through the right channels, at the right price with a good value proposition, always keeping in mind that the business must be profitable”.

Of the issues that follow from the above statement, the most challenging is always price, and it is also the one most directly related to revenue generation.

If we set the price too high, part of our potential customers will not buy the product. We will have lower sales, we will have a high stock, and we will have difficulties taking advantage of our economies of scale. On the other hand, if we set the price too low, we will lose profit margin, if sales exceed our estimates, we may suffer stock-outs and damage the perceived value of our product and the company’s image.

What is Pricing?

When we talk about Pricing, we refer to the process by which companies decide and set the prices of the products or services they offer. For Pricing to be successful, companies must align their strategies with the purpose of:

  • Adapt to the realities of the markets where the product or service is offered, e.g. as sales trends or competitors’ behaviour change.
  • Achieving the company’s financial goals and ensuring profitability.
  • Support the positioning of the product or service in the market and be consistent with the rest of the marketing mix.

These goals can take the form of different company-specific objectives. For example, a young company might aim to increase its market share; a company with a mix of products perceived as substitutes might seek a balance between them to prevent one from displacing the others; or in a regulated market, a company should comply with strict regulation while trying to increase its sales.

Pricing Strategies

To solve the Pricing problem, numerous strategies can be aligned to a greater or lesser extent with the different objectives pursued by companies.

By means of illustration, we include some of the most widely used strategies:

  • Unit profit. From the production costs, the price at which the product or service must be sold to obtain the unit profit that covers these costs and generates a certain profit for the company is calculated. This method does not take into account demand or other market factors, but it allows a simple calculation of an acceptable price and in non-competitive markets, it can be a good enough strategy.
  • Competitors Monitoring In markets where prices set by competitors are readily available (e.g. products or services sold online or regulated markets where prices are published), it is possible to replicate the changes in trends set by the main competitors. This is a passive strategy usually used when the market share to be maintained has stabilised, or when there is a dominant company and the aim is to monitor its pricing policy so as not to lose market share.
  • Rounding. When customers are highly price-sensitive, companies may scale their prices so that they are perceived as more expensive or cheaper than they are. This strategy is common in supermarkets, with prices marked $4.99. Conversely, if the perceived value of the product is to be increased, rounded prices are used. For example, for luxury items such as a handbag, the marked price would be $1,250 instead of $1,249.99.
  • Market Segmentation. This strategy consists of dividing the market into segments and setting a different price for each segment. For example, the market can be divided based on distribution channels, setting a specific price for the different online sales platforms and physical shops; the market can be segmented by region, either towns or provinces, for example; or time bands can be established, and promotions or price increases can be carried out at times of lower or higher demand.
  • Product portfolio. When the company has several products or services in the same family, a high price for one of the products to increase sales of the other can be set, or to change the perception of the first one so that, for example, it is perceived as the premium option. But you can also do the opposite and limit the price differences between the products so that customers do not always choose the cheaper one and lose sales of the more expensive one.

Not all strategies are mutually exclusive and it is common to combine several of them for pricing given that in most cases, companies have to address several, perhaps incompatible or at least non-convergent, objectives simultaneously.

In these scenarios, how can we know if we have set the optimal price for our product or service to achieve our objectives and generate the most value for the company without losing sight of production requirements, and business and market rules?

Can Operations Research be used to solve the Pricing problem?

The complexity of choosing the best price to meet the company’s objectives can be addressed through Operations Research, an area of applied mathematics that makes use of advanced analytical methods for decision making. Within this area, we find Price Optimisation.

We can divide this resolution approach into two stages. First, we seek to model the demand curve in terms of the possible prices offered for the product or service and then find the price that according to this demand curve, allows us to meet the company’s objectives in the best possible way.

The work of modelling demand, or estimating demand and its price elasticity, is crucial because it is the basis for the decisions we can make about the price of our product or service: If the demand estimate we obtain is far from reality, the decisions we have made will not bring us the results we expected.

Machine Learning techniques are commonly used to model demand as a function of price to analyse historical data relating sales to price and any other relevant market or environmental variables, but data from surveys and market research can also be used to better characterise the behaviour of potential customers.

Once we have a good estimation of demand as a function of price, we turn this price into the decision variable for optimisation. This is where the different pricing strategies and any other business rules that we need to comply with so that our decision is aligned with the company’s objectives, can come into play.

For example, through constraints in the optimisation model, the market can be segmented and prices can be rounded, besides taking into account competitors’ prices to include some monitoring rules.

These constraints delimit the possible prices for our product or service, and from the demand curve, we can define our objective function, e.g. to maximise sales or profit.

The opportunities of the Operations Research approach are related to that last point. In quite simple problems, when our objective is to maximise our sales, all we will have to do is to reduce our prices. But what happens when the sales of a product are related to the sales of substitute products, or when we have several outlets in a network and we do not want to create artificial competition between them? Moreover, are we sure that our product is price elastic? In real scenarios, the large number of variables that we must consider to make a decision makes the problem unmanageable, but the use of optimisation models, when these models correctly represent reality, allows us to solve the problem considering all its variables and thus achieve the best solution in the global terms.

Despite its advantages, this approach, used in sectors as diverse as retail or banking, does not always adapt correctly to the characteristics of the market, and for this reason, there are some alternative approaches within Operations Research that allow us to get closer to the reality of these markets. Below are some examples:

  • Revenue management. It is used when the supply can not be increased if there is an increase in demand, when the product or service is perishable (it cannot be offered past a certain date, so it cannot be stored for a long time) and when bookings can be accepted from customers for the sale of the product or service. Some business areas that meet these characteristics are airlines and hotels. Both airline and hotel capacity is limited, and after the date of service (the scheduled flight or hotel reservation day), the service cannot be sold.
  • Floating price It is used when real-time pricing is needed, i.e. when the price has to adapt quickly to continuously changing market conditions and therefore the same price fixed for hours or days can lead to losses. Moreover, in these scenarios, it is usually not possible to collect all the information that would normally be used for price optimisation before the decision is made. Examples of the use of variable pricing are auctions, foreign exchange markets or stock markets.

In all these cases, we see that through the different tools that Operations Research offers us when we can develop a mathematical model that represents the reality of the market in sufficient detail, the use of this model to solve the Pricing problem will always be a much more powerful approach than each of the Pricing strategies applied individually, which will provide partial solutions to the general objectives of the company.