February 08

Introduction

Business to business (B2B) pricing differs from business to consumer (B2C) pricing. In both paradigms modeling demand as a function of price is central, but the nature of demand in the two cases is different, necessitating different analytic models. B2C is characterized by large demand volumes, each transaction representing a very small proportion of total revenue. On the other hand, B2B is characterized by relatively smaller transaction volumes, with each transaction representing a much larger proportion of total revenue. The fundamental differences in transaction volumes and revenue per transaction require different analytic processes. In the B2C setting demand can be modeled in aggregate and individual price recommendations applied to multiple transactions. In the B2B setting, each transaction is analysed and priced individually, characteristics enabled by the relatively smaller volume of transactions, and necessitated by the much larger revenue impact of each transaction.

In the context of this chapter, B2B pricing decision problems are characterized by the following features:

• A distinct offering or deal, often characterized by a contract.

• Some degree of custom pricing, including discounts, freight costs and other deal terms.

• Deals can be characterized as won or lost.1

**Applications of B2B price optimization analytics**

Determining the optimal price for such decision problems has often been referred to as bid price optimization (Agrawal and Ferguson, 2007; Lawrence, 2003), or quote optimization, or customized pricing (Phillips, 2005). In this chapter, B2B price optimization means the same thing.

B2B price optimization analytics have been successfully applied in a variety of settings. United Parcel Services (UPS) has applied the analytic processes ultimately approved by sales management, usually by the ﬁnance department attached to sales. During the negotiation process if a proposed price meets the guidelines the deal can be closed without further pricing review. One of the ancillary beneﬁts of price optimization analytics is a streamlined price approval process, allowing sales to close deals faster. For proposals outside the guidelines exception pricing may be requested by sales, in which case, the pricing analytics team will perform further analysis to support a collaborative pricing decision involving the account representative, pricing analytics and sales management. Other duties of the pricing analytics team include measuring pricing performance, ensuring data integrity, monitoring the capture of loss data and gathering competitive pricing information. Key information systems leveraged include the quoting/proposal system, invoicing, product deﬁnition and conﬁguration, customer relationship management (CRM) data and competitive data. A price optimization software solution may also be included, but this system should be integrated with the quote system to ensure seamless presentation of price recommendations to sales.

**B2B price optimization: special considerations**

The objective of B2B price optimization is to maximize contribution by estimating the optimal price to quote. Important considerations include:

• compensation and incentives

• pricing performance measurement

• line item or total quote optimization

• marginalcosts

• what price to show sales

• businessprocess

• competition, strategy and market share.

In this chapter the primary focus is on the analytics, but some of these considerations with analytic implications will also be addressed.

The sales organization is often incented on volume or revenue, not contribution. In such cases these incentives are not aligned with the contribution maximization objective. To enhance the success of price optimization, contribution incentives should be implemented. This is a very sensitive organizational change and may not be achievable in the short run. The pricing analytics team can support this change process by consistently measuring pricing performance. These performance metrics may eventually be folded into the revised sales incentive structure.

Requests for proposal often have multiple line items. For example, a corporate ﬂeet account may have a long roster of make, model and trim options from which the customer can purchase. In many cases each line item may segment and other key driver variables. Examples of typical segmentation variables include order lead time, product and customer attributes like industry and the number of years they have been a customer (tenure). The key independent or driver variable is always the own offer price. It goes without saying that own price cannot be optimized without a demand model that is a function of own price. Besides price, many other driver variables should be considered in the MRM analysis. Foremost among these are competitive prices. Competitive price is usually a strong predictor of customer response to own price; however, competitive price is not absolutely essential as will be discussed in the section on data issues. Besides competitor price, other driver variables that are frequently strong predictors of price response include the types of discounts or promotions offered, package effects and economic factors such as the producer price index (PPI), interest rates, housing starts and a stock market index (NASDAQ). The distinction between segmentation variables and driver variables is blurred. Any variable may deﬁne a segment or serve as a driver variable. There really is no difference. Segments and driver variables are in essence independent variables in an equation where demand is the dependent variable. Categorizing as segment or driver variables serves as a way to organize the problem to compute the MRM.

The next logical step in determining optimal prices is development of the contribution model. The contribution in a B2B pricing context is not (typically) the same as in a ﬁnance context. Here the only concern is with costs that are truly incremental to winning the bid. By combining the MRM and the contribution model the expected contribution can be formulated as function of own price. Optimizing this function, subject to any other constraints gives us the optimal price recommendation. Continuous measurement of pricing performance closes the process loop. Analysis of pricing performance drives MRM and the contribution function changes, and the price optimization process starts again.3

Data requirements

Key data elements to support B2B pricing analytics include:

• Historic quote data

• “wins” and “losses”

• reason codes

• line item detail

• pricedata

• sales costs and discounts

• Product data

• all products

• product hierarchy (channels and segments)

• conﬁgurations

• marginalcosts

• Customerdata

• sales history

• D&B and other data for segmentation

• Competitive data

• competitors by product and by deal

• competitive quotes by deal

Detailed quote data is the most important data source. Often many of the other data elements, like costs can be found on quote detail records. Additional product detail can be found in product deﬁnition tables which may be part of a conﬁguration management system. Further customer detail may exist in a CRM system, and can often be supplemented by joining with other data sources like Dun & Bradstreet®.

Quote and product data provide price and cost used to build the contribution function. Quote and product data, along with the other data sources, provide additional attributes that explain customer response to quote offer-ings. When identifying data sources for B2B price optimization analytics, a key guiding principle is to collect all available data attributes that may help explain customer response to the own price offering.

**Common data issues**

Competitive data can be a very strong predictor of customer response to quote price, but can be difﬁcult to obtain in the B2B setting. Some quote systems allow account executives to identify the competitors for a bid. This 126 Revenue Management Theory and Issues

detail may often include competitive prices. Organizations often do not fully trust competitive intelligence reported by the sales force, thinking –often rightly so – that their estimates are biased low. The account represen-tative may feel incented to estimate competitive prices low, in order to get a low price from sales management, making it easier to win the deal. This tendency is often exacerbated when sales incentives are revenue or volume based, rather than contribution based. However, bias in the competitive rate data does not necessarily mean that it will not be useful in predicting cus-tomer response to own price (the MRM). If competitive price estimates are strongly correlated with the “true” competitive price, then even a biased estimate may prove to be a key driver in the MRM.

Keeping in mind that what is most important is a variable that is strongly correlated with competitor price, there are often suitable surrogates in cases where competitive prices are not available. For example, distributors often source their products from the same supplier. As a result, competitor prices will likely be strongly correlated to (own) procurement cost. In such cases cost of goods sold may prove to be a key demand driver. In other instances, competitors may offer the same products in both B2B and consumer chan-nels. Consumer prices can be obtained from websites or other accessible channels. Consumer prices are often strongly correlated with B2B prices.

Bids that are won have very detailed information, since these quotes are converted to orders which in turn generate invoices for fulﬁlled product. Losses, on the other hand, seldom have the same degree of detail as wins. Account representatives are not highly motivated to report lost deals, and sometimes don’t bother entering them at all. Further, entering detailed order lines and offered prices for losses is perceived by account representatives as extra, unnecessary work. Finally, companies rarely ever compete for every deal, so even if diligent in reporting losses the sum total of all win-loss records is a subset of the entire market. For example, one might observe a win rate of 80 percent from own quote data, but a have a market share (estimated from external sources) of only 10 percent – an extreme case of a biased win rate estimate. Even in this extreme case of bias, if the loss record-ing process is relatively consistent an adequate customer response to price can be predicted.

Though challenging, all of the loss data issues described here can be over-come and have been overcome in successful implementations of B2B price optimization. Incomplete loss data can be supplemented by sampling from detailed quotes or for similar wins. If there are no loss records, external estimates of market share can be used as a basis to construct loss data. Leveraging the expertise of customers, sales and product experts and applying survey techniques such as the Delphi Method (Linstone and Turoff, 1975) loss data can be estimated in cases where none exists.

Most companies constantly struggle to accurately measure costs at a detailed level. Isolating and estimating the truly incremental cost of winning a bid is almost always a signiﬁcant challenge. Part of the incremental cost is the opportunity cost of winning the bid. The author has conducted several studies with companies to measure the impact of cost estimate errors on determining optimal price, and has found that even large errors in cost lead to only small errors in price. Typically a 10 percent error in cost leads to only a 1 percent error in the computed optimal price which in turn results in much less than 1 percent reduction in incremental contribution. Price optimization can be successfully applied even with rough estimates of incremental cost.

**Computing the market response model**

From an analytic perspective, estimating the MRM is the most challenging step in B2B price optimization. The MRM predicts win/loss as a function of own price and other deal characteristics. Other characteristics are represented by the segment and driver variables discussed above in the section on B2B price optimization: special considerations. The equation below outlines the demand model where f is the MRM and s is a segment.

Win Probabilitys =f (Own Prices, Competitor Prices, Other Driver Variabless)

The magnitude of own price change relative to the competitors’ price change may also be a key driver. To model this effect an interaction term would be incorporated into the MRM. Simplifying the notation and ignoring other driver variables the MRM with interaction effects would be represented by the following equation:

There are many modeling decisions and challenges to overcome in developing the MRM.

• segmentation schemes

• driver variables, including potential interaction terms

• data issues.

Developing a MRM to support B2B price optimization is challenging, but the challenges are tractable. Each of the diverse applications described above –auto ﬂeet sales, industrial products, package delivery, telecommunications –and many others have successfully surmounted these challenges.

For the remainder of this chapter most of these challenges will be set aside, focusing on a simple model where demand is merely a function of own price, understanding that a “real world” MRM is more complex while assuring that the additional complexities can be handled.

**Market response model forms**

The universe of potential MRM forms is unlimited, but there are two common forms that have proven successful.

The logistic function is a common model form, and has a strong statistical foundation for estimating functions with a binary response (win-loss) (Neter et al., 1996).

Another common model is the capped linear model.

Figure 9.3 depicts these two model forms graphically.

The capped linear model closely approximates the logistic model over much of the price range. In practice the capped linear model has some advantages. As a linear function computations may be simpliﬁed. The linear model also imposes strict bounds on the optimal price. However, the logistic function is more statistically sound, and constraints on price recommendations can be imposed in the optimization step. The logistic model will be used for the remainder of this chapter.

For each model, β is the critical price response term and α is a constant. β should be a negative value, meaning as price increases, demand decreases. It is common that early attempts to develop the MRM yield positive β. When this occurs the segmentation and MRM analysis cycle need to be repeated, trying new segmentation schemes and different driver variables. Careful statistical analysis is required to estimate good MRMs.

Figure 9.4 depicts how the MRM is estimated from quote history. The points on the graph represent observed wins and losses; 1 = awinand0= a loss. The MRM is estimated using logistic regression methods (Neter et al., 1996). Readily available and widely used statistical packages like R (http://www.r-project.org/) and SAS® have built-in functions for logistic regression.

The β terms in the MRM are price response terms, not elasticity estimates. When practitioners talk about price optimization the term price elasticity is often used generally and out of context, leading to misunderstandings. Elasticity has a precise mathematical deﬁnition.

With a little calculus and algebra, elasticity can be given by the following equation:

To get a speciﬁc, numeric value for elasticity from an MRM, a price must be given as a reference point (unless the MRM is a constant elasticity model4). Elasticity at a speciﬁc price is called a point elasticity. For example, stating that the elasticity for a logistic MRM is −2.2 is incorrect. It may be correct to say that the point elasticity is −2.2 at a reference price of $300. Note that a linear MRM is not the same as a constant elasticity model. For both the linear and logistic MRM elasticity becomes less negative (less elastic) as price decreases and more negative (more elastic) as price increases. Where e > −1 demand is said to be inelastic, meaning the rate of decrease in demand is slower than the rate of increase in price. Where e < −1 demand is described as elastic. At the long-run average price elasticity generally (but not always) should be less than −1. As a rough guide −4 < e < −1 in most B2B settings. Any point elasticity that is well outside this range within normal pricing bounds should raise suspicions about the reliability of the MRM.

Determining the contribution function

Relative to computing the MRM, determining the contribution function is easy. The key challenges are typically identifying the correct cost components and ﬁnding reasonable estimates for the costs. For purposes of computing optimal prices, the contribution function should only incorporate revenue and cost that are truly incremental to winning the bid. To get to the right cost, you need to dig deeper than standard ﬁnancial metrics. Cost of sales from an accounting perspective includes selling and administrative expenses that are not incremental to winning a bid. Costs derived from ﬁxed assets like plant depreciation should be excluded. Production labor costs generally should be excluded, since labor costs do not typically change (sig-niﬁcantly) the likelihood of winning a bid. Sales department salaries and any other general sales expenses should also be excluded.5

Types of costs that should be part of the contribution model include:

• account discounts

• applicable promotions

• freight allowances

• any other truly incremental cost to serve.

As a guide, if incremental costs signiﬁcantly exceed 50 percent of incremental revenues, then costs that are not truly incremental may be incorrectly included.

For some applications (but not all) opportunity costs are an important consideration, and these costs can be quite large relative to revenues. In this context opportunity cost is the contribution you would forgo (or the step cost you would incur) if you win the bid. Most B2B price applications have opportunity costs that are so small they can safely be ignored. The following is a list of applications where opportunity costs can be safely omitted:

• telecommunications services

• package delivery services

• automotive ﬂeet sales

• print advertising.

A common property of the above applications is that delivery capacity and/or delivery time are ﬂexible. Opportunity costs are more signiﬁcant in constrained capacity applications. Consider hotel group pricing (Cross et al., 2009). If a hotel “wins” a group the associated rooms will be removed from sale. If the hotel “loses” the group they can sell those rooms to another group or to individual customers. For hotels precisely estimating the opportunity cost – also referred to as the displacement cost – can be extremely complex. In fact, solving for the minimum displacement cost can be far more complex than all other parts of group price optimization. Some organizations have stalled efforts to implement group price optimization until they have solved the displacement cost problem. In the author’s view this is a mistake, since typically a 10 percent error in estimating cost commonly results in only a 1 percent error in price (Figure 9.5).

All the example applications cited in this chapter utilized less than ideal cost data. For nearly all companies improving the measurement costs is a continuing and never-ending process. The beneﬁts of immediately implementing price optimization outweigh the requisite investment and delay of pursuing perfect cost data.

**Determining the optimal price**

The aim is to determine the price that maximizes expected contribution. Expected contribution is simply the product of the contribution function and the win probability function.

Some practitioners are intimidated by the prospect of optimization; it sounds too complex. Though optimization methods can be complex, expressing the price optimization model is straightforward, and solution methods are available. Even for models that are non-linear and represented by a system of equations there are approaches that will yield a near optimal, if not a provably optimal solution.

In the following example a linear contribution function and a logistic win probability function are used; therefore the resultant expected contribution function is convex. Because it is convex the optimal price can be determined using simple differential calculus. The optimal price is the point at which the derivative of the expected contribution function with respect to price equals zero.

Determining the optimal price for this example is succinctly illustrated in Figure 9.6.

First, segmentation and regression techniques are applied to estimate the MRM. Next, relevant cost and revenue elements are gathered to construct the contribution function. Finally, the expected contribution function is expressed as a product of the contribution function and the MRM. Finally, an optimization method is applied (in this case simple differentiation) to determine the price that maximizes expected contribution.

**Concluding remarks**

The aim of this chapter has been to remove some of the mystery and fear preventing the reader from implementing B2B price optimization analytics. Though there are certainly obstacles, as there are in any application of analytics to business, these obstacles can be overcome and have been over-come by many companies. There is a good chance that one or more of your competitors have already implemented price optimization.

There exists a litany of excuses proffered to forestall implementing price optimization:

• “Our loss data is incomplete or missing.”

• “Competitive price data is poor or nonexistent.”

• “Let’s wait until the latest activity based costing initiative is complete. Then we will have accurate cost data.”

• “First we need to perfect the opportunity cost model, then we can move on to price optimization.”

• “It is not possible to model our customer demand.”

• “Optimization is too complex. We are not ready for that.”

There will always be data issues. Loss data, competitive prices and cost information are never going to be perfect. Companies need to make the best decisions immediately with the available information while continuously striving to improve data quality. Though daunting and often frustrating, particularly in the beginning, customer demand can be modeled. Take heart from the knowledge that others have succeeded. Optimization is not as scary is it may sound. Think of it as simply a method for deciding what price to offer, and in business you have no choice but to offer a price for your product. It makes sense that by applying analytics companies can do no worse, and can do better, than they are now.I emphatically urge you to start employing B2B price optimization analytics right away. The beneﬁts are substantial, and I hope that after reading this chapter you will conclude that the beneﬁts are also achievable for your company.

**Notes**

1. In some cases contracts may be accepted by the customer, but the volumes ordered against the contract are zero, or much smaller than would be expected. These cases are typically characterized as a loss.

2. Contribution, in the context of B2B price optimization, is proportional to but is not necessarily the same as contribution margin as measured by ﬁnance. We will further clarify what is meant by incremental contribution later in this chapter, but for ease of understanding the reader may think of it as contribution margin.

3. Price optimization performance measurement is an important topic, but one that rightly deserves its own chapter and is only lightly treated here. Unfortunately the topic is not adequately covered in the literature. Pricing performance measurement is covered in depth in Higbie et al. (2007), a workshop presented at the 4th Annual Revenue Management and Price Optimization Conference.

4. Constant elasticity models are generally not suitable for B2B MRMs and are not discussed here. To learn more about constant elasticity models, see Phillips (2005), pp. 49–52.

5. In some cases sales commissions are counted as incremental costs, but typically they are not. The rationale for excluding commissions is that the sales incentive plan is aligned with company proﬁt objectives; however, when incentive compen-sation is based on revenue, not contribution, as is common, it can be argued that sales commissions should be considered incremental costs.

**References**

Agrawal, V. and Ferguson, M. (2007) Bid-response Models for Customised Pricing, Journa*l of Revenue and Pricing Management,* 6(3), 212–228.

Cross, R. G., Higbie, J. A. and Cross, D. Q. (2009) Revenue Management’s Renaissance, *Cornell Hospitality Quarterly*, 50(1), 56–81.

Garrow, L. and Ferguson, M. (2008) Revenue Management and the Analytics Explosion: Perspectives from Industry Experts, *Journal of Revenue and Pricing Management*, 7(2), 219–229.

Higbie, J. A., Cross, D. Q. and Cross Z. N. (2007) How Good Are We Really? Measuring Pricing and Revenue Management Success, workshop presented at the *Revenue Management and Price Optimization Conference*, Atlanta, October.

Hormby, S., Morrison, J., Dave, P., Myers, M. and Tenca, T. (2010) Marriott International Increases Revenue by Implementing a Group Pricing Optimizer, *Interfaces*, 40(1), 47–57.

Lawrence, R. D. (2003) A Machine-learning Approach to Optimal Bid Pricing. In H. K. Bhargava and Y. Nong (eds) Computational Modeling and Problem Solving in the Networked World. Norwell, MA: *Kluwer Academic Publishers*, pp. 97–117.

Linstone, H. A. and Turoff, M. (eds) (1975) Delphi Method: Techniques and Applications. Reading, MA: *Addison-Wesley*.

Neter, J., Kutner, M. H., Nachtsheimm, C. J. and Wasserman, W. (1996) *Applied Linear Statistical Models*, 4th edn. New York: McGraw Hill.

Phillips, R. L. (2005) *Pricing and Revenue Optimization*. Stanford, CA: Stanford Business Books