For example, Ford Motor Co. "has quietly been enjoying a huge surge in profitability... Between 1995 and 1999, U.S. vehicle sales rose just 6 percent, from 3.9 million units to 4.1 million units. But revenue was up 25 percent, and pretax profits soared 250 percent, from about $3 billion to $7.5 billion. Of that $4.5 billion growth, Ford's Lloyd Hansen, controller for global marketing and sales, estimates that about $3 billion came from a series of revenue management initiatives" [2].

The attention that RM commands may lead other disciplines to claim ownership, and it is true that modern RM has its conceptual roots in several disciplines, including pricing and demand models from economics, and market segmentation concepts from marketing. O.R., however, can claim historical rights from the earliest work on practical RM from the early 1960s, and can support this claim through the fact that current practitioners of RM rely heavily on O.R. methods and models.

RM brings several high-value contributions to the business school O.R. course. RM can be presented as a real-world, high-payoff application of optimization, heuristics, inventory models, forecasting and stochastic processes, thereby bringing an important real-world dimension to the O.R. course. Senior executives know of and care about RM. Some knowledge of RM can provide the student with a source of personal competitive advantage, which might well provide the basis for a strong impression during a job interview. In addition, RM offers a variety of entrepreneurial opportunities for students interested in starting their own business. Finally, almost everyone now has direct experience of RM as a consumer — and frequently wonders why firms do some of the apparently crazy things that we see going on around us. Some knowledge of RM will equip the business student to explain all this craziness to their friends; they might even use the words "operations research" or attribute their newfound knowledge to your course.

Business school O.R. courses have much to cover, and so there is likely little time to devote to RM; however, RM algorithms are complex mathematical procedures buried within equally complex information systems. There is little chance of making an impact on the MBA by crawling through the algorithms that leading-edge firms actually use; rather the key to a successful experience is to focus on demonstrating the key ideas and concepts used by the RM firm.

What follows is my view of what every business student should know about RM, and how we can integrate these materials into the O.R. course by using our O.R. techniques to demonstrate how the concepts work and how these tools generate competitive advantage for the firm.

RM Content for the O.R. Course


The key content of any RM presentation is the five pillars of RM: RM pricing approaches (including prices optimized for market segments and dynamic pricing), discount allocation, trading-up including protection levels ("EMSR"), overbooking and re-planing. The trade uses a host of other terms (such as "markdown optimization," "enterprise profit optimization," etc.), but all these can be reduced to variants of these five basic concepts.

In addition to these concepts, it seems appropriate in a business school to include some business background. This might include the firms that use RM (initially airlines, hotels and rental cars, but spreading to manufacturing and retail), and how they implement RM (initially through the SABRE system, but now through Web sites and point-of-sale technologies). It could also usefully include some discussion of the firms that supply RM, which customers are linked with which suppliers, and the issue of whether a firm should outsource its RM or attempt to do it in-house. Finally, some speculation about the future could liven up a classroom session: Many customers do not like RM pricing — could this lead to legislation? What technical developments are on the horizon? The merger of supply chain optimization with revenue management appears to have great potential, but what is the current state of the art?

Presenting the RM Concepts


The key to understanding RM pricing is understanding demand and market segmentation. To motivate presentation of this material, try starting with the multi-segment deterministic revenue optimization problem as an example of non-linear optimization. This price optimization problem can be expressed as: Find a set of prices (p_i) for N market segments [with demand functions q_i = f_i(p_i)] that maximize revenue (R) while selling inventory (I).

This formulation presents RM pricing as an example of optimization, and allows a demonstration of the impressive revenue gains that are generally possible when moving from a fixed pricing policy (p_i = p for all i) to a variable pricing policy while selling the same quantity of product. This model also demonstrates an important side benefit of variable pricing, which is the smoothing of demand. Supermarkets could devote less valuable floor space to checkout stations if they raised the price of groceries at peak periods (which they do effectively anyway, by making the customer stand in line for long periods at peak times).

Most students will object strenuously to any suggestion of raising the price of groceries on Saturdays, but the idea of discounts at off-peak times is usually very appealing. The example of the soda machine that raises the price of cold drinks when the temperature rises [4], as opposed to the one that discounts the cost of drinks on cold days, can be introduced to further demonstrate the importance of marketing variable prices effectively.

Market segmentation drives RM pricing. Time of purchase and current daily temperature are two ways of segmenting one market into a number of sub-markets. Presenting the idea that segmentation is not usually perfectly effective since customers "leak" from high-priced segments to low-priced segments (for example by delaying their purchase in the hope of an improved price) introduces some interesting business issues. Designing effective "fences" is a challenge for the revenue manager. Fences are devices used to slow down or eliminate leakage between market segments. The Saturday night stopover, for example, is a common fence for airline travel (it separates the business traveler from the leisure traveler) as is the $100 fee to change a booking (this discourages a buyer switching from an early segment to a later one if the price declines).

This model also makes clear the importance of the "demand side," or the link between price and quantity sold. Demand modeling or demand curve estimation is an art about which little has been written in the RM literature. It is one of the areas where firms can customize their RM systems in an attempt to gain an advantage over their competitors. Demand modeling requires lots of valid price and quantity data — together with good data management systems and processes — so it is also an area where the established RM firm has an advantage over the newcomer.

Pedagogically, demand modeling links RM to statistical methods, and so it can provide a vehicle to add real-world content to the presentation of statistics. Try having the class estimate a demand curve from data as a regression exercise. Key issues in doing this include the choice of the shape of the regression and what range of prices to focus on in fitting the model. Typically, a linear approximation works well if the range of prices is kept small, but if the price range is extensive, the fit can be improved by switching to a non-linear model. Finally, if some exogenous variables are available (such as weather, competitors' prices, advertising spending, etc.), the art of building multiple regression models can be practiced, including accessing issues such as the impact of the regression prediction errors when one or more of the independent variables are only known as forecasts.

Recognition of forecast errors leads directly to the observation that the deterministic RM price optimization runs into the problem of stockouts and leftover inventory, and provides the motivation to examine the optimum dynamic pricing model. In this multi-period problem, at the end of each period the firm solves the deterministic RM price optimization for each future period after sales for the current period become available, adjusting the remaining inventory to reflect actual demand to date: For each period t from 1 to T:

This model can be used to illustrate the concept of "revenue opportunities." These occur when demand in a period is unexpectedly high and, as a result, the firm has less inventory moving forward and can raise all future prices to extract additional revenue from the marketplace.

This model also allows construction of a booking curve that is a tool that forms the basis for a number of pricing heuristics. The booking curve is simply the plot of cumulative sales over the booking period (or

If the price optimization is set up as a Solver model in Excel, the booking curve can be linked directly to the optimization and can be live. The class might come up with the insight that revenue generally increases as prices are adjusted to produce a more linear booking curve. This insight can be shown to be true (or false) depending on the demand functions used.

The multi-channel version of this model simply adds a second subscript to identify the channel and a second summation across channels, but maintains a single inventory. The multi-channel dynamic model facilitates a discussion of the impact of cross-channel marketing tools such as the low-price guarantee. Some travel suppliers try to attract shoppers to purchase product on their own corporate Web sites (where they have very low booking costs) by offering low-price guarantees. These guarantees take many forms from agreeing to match (or better) any other price found within 24 hours (Marriott Hotels) to matching any future lower price [5]. The desirability of changes in pricing policy and the revenue impact of these various guarantees can be demonstrated by adding various constraints to the multi-channel model.

While these optimization models do not provide insight into how firms actually implement RM pricing, or into the pricing algorithms that are actually used, they do convey powerful insight into the concepts and potential benefits of variable pricing and optimum dynamic pricing, as well as some of the business issues in implementing these leading edge practices. In my experience this is a very important take-home for the business student and something that makes the O.R. course memorable.

Discount Allocation, Reservation Levels and Trading-up


The concepts behind discount allocation can again be illustrated using an optimization model. Suppose a firm sells a product in singles (at price p₁) and 10-packs (at price p₁₀) and has I units available. The single-period revenue maximization problem is:

Solving this model gives the optimum prices (p₁* and p₁₀*) but also the quantities to sell at each price [q₁ = f₁(p₁*) and q₁₀ = f₁₀(p₁₀*)]. Since single-unit sales provide the highest revenue, when the firm implements the optimal prices and faces the uncertainty of the market demand, it should reserve f₁(p₁*) units of product for single-unit sales in order to maximize revenues. This basic deterministic model is easily extended to multiple periods and more than two products sharing multiple inventories: a hotel having daily, weekend and weekly rates and taking booking over multiple periods provides an example of this extended problem. Solving this model provides a reservation level for each high-priced product category for each period.

The optimality of such an array of reservation levels prompts the business issue: How do you manage bookings in this situation? When a customer attempts to make a reservation, a decision has to be made to accept or reject that customer, taking into account the remaining product inventory. Developing the concept of accept/reject decision-making over time in the real world where customer arrivals are stochastic leads to Littlewood's [6] rule. This rule says that you should keep accepting low-price reservations as long as the price you receive is greater than the expected revenue from holding onto the unit (which is the higher price multiplied by the probability of selling the unit at the higher price).

If you have time you can cover Belobaba's [7] expected marginal seat revenue (EMSR) heuristic that extends Littlewood's two-price model to more than two prices by aggregating price categories from the bottom up and applying a rule similar to Littlewood's.

Trading-up emerges as an obvious option when accepting a low-price customer overshoots a protection level and when the reserved product represents a higher value to the customer. Airlines often put passengers paying economy fares into business class seats, and so this is an immediately recognizable practical issue; however, there are other potential applications. When I shop for track shoes, I often choose a shoe (say a $99.95 model) and am then told that the store does not have my size. Trading me up to the next price point (say $109.95) seems to have many advantages (including keeping a customer, bringing in revenue that still represents a considerable unit profit, and simplifying inventory policies), but I have never been offered this option. Littlewood's rule and Belobaba's EMSR model provide the basis for a discussion of a trading-up policy when the difference in the cost of providing the products is included.

Overbooking and Re-planing


Every class will almost certainly include students who have been on an "overbooked" flight and made a deal to give up their seat. Usually they are pretty happy with their "deal," and so they are receptive to a discussion of why firms overbook, customer no-show rates, and the model that determines the optimum overbooking level [3]. In this model, the firm chooses a booking level to maximize the difference between the revenue from the flight and the expected overbooking cost where the expected overbooking cost is zero if the firm sells less than capacity but increases sharply as sales increase above capacity.

For business students the management issues surrounding overbooking are usually of interest. How do you reduce no-show rates in a customer-friendly way (deposits, non-refundable tickets, etc.)? How should you treat the passenger denied product so that the firm can gain the considerable advantages of overbooking but the few customers denied service do not pay a high cost? What other products might benefit from overbooking (Thanksgiving turkeys)?

Re-planing [8] is not yet fully implemented, and so you cannot rely on finding members of the class who have been re-planed. The basic idea of re-planing is that a customer holding a reservation for a product would be contacted a few days before delivery and "incentivized" to change their reservation to another product. Re-planing is used to create inventory for high-paying customers when in a stockout or fully overbooked situation. A revenue gain to the seller occurs when a new customer will pay more for the product than it costs to incentivize a booked customer to switch product, including the cost of the alternative product.

From re-planing comes the idea of dynamic passenger allocation (DPA) where a customer buys a ticket for travel during a set period but is not given flight details until a couple of days before the flight. Interesting issues that usually provoke discussion include the differences between DPA and "standby," and the fact that these were developed as airline products, but where else do they have potential?

Teaching Materials


RM teaching materials suitable for a business school class are scarce, but more are appearing all the time. I use my own on-line "MBA" level course that works through the above concepts and includes some problems. We use three cases:

• Four Star Motorsports [10] provides an example of demand curve estimation (regression) and use of a non-linear Solver model to compute optimum variable prices and then dynamic prices.

• National Car Rental [11] is a strategic case that looks at RM as a turnaround strategy. The focus is on National's prior business situation and the results of introducing RM. There is a 10-minute video for classroom use that shows the RM system in use and discusses the impact of the work. There is also an Interfaces article and a longer tape describing this application.

• On-line Low-Price Guarantees — Dollar.com (A) [5] is about one particular pricing method and introduces some interesting marketing and estimation issues.

How Much Course Time?


In the Ivey EMBA programs, we cover the above materials in one half-day class in the core O.R. course. In our full-time business programs, we devote about three classes (an hour and 20 minutes each) of our core course to these materials. The EMBA students do a major course project, and typically about half the students choose a RM application in their firm. Examples include introducing some degree of variable pricing at work (rail freight, ice rinks, apartment leases), or developing a business plan to bring RM to a non-traditional product (cinemas, magazines, golf courses).

Conclusions


RM is a powerful combination of O.R., management and real life, and can be a "memorable" component of any business school O.R. course. Comments such as these from our open-ended teaching evaluations confirm this impact:

• "RM was great! It showed me a new way to look at and evaluate competition that I was totally unaware of."
• "RM is really neat stuff."
• "RM gave me the knowledge to gain revenue for my company."
• "I really enjoyed the (RM) sections — most applicable to my day-to-day career."

Many business school O.R. courses do not include RM. Perhaps this is because the practice of RM involves complex algorithms operating within large information systems, but including RM in the O.R. course does not have to be a heavy mathematical/algorithmic exercise. By sticking with the basic concepts and the management issues, students can grasp practices that they have experienced but have not understood. Students armed with an understanding of these basic ideas are better equipped to manage in a world where RM is now commonplace. They will remember you and your course for opening their eyes to the world of RM.

References

1. Cook, T.M., 1998, "SABRE Soars," OR/MS Today, June 1998, pgs. 26-31.
2. Leibs, S., 2000, "Aided by New Software, the Automaker is Using Revenue Management to Boost the Bottom Line," CFO Magazine, August 2000 (www.cfo.com/Article?article=1776).
3. Taylor, C.J., 1962, "The Determination of Passenger Booking Levels," Proceedings of the Second AGIFORS Symposium, American Airlines, New York.
4. Staff and wire reports, 1999, "Coke Price Rises with Heat," CNN Money, Oct. 27, 1999 (http://money.cnn.com/1999/10/27/companies/coke/).
5. Anderson, C.A., 2004, "On-Line Low Price Guarantees - Dollar.com (A)," (9B04E016), available from Ivey Publishing.
6. Littlewood, K., 1972, "Forecasting and Control of Passenger Bookings," AGIFORS Symposium Proceedings, Vol. 12, pgs. 95-117.
7. Belobaba, P.B., 1989, "Application of a Probabilistic Decision Model to Airline Seat Inventory Control," Operations Research, Vol. 37, No. 2, pgs. 183-197.
8. Cook, T., 2001, "Revenue Management: An OR Success Story," plenary talk to the INFORMS Practice Conferences, San Jose, Calif., May 20-22, 2001. (Abstract: www.informs.org/Conf/Practice2001/speakers.htm).
9. Bell, P.C., 2002, On-line revenue management course at www.strategicmanagementscience.com.
10. Rosenshein, I.J. and Bell, P.C., 2002, "Four Star Motorsports," (9B03E006), available from Ivey Publishing.
11. Roth, D. and Bell P.C., 1998, "National Car Rental" case, available from INFORMS.

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