1.What is the problem, in words?
2. Very briefly, describe the current method of finding matchings in the exchange?
3. Come up with a solution to the problem using some common sense rules using data from Tables 1 and 2. 4. Develop a mathematical programming approach for determining an optimal exchange schedule. What are your variables? How will you choose your objective function? What are your constraints?
Timeshare Business Overview
The value proposition of timeshare is rather simple: An individual or family purchases vacation time at a shared resort property and in so doing, guarantees quality vacations for a substantial part of their lifetimes—at effectively current prices.
Timeshares originated in the early 1960s, when Alexander Nette of Germany and his friends each wanted to purchase an apartment in a ski resort in the French Alps, but could not individually afford the cost. He realized that if the group pooled its money and shared the apartment it could afford the purchase; then one person would use the apartment one week, the next person another week, and so on. Nette’s idea led to the development of Hapimag Company (http://www.hapimag.com; accessed 7 August 2007), which is still a major player in the European timeshare industry.
Timeshare development in North America began in Florida in the late 1960s by effectively reproducing Nette’s original idea. After a promising beginning, the industry experienced some overheating in the 1970s and early 1980s; however, from 1984 to 2007, it exhibited 14% to 17% annual growth. Even the “dot-com” economic downturn of the early 2000s did not seem to curtail its growth. Some ownership and sales statistics are presented in Exhibit 1. With $6 billion in sales in the United States and nearly $10 billion worldwide, timeshares have become a substantial factor in the global hospitality industry.
Some of this growth was fueled by the participation of major hotel firms. Marriott began building and marketing timeshares in 1984 when it acquired American Resorts. By 2007, Hilton, Hyatt, Four Seasons, Radisson, Ramada, Ritz-Carlton, and others were among the lodging companies that offered timeshare intervals. Large independent players were also active in the market: Shell Vacations had 40,000 members and 15 resorts; Fairfield Communities (owned by
Cendant Corporation) had 260,000 owners and 22 locations; CFI/Westgate had 120,000 owners; and even Disney, with 40,000 timeshare members, had entered this market.1
The reason the timeshare industry was able to grow so quickly was that it adapted to differing lifestyles, income levels and traveling styles.
With timeshares, consumers made one-time purchases of “intervals” (usually one-week periods) of furnished resort accommodations, at a fraction of what the full ownership costs of a resort condominium would be. The accommodations were priced according to a variety of factors, including the size of the unit, resort amenities, location, brand name of the developer, and season of the year. Prices of resort intervals varied from about $3,000 on the low end to $15,000 or more on the high end (the average price for one timeshare week was $14,500 in the United States, and $11,600 wordwide). Intervals could be resold on a secondary market for prices that were often much lower.
Even though the purchase of an interval was called “ownership,” it was really just the right to utilize a given week at the resort each year. Other aspects of ownership such as changing the décor were neither the right nor the responsibility of the owner. Instead, the owner paid annual maintenance fees to the property management organization, which was often different from the original resort developer. And, in turn, the property management firm was responsible for maintaining and updating the condominium. Annual maintenance fees varied from approximately $300 to $800 for a week-long interval (the average maintenance fee was $385 in the United States, and $325 worldwide).
Unit sizes ranged from studios to three or more bedrooms. Most units included a fully equipped kitchen with dining area, washer and dryer, stereo, television, DVD/VCR, and more. Resort amenities typically included on-site restaurants, planned children’s activities, swimming pools, tennis courts, hot tubs, golf, bicycles, and spa and exercise facilities. They often featured boating, skiing, or equestrian facilities either on-site or nearby. In 2007, the selection of resorts was very broad: There were more than 5,400 timeshare resorts in some 100 countries worldwide. There are about 1,600 resorts in the United States, most of which are in Florida (366), California (125), and South Carolina (119). The average resort size was 83 units in the United States and 60 units worldwide
Over time, the way timeshares were sold evolved. The traditional interval week program offered owners the use of their property for one week—either for a specific week during the year or for a week during a time period or season (summarized in the concept of color; see below). During the early to mid-2000s, consumers sought enhanced flexibility, which fueled multiple-use options. Vacation clubs gave members access to resorts within a resort group, under a variety of different plans. In point-based programs, owners purchased points that could be redeemed for access to various types of accommodations, locations, amenities, number of days’ use, and other travel services. Point-based programs appealed to owners because they provided the flexibility to
design their own vacations. For example, points could be used to purchase airfares or car rentals, or they could be banked, borrowed, or sold back.
According to a survey2 by Ragatz Associates, typical timeshare owners were married couples who owned their home; usually at least one of the partners had a college or professional degree. Median annual household income for U.S. owners as of 2002 was reported at $85,000. Timeshare owners reported being very satisfied with their purchases—nearly 85% of U.S. owners indicated that they were either satisfied or very satisfied with their experiences. “We have taken more vacations in the last five years than we did in the 25 years before that,” said one owner, a resident of Oregon. “It’s the best purchase we ever made!” The number of satisfied or very satisfied owners varied from 67% to 92% worldwide among all owners, residing in nearly 270 countries. Among the U.S. public who had never owned a timeshare, 87% had heard of the concept, and 68% had a positive or neutral opinion of the concept. Those who owned a timeshare ranked flexibility (including location, unit size, and time of year), opportunity to exchange with other resorts, certainty of accommodation, and credibility of the timeshare company as the key factors that influenced their buying decision. On average, respondents owned the equivalent of 1.8 timeshare weeks.
Even though it is typical for timeshare owners to buy into resorts they are interested in visiting, data showed that owners were much more likely to exchange for a different resort or week than use the interval they originally purchased. Only 26% used their own intervals—that is, took vacation during the week and at the resort they actually owned. Twice as many owners (58%) chose to exchange or bank their vacation time, 4% gave it to family or friends, and another 4% rented it.
The importance of the exchange privilege is further corroborated by the fact that almost all owners (96%) belonged to at least one exchange company, and almost three-quarters (72%) indicated that they would not have become involved in timesharing without the exchange system. On a 3-point scale, (3 = very important, 2 = somewhat important, 1 = not important), the exchange opportunity (mean = 2.63) ranked just behind certainty of accommodation (2.74) and good value for money (2.65) and was right on par with liking the resort or some particular aspect thereof (2.63).
Interval-exchange companies made it possible for timeshare owners to vacation at resorts other than the one(s) at which they owned property. Two large trading companies, RCI and Interval International, became successful by facilitating the trading of one owner’s week for someone else’s week in another location. Both companies were founded in the 1970s, but RCI, now located in Parsippany, New Jersey, and owned by Cendant Corporation,, is the larger, with
2.5 million participating owners and 3,500 participating resort properties. Located in Miami, Interval International (II) offers 1,800 properties for its 1.8 million members. Although several small trading companies existed, in 1998, a total of 2,414,336 exchanges, or 99% of all timeshare exchanges in the United States, were conducted by RCI and Interval.4 Both companies levied a fee ($129 to $179) per exchange, which the owners paid for facilitating the interval trades (the average exchange fee was $165 in the United States, and $120 worldwide). Some of the timeshare companies themselves also offered interval-trading options. For instance, Marriott offered its owners the opportunity to trade intervals with other Marriott locations.
As previously mentioned, there was a secondary market for timeshare intervals that was discounted from the primary market. One reason for this was that some owners no longer desired to use their resort weeks, but had to pay the annual maintenance fees nonetheless. It could be more attractive to sell the interval for a fraction of the original purchase price than to simply stop paying the maintenance fees and thus forfeit the property. An alternative, however, was to gain renewed value by paying the exchange fee and attempting to exchange the interval for intervals at different resorts and at different times of the year. Thus, timeshare exchange could be an important value-adding activity.
There were two main business models for timeshare exchange: “ongoing exchange” and “exchange fair.” In the ongoing model, an owner submitted his or her interval(s) at any time, paid an exchange fee, and had the option to select an interval of his or her choice from the trader’s database at that moment or some later time. In the fair model, all owners’ requests were collected into a centralized pool and on a specified day a one-shot exchange was executed. Exchange fairs also typically involved an exchange fee. Although the ongoing model provided more flexibility, its main criticism was that the quality of the exchange could not be guaranteed due to its dependence on random arrival of customer intervals and requests. In particular, an owner’s “best match” could arrive after his or her request had been satisfied, leaving that owner with a less desirable interval. The exchange fair had the potential to mitigate this issue, if owners were willing to comply with its timing and structure.
Ongoing exchanges were much more common than exchange fairs. Historically, the ongoing model emerged first, and both RCI and II facilitated this kind of trade. Several success strategies were used to improve the ongoing exchange results: Owners were advised to submit their requests well in advance, “be as flexible as possible,” and even “consider a trip in the off- season or visit a lesser-known destination.”
Exchange fair models were less common, largely because they were not provided by major exchange companies. But they held much promise because they could provide better probabilities of successful exchange.
Timeshare Resorts and Exchanges, Inc.
Richard A. Wall was a president of Timeshare Resorts and Exchanges, Inc. (TRE), a timeshare management company that provided exchanges within the properties it managed. This timeshare trader had some 20,000 registered owners, owning in total about 47,000 timeshare intervals at nearly 60 resorts in North America. TRE did not develop new resorts; nor did it sell timeshares on the primary market. It was in the business of managing existing resorts, which included collecting annual maintenance fees, maintaining properties, paying insurance and other fees, and staffing the properties. TRE also managed the exchange mechanism. For exchanges outside of TRE properties, TRE was affiliated with both RCI and II, allowing owners to have much broader exchange opportunities. But one advantage of TRE owners’ exchanging within TRE’s network of properties was that the exchange fee was about $75—much lower than RCI or II fees. In addition, RCI and II charged membership fees, which TRE did not.
TRE provided a regular ongoing exchange, and for several years they had also organized an annual exchange fair event that took place in May/June. In these fairs, participating owners submitted (by phone, by regular mail, or on-line) their existing timeshare intervals (or their point-equivalents), together with their preferences on the resort weeks they wanted to obtain. Owners had several months to submit their requests before the exchange deadline. It was then up to TRE to come up with the exchange schedule—that is, who gets which interval.
TRE’s strategic mission was to provide “a better exchange.” Maximizing the number of satisfied requests (i.e., the quality of exchange) was also critical from two different financial perspectives: (1) exchange fees were a major source of traders’ revenues; and (2) the marginal cost of executing an additional exchange was negligible. Putting it simply, a dollar earned from exchange contributed directly to the profits.
Functioning of the Exchange Fair
There are several factors influencing the functioning of the exchange:
Quality of an interval (ownership)
The standard way timeshare companies denoted the quality of an interval was by assigning each week at each resort a color: Red stood for the highest quality; White signified medium quality; and Blue indicated a standard-quality interval.
Owner type (status)
Normally, owners would be associated with the same color as their submitted intervals. There were two exceptions to this general rule. An owner who submitted several intervals with different colors possessed all the colors. For example, if an owner submits a Red and a Blue week, then he or she would be simultaneously a Red and Blue owner (another way of looking at
this is that the owner would have two credits—one Red and one Blue). The second exception was the so-called Gold status. This special status could be purchased by an owner of any color, and provided these benefits in the exchange: A Gold owner could request an interval of any color, regardless of his or her submitted interval, and he or she was guaranteed to get one of his or her preferred choices, or get his or her submitted interval back.
Intervals and color conversion
It was rather typical to value ownership at the same resort differently depending on the time of year. For example, Christmas week was often categorized as Red, even at a medium- or regular-quality resort. On the other hand, a week in mid-May in San Diego, California, was Red (because it was a popular location and time). The same week at the Horseshoe Resort in Ontario, Canada, was Blue (because of the location and the midseason decline in available activities)
Types of units available
Most resorts have a variety of units—such as hotel-style rooms, condominium apartments with several bedrooms, or even detached bungalows. The pool of available units consists of two components—units submitted by the participating owners, and units owned by the company for exchange. The latter units could represent the unsold units, as well as the units booked for the owners participating in the point-based ownership.
As discussed above when putting his or her resort week on the Exchange Fair system, the owner also requested the location, unit type and interval he or she wanted in return. This was done by ranking the choices. For example, first choice, Orlando, Florida, January 4 through 12, hotel room; second choice, San Diego, California, April 11 through 18, one-bedroom condo, and so on. Any number of choices would be allowed. During a 2007 fair, Wall’s firm observed that the average number of choices was 18, with the standard deviation of 22. Some 400 owners submitted only one choice; however, there was one owner with 109 choices.
A non-Gold owner was allowed to request resort weeks only up to the number of intervals (credits or point-equivalents) he or she actually submitted in the corresponding color. This restriction relied on two fundamental concepts: fairness and brand equity. Allowing higher- color owners to access lower-color intervals would leave the lower-color owners with a smaller pool of intervals to select from, and was therefore unfair. The reverse could potentially lead to long-term negative effects of diluting the brand equity of higher-color (and therefore more expensive) ownerships. Despite these restrictions, some owners, either by mistake or intentionally, at times submitted requests in colors they did not own. Such requests (of non-Gold owners) must not be satisfied.
Traders’ beliefs played a crucial role in estimating the relative importance of matching a particular owner with various types of units at a particular resort and week. This can be viewed as a proxy for perceived profitability or preferability of matching. That was done through the notion of priority: Owners of Red resort weeks were given priority over those with White and Blue weeks with respect to their choices of the same rank. Similarly, an owner’s higher-ranked choice has higher priority than his or her own choice of lower rank, as well as a lower-ranked choice of an owner of the same color resort/week.
From the timeshare trader’s perspective, the exchange schedule should achieve two potentially conflicting goals—(1) maximize the number of owners who received their higher- ranked choices and (2) maximize the total number of owners who received any of their choices.
Although the second goal clearly represented the short-run financial benefit (recall that a fee was charged per exchange), both of them were important for spreading the benefits of participating in exchange fairs, which increased a trading company’s revenue potential in the long run. The problem was that maximizing the assignment of higher-ranked choices could potentially mean (and in fact often did mean) that some owners would get their higher-ranked choices at the expense of other (low-priority) owners getting none.
To execute the exchange, Wall’s firm used the following preference-ranking procedure. First, a numeric preference score was associated with every request. Then all requests were sorted in descending order of their preference scores. Finally, the trader satisfied all the requests he or she could starting at the top of the list (provided that the corresponding owner had not yet had all of his or her requests satisfied) leaving the rest empty-handed.6 The rationale for using such an approach is evident—it assured that the requests that were more important (i.e., had higher preference scores) were satisfied prior to those that were less important. It also matched well with the priority system currently in place.
Wall had recently heard about optimization techniques and, among them, about linear programming. He believed that these could be used to further increase the quality of the exchange, and potentially increase the number of satisfied requests, which would result in additional revenues for his firm. But neither Wall himself nor any of his staff was experienced with optimization, and they had no software to do it. They had to make a case to support investment into the development of the optimization system, purchase the software, and build human capability in this area. He believed that a simple example, illustrating the potential inefficiency of the current ranking procedure, could be of great value. Apart from optimization, Wall was thinking about whether it was possible to somehow improve an existing exchange schedule.
Creating an “Optimal” Exchange Schedule
Wall was becoming more and more concerned that the schedules they were creating were not optimal and could be improved. This meant that TRE was not achieving its revenue potential, and was not providing the best service to its clients—the owners.
The owners’ requests were distributed very unevenly: 75% of the requests were for 25% of the properties, and the “hottest” interval had 60 requests per available week. That is, many requests could not be satisfied under any circumstances. On the other hand, across all properties, there was an average of 11 requests per available week. Given that on average each owner submitted 18 requests per week he or she owned, the overall problem looked promising for further “optimization.”
Wall put together a small team, which started to think about how to employ linear programming for their exchange fair. It all seemed to work: On one side they had the owners with their submitted resort weeks, and on the other side were the requests, some of which had to be satisfied, keeping in mind the existing restrictions and priorities. Yet they had trouble formulating a linear program. Specifically, Wall was very concerned that linear programming assumed a single objective, whereas he had two: to maximize the number of owners getting their top choices, and to maximize the total number of fulfilled requests.
Wall understood that taking care of Gold owners’ mixed-color requests would only make the problem more difficult. Therefore, for training purposes, he temporarily did not consider the benefits of Gold status. He pulled out a sample of 15 owners and their first two requests from his database and simplified it to four seasons instead of 52 weeks (Appendix 1, Table 1). Color designations were applied to resorts during various seasons based on their desirability in general and their appeal during certain seasons of the year (Appendix 1, Table 2).
This did not look that difficult, and heading for the first team meeting, Wall was confident they would have no difficulty making the exchange for this example. Thus he was already considering something trickier. In particular, for a long time, Wall had been concerned with allowing owners to request intervals in colors they did not own (which was forbidden). Indeed, there were two restrictions. The first forbade lower-color requests (downgrades)—for example, a Blue request of a White owner. The second did not allow higher-color requests (upgrades). Wall believed that these restrictions might result in substantial opportunity cost for TRE. Specifically, removing them (at least partially) could lead to satisfying more requests, and therefore earning higher revenues. Moreover, these upgrade or downgrade requests would be the requests that were at least as desirable as the ones satisfied with the restrictions in place; therefore owner satisfaction should also increase.
Wall was not about to start matching upgrade or downgrade requests—it was forbidden by the contracts TRE has with homeowners’ associations (TRE’s main clients). Yet quantifying these opportunity costs was very important from the standpoint of negotiating new contracts (or