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Article Excerpt
This paper reports on an application of network-flow integer programming to a vacation timeshare exchange problem. A typical timeshare owner has purchased yearly access to a specific week at a specific resort. The resulting lack of vacation variety is mitigated by systems that allow owners to exchange owned weeks for different weeks at different resorts according to their preferences, the assessed value of what they are exchanging, their contractual priority, and resort availability. The timeshare exchange problem is similar to other preference-based assignment problems such as labor scheduling, preferential bidding, and traditional timetabling, but different in the formulation of the objective function how the effectiveness of timeshare exchange processes can be improved through mathematical optimization, as measured by increased satisfaction of participant preferences. Optimization also presents exchange managers with the opportunity to more precisely manage preference and priority trade-offs among various classes of participants. The trade-off decisions are aided by sensitivity analysis utilizing a minmax criterion.
Subject classifications: operations research applications; optimization; service sector.
Area of review: OR Practice.
History: Received April 2005; revisions received December 2005, September 2006, January 2007; accepted May 2007.
Introduction
This paper reports on a study of customer scheduling that exists in the hospitality portion of the service sector. Specifically, the situation involves the timeshare industry, where individuals "own" specific weeks of resort properties or own credits for annual access tow weeks of resort properties. (These units of ownership are called intervals.) In the United States alone, there are more than 1,6000 timeshare resorts with an estimated annual economic impact of $29 billion (American Resort Development Association 2006).
This research considers an assignment problem that occurs in a timeshare exchange system. Timeshare exchanges are extremely popular because they allow timeshare owners to have vacation variety from year to year (Withiam 1993). A 2002 survey of 1,062 timeshare owners revealed that 62% planned to participate in an exchange within the next 12 months, which emphasizes how important exchanges are to the timeshare industry (RCI 2002). The company studied in this paper is Owners' Resorts and Exchange (ORE), a timeshare management company based in the United States, which manages resorts in North America. ORE offers a program called "Annual Scheduling" (AS), in which owners of various resort intervals can participate in an exchange process that occurs once per year. AS differs from traditional timeshare exchanges in that AS is an event, whereas traditional exchanges are ongoing.
AS operates as follows: Once each year all interval owners desiring to participate in AS submit their owned intervals to the AS exchange pool and also submit lists of choices for substitute intervals. The participants are given assignment priorities based on what they own, including subpriority levels that rotate values year to year (to give more people access to the best resort weeks). Priority rules are dictated by ownership contracts and company policies, yet are nonetheless subject to some degree of interpretation. All exchange choices must be submitted to ORE by May 31 of the specific year, with the choices being for resort assignments for the following calendar year. On a day in June, the AS participants' choices are considered as a large-scale assignment problem.
Most interval owners who are allowed to participate in AS have the option of instead participating in a more traditional exchange, wherein they submit their intervals and look for substitute intervals at any time of the year. In the past, AS has been quite effective at satisfying the requests of most participants at a level that is believed to be superior to traditional exchanges. Nevertheless, ORE management would prefer to increase the effectiveness of AS as much as possible because more successful exchanges means more collected exchange fees and greater loyalty from the interval owners associations who contract with ORE.
The purpose of this paper is to describe the successful application of optimization of the AS problem. Three major objectives of this paper are: (1) to demonstrate how the complexities of AS were incorporated in a solvable optimization model, (2) to illustrate the dilemma that comes from having multiple objectives, and (3) to show how sensitivity analysis can be used to mitigate that dilemma.
The next section will discuss related literature. A mathematical formulation is then developed, including the complexities of interpreting the priority rules in forming candidate objective functions. A section discusses the solution methodology, data collection, and results. Managerial decision implications are then discussed. A letter from the company president, which attests to the value of this application, is included in the online appendix. An electronic companion to this paper is available as part of the online version that can be found at http://or.journal.informs.org/.
Summary of Related Literature
A search of literature revealed no prior published research concerning the application of optimization techniques to the timeshare industry. The closest published research involves fractional aircraft ownership scheduling, which Martin et al. (2003) says is similar to timeshare resort scheduling except "owners are guaranteed access to an aircraft whenever and wherever they need it with as little as four hours of notice" (p.23). One key element of successful timeshare resort scheduling is advance planning, which is particularly important in applying mathematical optimization as we describe below.
The AS problem is a people-scheduling problem, and is related to other people-scheduling problems such as services staffing (Mabert 1986) and scheduling (Mason et al. 1998, Sarin and Aggarwal 2001). Some of the service labor scheduling research assumes the task assignments are homogenous (Easton and Rossin 1996, Mason et al. 1998, Thompson 1992), thus allowing preferences for time periods but not task assignments. However, other such research considers multiple tasks with distinct preferences for assigning given individuals to given tasks (Loucks and Jacobs 1991, Love and Hoey 1990, Ritzman et al. 1976). In some cases, the assignments are governed by complex rule systems, as is the case with AS (e.g., Loucks and Jacobs 1991, Rachamadugu 1991). Perhaps the most similar problem type is nurse scheduling (Jaumard et al. 1998).
A primary difference between traditional labor scheduling problems and the AS assignment problem is in objective function specification. A variety of objective functions have been used in labor scheduling (Bechtold et al. 1991). One common objective is maximizing the total labor hours scheduled (e.g., Mabert and Showalter 1990, Mason et al. 1998). Other objectives include minimizing the number of employees scheduled (Baker et al. 1979, Easton and Rossin 1991, Hung 1994), minimizing labor costs (Easton and Rossin 1996, Jaumard et al. 1998, Lauer et al. 1994), minimizing overstaffing (Loucks and Jacobs 1991, Love and Hoey 1990), and maximizing the utilization of employed labor (Jacobs and Bechtold 1993). These are all highly correlated with minimizing the total number of labor hours.
Granted, some instances of labor scheduling take into consideration employee preferences for assignments (Thompson 1999). This is particularly true of nurse scheduling (Miller et al. 1976, Warner 1976). Nevertheless, even in nurse...
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