Prescriptive analytics for FIFA World Cup lodging capacity planning

Abstract The FIFA World Cup, comprising sixty-four matches spanning an entire month, has, in recent years, been attended by about three million spectators of which over half a million are visitors requiring lodging. Planning lodging capacity for an event of this magnitude is necessary for host nations where pre-existing infrastructures are either inadequate or lacking. This paper develops an optimization analytics framework that sequentially employs two integer programming models for foreign spectator analysis and the consequent lodging requirements. The framework is applied to assess the preparedness of lodging infrastructure in Qatar for FIFA 2022.


Introduction
Examination of existing and planned infrastructures for holding football matches and lodging foreign spectators is central to hosting the FIFA World Cup. Infrastructure planning for Qatar 2022, with much of the lodging capacity yet to be constructed, is unique and departs from past FIFA World Cups. Lodging infrastructure has not been an issue for recent FIFA World Cups since matches have been held in cities with large populations and an established hotel industry. The currency of examination of the potential demand for lodging is a consequence of the expectation that much of the attendance will be made up of foreign spectators given that the entire country's population is a mere fraction of that of most host cities in past World Cups. The total population in the host cities was over twenty million for South Africa 2010, over thirty-five million for Brazil 2014 (with individual host city populations ranging from about half a million to over eleven million), and over twenty-four million for Russia 2018. Qatar, which has the third highest GDP per capita, has committed $20 billion for investment in tourism infrastructure under the ''Qatar 2030 Vision'' for economic growth and development (Cighi and Gandhi, 2011).
Planning expansion of Qatar's hotel capacity of 13,123 rooms in 83 approved hotels, in 2013, is necessary years in advance of the upcoming World Cup to allow for construction lead time. To determine appropriate capacity for lodging, it is necessary to account for, and incorporate, likely variation in foreign spectator attendance. The variation that must be taken into account is contributed to by the makeup of the qualifying teams, the buying power in, and the ability of fans to travel from, the associated nations, the groups for the World Cup that are constituted by FIFA, and the detailed match schedule. As such this work lies at the interface of attendance forecasting and scheduling. The work furthers the existing body of literature on operations research studies in sports management that has, hitherto, not included lodging capacity analytics. Foreign spectator attendance is influenced by the buying power in nations, and hence, multiple scenarios that differ in the composition of qualifying teams must be considered. For each scenario, the total number of spectators will depend on the capacity of the stadiums in which matches are held. Hence the specific match schedule must be taken into consideration. In Section 1.1, we familiarize the reader with the FIFA process of group formation and the World Cup schedule characteristics. In Section 1.2, we review the relevant literature on sports and tourism management. In Section 1.3, we provide an outline of the paper.

Background
Since 1998, teams from thirty-two nations drawn from six football confederations 1 compete in the FIFA World Cup. The 1 past five and upcoming World Cups have been held in either G7 (namely, France 1998, Japan/South Korea 2002, and Germany 2006 or BRICS nations (namely, South Africa 2010;Brazil 2014;Russia 2018). Table 1 summarizes the characteristics of FIFA World Cups since 1998 as reflected in the geographic and demographic attributes of the host country, the number of stadiums, the attendance, and the host confederation. The World Cup has been predominantly hosted by CONMEBOL and UEFA nations and, only relatively recently, hosted once by an AFC and a CAF nation where significant investment in infrastructure development was required.
The sixty-four matches that the FIFA World Cup comprises are played in two stages: Pairs of teams from 32 qualifying nations compete in the forty-eight matches of the group stage; there are sixteen matches in the knockout stage which has half as many competing teams. In the group stage, there are six matches for each group of four nations-labeled A through H-with each team playing three matches. The teams in each group are ordered (from 1 to 4) with respect to the FIFA ranking, which is inversely related to the FIFA points for a team. Teams are assigned to a group letter using FIFA's random selection mechanism that iteratively draws teams sequentially from four pots of eight teams that are ranked on the most current FIFA points. The drawings abide by two primary governing FIFA stipulations: (i) Nations in any pairing from the same pot must be assigned to distinct groups; and (ii) nations in any pairing from the same confederation must be assigned to distinct groups, except for UEFA for which up to two nations can belong to the same group (Frawley and Adair, 2014).

Relevant literature
Lodging capacity management for the FIFA World Cup is novel and has not been studied in the academic literature despite the wealth of analytics studies in sports management (Wright, 2009;Rabadi et al, 2015). It is pertinent to situate this paper within the two relevant themes that it ties together, namely forecasting attendance at mega-sport events and analytics for scheduling sport events.
Within the literature on general tourism forecasting, a few studies pertain, specifically, to forecasting the number of foreign and domestic attendees for a mega-sports event. Rabadi et al (2015) point out that the influence of mega-events on inbound tourism is not straightforward to predict. A few studies have focused on assessing the impact of holding a mega-sports event in a nation on tourism (Fourie and Santana-Gallego, 2011). Whereas the FIFA World Cup, the Summer Olympics, or the Cricket World Cup was found to increase inbound tourism in the host nation, the Winter Olympic and Rugby World Cup negatively impacted tourism during the hosting of the event. Keum (2010) employed a gravity model to assess tourism activity between two nations in general, without any particular focus on mega-sports events. Further, some studies employ qualitative approaches such as the Delphi method to ascertain short term inbound tourist flows for a host nation. Lee and Kim (1998) examined the expected foreign tourist demand for the 2002 World Cup in South Korea using a Delphi study that involved responses from 41 experts over two rounds of questionnaires.
Topics in sports analytics over a 50-year period, as surveyed by Wright (2009), have included game strategies and tactics, predictive analytics for the outcome of different matches, fixture and official scheduling, and a variety of other operations research studies (e.g., Duckworth and Lewis 1998). The methodologies used in sport analytics (Kendall et al, 2010) include optimization, probabilistic modeling, and choice models (Fry and Ohlmann, 2012). A rich body of literature on sports scheduling covers sports such as basketball (Westphal, 2014), soccer (Durán et al, 2012), and tennis (Ghoniem and Sherali, 2010). Integer optimization models have been extensively used for scheduling sport events (Fry and Ohlmann, 2012), employing objectives and constraints that are tailored to specific recreational and professional tournaments (Ribeiro and Urrutia, 2012;Durán et al, 2012;Ali et al, 1986a, b;Ghoniem and Sherali, 2010).

Paper organization
The optimization analytics developed in this paper incorporates FIFA specifications and processes that dictate foreign spectator attendance. Section 2 introduces salient aspects of the FIFA process of group formation and the World Cup schedule characteristics to establish the premise for an overview of the proposed framework. We assume that groups of comparable strength will lead to greater spectator interest and, therefore, attendance. Our methodology, developed in Sections 3, 4, and 5, is accompanied by a detailed illustrative example. In Section 3, we present an integer programming model that incorporates FIFA stipulations to partition the 32 qualifying nations into eight subsets of comparable skill. In Section 4, a second optimization model assigns these eight subsets of teams to lettered groups, A through H, such that the percentage fill of stadiums is maximized. In Section 5, we detail the calculation of foreign spectator attendance at each match and, therefore, the total daily foreign spectator attendance and the associated lodging requirement. Section 6 applies the framework to determine required lodging capacity for FIFA 2022 by examining the data obtained from 144 instances based on 16 scenarios that differ in the composition of qualifying teams. In Section 7, we make concluding remarks.

Framework for attendance analytics
Overall attendance, and consequent demand for lodging, varies due to the strength and popularity of the qualifying teams and on whether the matches that a nation plays are in high-or lowcapacity stadiums. It can be expected to be higher when matches between highly ranked teams or teams from neighboring countries are assigned to higher-capacity stadiums. Attendance is further influenced by the pre-specified percentage of stadium seats that FIFA allocates to officials and spectators from the competing nations, other nations of the world, and the host nation. Offered seating capacity for fans from a nation is 12% of the 91% of seats in a stadium, since 9% of the seats are reserved for officials. Attendance is heavier during the group stage and, in particular, during its last four days when four matches are held daily. Table 2 displays a prototypical group stage schedule with twelve stadiums (as for Brazil 2014) specifying the day-1 through 15-and the stadium for each match. Each row in the schedule specifies a subset of four matches, henceforth referred to as a row-set, that are to be held in a pre-designated stadium of known capacity. The methodology we develop for planning purposes aims to determine the highest possible attendance for an array of plausible scenarios of 32 qualifying nations. To gauge maximal attendance requires departing from FIFA's randomly determined lettered group formation and the pre-assignment of stadiums to each row-set. The methodology forms subsets of teams that are optimally balanced with respect to total FIFA points and, further, assigns more popular matches to largercapacity stadiums. Popularity of matches is guided by the popularity and strength of teams as summarized by, what we refer to as, the spectator index which estimates the percentage of seats allocated to a qualifying nation that will be filled. To illustrate the methodology, we refer to the set of 32 nations that might qualify for Qatar 2022 listed in Table 3 which reports the confederation and FIFA points for each nation.
The spectator index is a weighted average of the ratio of expected attendance to offered seating capacity for each of the three matches for a nation. The expected match attendance by fans from a nation, denoted g, is taken to be a third of the nation's total number of spectators in South Africa 2010. For a nation that did not participate in South Africa 2010, the value for g is based on that for the closest nation from its confederation adjusted by the ratio of their GDP per capita. Neighboring countries are assigned an index value of 100%. For Qatar, the largest stadium is Lusail with a capacity of 86000, the second largest is Khalifa with a capacity of 65000, and the other ten stadiums have capacities of about 45000 seats. Noting that each stadium hosts four matches, the probability that a match is held in Lusail and Khalifa is 4 48 , and in one of the other stadiums is 40 48 . Using FIFA's seat allocation percentages, the number of seats offered to spectators from a nation would be either 9391, 7098, or 4914 if the match is held in, respectively, Lusail, Khalifa, or one of the other ten stadiums. The spectator index is computed as a weighted average using the probability of a match being held in a specific stadium: minf1; 4 48 ðg=9391Þ þ 4 48 ðg=7098Þ þ 40 48 ðg=4914Þg. Table 3 also reports the estimated spectator index values for our illustration. The value is low for nations that are distant from the host nation and/or have a lower GDP per capita, e.g., Honduras. It is higher for countries that have a loyal fan base or a high GDP per capita, such as England, USA, or Brazil.

Formation of eight team subsets with comparable FIFA points
In this section, we develop the Group Formation Model that optimizes the partitioning of the 32 qualifying nations into eight team subsets. The model identifies subsets of comparable strength, as reflected by the FIFA points accumulated by each nation using a Chebyshev objective function. The notation, variables, and model follow:

Data Sets and Input Parameters
• N : Set of 32 qualifying nations.
• p i : FIFA points for nation i; 8i 2 N .
• c i : Confederation to which nation i belongs, 8i 2 N .
. . .; 4: Pot of eight nations at the k th level of FIFA points; p i ! p j ; 8i 2 P k 1 ; j 2 P k 2 jk 1 \k 2 . (The teams in the first pot have the highest points and teams in the last pot, the least.) • G f1; . . .; 8g: Index set of team subsets to be formed.

Decision Variables
• x ig 2 f0; 1g : x ig ¼ 1 if and only if nation i is assigned to subset g, 8i 2 N ; g 2 G.
The objective function (1a), in conjunction with Constraint (1b), maximizes the minimum total FIFA points in a subset, thereby forming subsets of comparable strength. Constraint (1c) assigns four teams to each subset and Constraint (1d) assigns each nation to a unique subset. Constraint (1e) not only ensures that the top eight nations, i.e., 8i 2 P 1 , seed different subsets, but, more generally, ensures that any pair of nations in the same pot is assigned to distinct subsets. Constraint (1f) ensures that nations in the same confederation are assigned to distinct subsets and Constraint (1g) imposes a similar, more relaxed, limitation for UEFA. Because UEFA has a quota of 13 qualifying nations, five of the eight subsets will necessarily include two UEFA teams. Constraint (1h) introduces logical binary and non-negativity restrictions on decision variables. For the example of 32 nations in Table 3, introduced in Section 2, the FIFA points range from 300 for Qatar (the host nation) to 1770 for Germany, with an average of 935 points. The optimally balanced subsets obtained by applying the Group Formation Model are reported in columns 2-5 of Table 4. The subsets are remarkably balanced with total FIFA points ranging from 3732 to 3770 and both high-and lowperforming teams distributed across subsets. Each of the eight subsets has one nation from the highest FIFA points pot, i.e., P 1 . 2 In optimizing the assignment of nations to subsets that are balanced with respect to total FIFA points, the formed subsets are expected to be more competitive than alternative FIFAcompliant subsets. Heuristically formed groups are likely to exhibit a greater discrepancy between the lowest and highest group points. A ''profile-fitting'' heuristic that iteratively assigns a team with the lowest points to the group with the largest total points at that iteration is reported in columns 7-10 of Table 4. This grouping is not as balanced, obviously, as reflected by a spread of 791 FIFA points (the minimum subset FIFA points is 3090 and the maximum is 3881) compared to only 38 in the obtained optimal grouping.

Lettered group and stadium assignments
The larger purpose of the Group-Letter Assignment Model is to spread popular matches across different stadiums while ensuring that the more popular matches are predominantly assigned to high-capacity stadiums. We introduce the construct of match popularity denoted by p g;ði1;i2Þ , 8g 2 G; ði 1 ; i 2 Þ 2 M g where M g is the set of six group stage matches for subset g. The attendance for a match comprises fans from the two competing teams, fans from other nations, and officials. For a match between teams i 1 and i 2 in subset g, it is defined as the summation of spectator indices for: • the first competing team, f i 1 2 ½0; 1; • the second competing team, f i2 2 ½0; 1; • other nations,f gði1;i2Þ ¼ We point out that a match between high-performing teams and/or neighboring nations, i.e., with fan participation indices of 1, will have a popularity value of 4.
The row-set popularity is the sum of the match popularity values of the matches scheduled in the row. It is only when a group letter is assigned to each subset of nations that the match popularity values can be determined. The assignment of group letters must simultaneously address the impact on the rowpopularity of six different stadiums because the six matches for each group are held in six distinct stadiums. Since we seek to estimate maximal possible attendance for planning purposes, the assignment should balance popular matches across stadiums. To ensure balanced attendance across all stadiums the model that we develop maximizes the minimum row-set popularity. Further, to ensure high attendance at larger-capacity stadiums, the model also maximizes the maximum row-set popularity. Given the complexity of this scheduling task, it would be difficult to construct a heuristic scheme that achieves these objectives. The notation, variables, and model follow:

Data Sets and Input Parameters
• R: Index set for row-sets.
• G: Index set for the eight subsets of teams obtained from the Group Formation Model, with the host nation assigned to Subset 1.
• L fA; B; . . .; Hg : Group letters. The host nation should belong, by FIFA convention, to Group A.
• M g : Set of matches for subset g, 8g 2 G.
• q i : Rank order of team i within its subset based on FIFA points (except for the host nation which, by convention, leads its subset).
• v r 2 f0; 1g: Binary variable to effect computation of the maximum row-set popularity 8r 2 R.

Model
Maximize w min þ w max ð2aÞ subject to w min y r ; 8r 2 R ð2bÞ w max ! y r ; 8r 2 R ð2cÞ z; v binary; y; w min ; w max ! 0: The objective function in (2a) maximizes the sum of the maximum and minimum row-set popularity values which are computed via Constraints (2b)-(2e). Constraint (2b) enforces maximization of the minimum row-set popularity. To enforce the maximization of the maximum row-set popularity is more complex and requires the introduction of the auxiliary variable v r in Constraints (2d) and (2e) without which the objective would be unbounded. Constraint (2f) computes the row-set popularity, and Constraints (2g)-(2h) are assignment constraints for the eight team subsets and group letters. Constraint (2i) pre-assigns the host nation subset to group letter A. Constraint (2j) enforces logical binary and non-negativity restrictions on variables.  The obtained solution to the model is used to assign stadiums to row-sets by maximizing P s2S P r2R j s y r , where S is the set of stadiums with capacities j s ; 8s 2 S, and y r ; 8 2 R, the optimal row-set popularity values. The obtained solution in Table 5 reports the capacity of the assigned stadiums, the corresponding row-set popularity, and the popularity of each of the 48 matches, ranging from 0.13 to 4.00 in our example. The largest capacity stadium (Lusail with a capacity of 86,250) is assigned to the row-set with the maximum popularity and the smallest stadium (Qatar University with a capacity of 43,520) hosts the row-set with the minimum popularity. In the optimized solution, Group 1 through is assigned to, respectively, letter A, D, H, E, B, G, F, and C. Consequently, the popularity of 1 is 12.94/16. In contrast, row-set 12 has the lowest popularity of 5.35/16.

Foreign spectator attendance and lodging
In this section, we detail the calculation of the projected foreign spectator attendance at a match by applying the spectator indices and FIFA seat allocation percentages to the capacity of the stadium at which the match is scheduled. This, in turn, allows the estimation of daily lodging requirements over the fifteen days of the group stage.
The FIFA seat allocation for each match is based on the percentage of stadium seats reserved for officials, denoted by a, and the percentage of the remaining seats, denoted by b, that is offered to each of the two competing and other nations. Following FIFA practice, for a match m ði 1 ; i 2 Þ 2 M g between two nations in subset g, held at a stadium with capacity j ði1;i2Þ , the number of seats reserved for officials is a Â j ði1;i2Þ and for each of the two nations and other nations is ð1 À aÞ Â b Â j ði 1 ;i 2 Þ . The remaining, namely ð1 À aÞÂ ð1 À 3bÞ Â j ði 1 ;i 2 Þ , seats are offered to the host nation. Applying the spectator indices to the allocated seats for a match, the projected attendance is calculated as follows: • Number of officials:F m ¼f g;ði 1 ;i 2 Þ Â Â aj ði 1 ;i 2 Þ Ã .
The lodging requirement for the group stage depends on the number of nights spent by spectators from qualifying nations, other nations, and officials. Spectators from a qualifying nation might attend only one ({1}, {2}, or {3}), two ({1, 2} or {2, 3}), or three ({1, 2, 3}) group stage matches. 3 We assume that spectators from non-competing nations and officials attend, on average, a single match. The possibility of extended stay will be different for spectators from neighboring nations, non-neighboring nations with low, and non-neighboring nations with high GDP per capita. We denote the percentages of spectators from a neighboring nation i that will attend all three matches by p N 123 , two matches by p N 12 or p N 23 . Similarly, percentages for non-neighboring high and low GDP per capita nations are denoted with a superscript of, respectively, H and L. These percentages are applied to the number of spectators, F i m1 ; F i m2 ; F i m3 , for nation i attending the individual group stage matches, m 1 , m 2 , and m 3 , to calculate number of spectators that attend one or more matches. The computations are as follows: 1. Spectators attending all three matches: 2. Spectators attending matches 2 and 3: U i;23 ¼ p N 23 minfF i m 2 ; F i m 3 g j k ; Figure 1 Allocated and filled seats for foreign and local spectators for group stage matches.
3. Spectators attending matches 1 and 2: U i;12 ¼ p N 12 minfF i m 1 ; F i m 2 g j k ; 4. Spectators attending match 1: U i;1 ¼ F i m1 À U i;123 À U i;12 ; 5. Spectators attending match 2: U i;2 ¼ F i m2 À U i;123 À U i;12 À U i;23 ; 6. Spectators attending match 3: The number of nights required for each of the six spectator categories is the number of spectators multiplied by the number of nights spanning the first and last matches they attend.
For our example, we use the established FIFA values for the two seat allocation parameters, a ¼ :09 and b ¼ :12. Figure 1 displays the data reported in Table 6 for the stadium capacity, projected foreign and local attendance, the percentage foreign and overall attendance-assuming a 100% fill of the seats allocated to the host nation. The projected number of foreign spectators for the England-Iran match (Match 39 in Table 6) 28,406 since both the spectator indices are 1. That for the Qatar-Germany match (Match 1) is 32,569 (i.e., 90% of the 36,016 seats allocated to foreign spectators and officials). The average percentage attendance at stadiums varies significantly, with a high of 82% for foreign attendance and 92% overall at Lusail (Matches 1, 21, 33, 45) and a low of 34% for foreign attendance and 72% overall at Qatar University (Matches 14,26,36,48). A relatively higher lodging requirement for fans from a nation can be due to not only a higher spectator index value, but also the assignment of its matches to high-capacity stadiums. Aggregating the lodging requirement for qualifying nations, other nations, and officials, the number of hotel rooms, assuming double occupancy, varies from 21,334 (day 1) to 65,004 (day 14), as summarized in Figure 2. Just about half of the lodging requirement is for spectators from qualifying nations, while the other half is due to spectators from other nations and officials. The requirement peaks over the last four days of the group stage during which four matches are played daily.

Attendance and lodging capacity analytics
To determine a robust level of lodging capacity, we analyze 144 instances of foreign spectator attendance and the daily lodging requirement. In Section 6.1, we describe the data instances, which are based on 16 combinations of 32 qualifying nations from the six confederations, and three levels each for two key lodging determinants, namely the spectator index and the probabilities of extended stay. In Section 6.2, we analyze the data for these instances, using the FIFA allocation of seats (b ¼ 12%) for competing nations. Since Qatar is a small nation, this allocation implies that about 58% of the total stadium capacity at each match will be filled locally, i.e., not by visiting spectators. Consequently, we also examine another 144 instances in which the FIFA seat allocation percentage, b, is increased from 12% to 16% to analyze the impact of increased foreign spectator attendance on lodging.

Description of data instances
To obtain scenarios with representative and probable sets of 32 nations, we take into account criteria that include the number of appearances in past World Cups, average FIFA ranking over recent years, the most recent FIFA points, and the number of confederation cup titles. 4 The makeup of the 32 qualifying nations can impact the ordering of teams in the four pots that group composition rests on. This further determines whether or not more popular matches are held in larger stadiums with a consequent change in the lodging requirement. To reflect the  The number of slots that FIFA allocates for CAF and UEFA is certain, respectively 5 and 13. For AFC, CONCACAF, CONMEBOL, and OFC, the allocation is, respectively 4.5, 3.5, 4.5, and 0.5. The ''half-slots,'' are determined by qualifying matches between teams from these confederations. No OFC nations are included. Only one OFC nation has been included in 4 World Cups (1974, 1982, 2006 and 2010) of which Australia, now in AFC, participated twice. impact on attendance due to variation in qualifying nations and the associated spectator index values, we consider sixteen (1 Â 1 Â 4 Â 2 Â 2) scenarios of confederation lineups in which the allocated quota of nations is filled uniquely only for CONCACAF and UEFA: • CONCACAF: Costa Rica, Honduras, Mexico, and USA.
Nine instances of spectator attendance are generated for each of the 16 scenarios of qualifying nations. The three levels of probabilities of extended stay that we employ are summarized in Table 7. The three levels of spectator indices are: (i) Base level which varies from 3% for Honduras to 100% for England, based on historical data from South Africa 2010 and Brazil 2014; (ii) an increase of 10% in spectator indices; and (iii) an increase of 20% in spectator indices.

Analysis of results
In this section, we first analyze the data obtained from the 144 instances to examine how foreign attendance is impacted by the specific combination of qualifying nations, spectator index, and probabilities of extended stay. To do so, we focus on the effect these three determinants have on the peak lodging requirement, i.e., the maximum number of hotel rooms, assuming double occupancy, across the fifteen days of the group stage. Figure 3 summarizes the peak lodging requirement for the 16 instances with base parameter settings for spectator index and probabilities of extended stay. The base peak lodging requirement averages 67000 rooms and ranges from 63000 to 72000 for the sixteen scenarios. The difference in lodging requirement can be due to a slight change in the makeup of the qualifying teams. The scenarios with the least and most requirement, Scenarios 8 and 9, differ in three qualifying nations. The spectator indices for the three in Scenario 8 (Côte d'Ivoire, 0.19; Chile, 0.26; and China, 0.51) are lower than  those for the three with which they are swapped in Scenario 9 (Columbia, 0.38; Algeria, 0.50; and Iraq, 1.00). The difference has a significant impact on the group composition and stadium assignment of matches which can result in several popular matches being held on consecutive days.
As depicted in Figure 4, our analysis reveals that an incremental increase of 10% in the spectator index values increases the lodging requirement by about 3000 rooms and an increase of 5% in the probabilities of extended stay increases the capacity requirement by 600 rooms. Thus the average lodging requirement can increase from its base estimated value of 67000-75000 rooms. This suggests that it is likely that demand for lodging will require on average 7000-15000 more rooms than the FIFA minimum requirement of 60000. An interesting artifact of an increase in the probabilities of extended stay is that more matches are attended by the same spectators, with an accompanying reduction in the total number of foreign spectators in the group stage.
For the host nation's allocation from FIFA of 1.4 million seats during the group stage to be filled locally, it would require 460000 football enthusiasts, 20% of the 2.3 million inhabitants (of which only 280000 are Qatari), to attend at least three matches. This being improbable, we consider the possibility that some of these seats would be bought by visiting spectators. Whereas this would relieve the ''pressure'' on local attendance, it would generate a higher demand for lodging. To quantify this trade-off, we examine an additional 16 Â 9 instances in which the host nation's share of stadium capacity is reduced from 58% to 47% by increasing the FIFA seat allocation percentage, b, from 12% to 16%. This reallocation of about 11% of the local seats increases the lodging requirement by a substantial 25% with the average peak lodging requirement of 85000 rooms.

Conclusion
The host nation for a FIFA World Cup must plan lodging capacity well before the event. The analytics framework for lodging capacity planning presented in this paper evaluates alternative scenarios of 32 qualifying teams, incorporating key determinants of foreign spectator attendance and the FIFA seat allocation mechanism. Our study reveals that small differences in the makeup of the qualifying teams can significantly impact foreign spectator attendance and lodging demand due to resulting differences in group composition and the assignment of matches to stadiums. The optimization methodology is used to examine possible variations in these factors to determine the range of lodging demand. This, in turn, informs planning of adequate infrastructure development years in advance.