Restaurant Table Management to Reduce Customer Waiting Times

Journal of Foodservice Business Research ISSN: 1537-8020 (Print) 1537-8039 (Online) Journal homepage: http://www.tandfonline.com/loi/wfbr20 Restaurant Table Management to Reduce Customer Waiting Times Johye Hwang To cite this article: Johye Hwang (2008) Restaurant Table Management to Reduce Customer Waiting Times, Journal of Foodservice Business Research, 11:4, 334-351, DOI: 10.1080/15378020802519603 To link to this article: https://doi.org/10.1080/15378020802519603 Published online: 12 Dec 2008. Submit your article to this journal Article views: 9056 View related articles Citing articles: 6 View citing articles Full Terms & Conditions of access and use can be found at http://www.tandfonline.com/action/journalinformation?journalcode=wfbr20

WFBR 1537-8020 1537-8039 Journal of Foodservice Business Research, Vol. 11, No. 4, October 2008: pp. 1 23 REFEREED Restaurant Table Management to Reduce Customer Waiting Times Johye JOURNAL Hwang OF FOODSERVICE BUSINESS RESEARCH Johye Hwang ABSTRACT. Long waiting times can be a major source of customer dissatisfaction. Restaurant table management is an effective operational strategy that can be used to reduce waiting time, improve seat turnover, and increase customer satisfaction without costly capacity expansion. This study investigated the impact of table assignment polices on waiting time performance and the effects of key demand features (party size distribution and arrival rate) on best policy selection. A restaurant simulation model with the spatial priority concern for table location and combination showed the best policy varied by party size distribution and arrival rate. KEYWORDS. Table management, waiting time, customer demand, simulation, restaurant seating Johye Hwang, PhD, is an Assistant Professor for the Hotel and Restaurant Management Program at the University of Missouri, 220 Eckles Hall, Columbia, MO 65211 (E-mail: hwangj@missouri.edu). Address correspondence to: Johye Hwang, 220 Eckles Hall, Columbia, MO 65211 (E-mail: hwangj@missouri.edu). Journal of Foodservice Business Research, Vol. 11(4) 2008 2008 by The Haworth Press. All rights reserved. 334 doi:10.1080/15378020802519603

Johye Hwang 335 INTRODUCTION Long waiting times in restaurants can be a major source of customer dissatisfaction. Managing restaurant table capacity is recognized as an effective operational strategy that can be used to reduce customer waiting times without costly capacity expansion. Table management is the process in which a host assigns dining room tables to customers and to wait staff stations (Bendall, 1995). This also involves management of when the seats are assigned and how the server handles the station (Durocher, 2005). According to Bertsimas and Shioda s (2003) communication with the owner and manager of Soto s in Atlanta, restaurant floor managers make a considerable difference in the financial outcome by deciding when and where to seat customers. Efficient table management can increase revenue by increasing table turnover (Kimes & Thompson, 2004; Thompson, 2002, 2003). For example, restaurant tables can be combined to handle parties of any number of customers. Restaurants configured with combinable tables offer the flexibility to match the customer s party size with the restaurant table mix and achieve higher seating occupancy. Effective and efficient table management can reduce the waiting time for customers before being seated. Customers tend to be more dissatisfied with having to wait prior to service (Maister, 1985). Initial waiting time is a critical factor that determines customers wait behavior. Customers may balk upon their arrival if they see long waiting lines, or may leave during their wait if they are not seated on or near the time expected. By adjusting the configuration of restaurant tables, restaurant operators can reduce customer waiting times and provide prompt service. This strategy should lead to higher service quality and increased customer satisfaction. Despite recognizing the benefit of managing tables, researchers have traditionally limited their focus to revenue management (Bertsimas & Shioda, 2003; Kimes & Thompson, 2004; Thompson, 2002, 2003). For the objective of revenue maximization, those studies incorporated maximum tolerance wait time into their table mix model and used the wait time as a constraint. The focus of this study, however, is reducing waiting times by recognizing that waiting time is strongly related to customer satisfaction. Thus, this study focuses on waiting time, instead of revenue, as the fundamental criterion for overall system performance, which clearly demonstrates the outcome of effective and efficient table management. The challenges of managing table capacity also need to be recognized. Fluctuating and uncertain demand is one challenge identified by service firms

336 JOURNAL OF FOODSERVICE BUSINESS RESEARCH (Parasuraman, Zeithmal, & Berry, 1985). Restaurant demand is complicated because of its variability and uncertainty across many dimensions (i.e., party size and customer arrival time), which have long been recognized by many practitioners as the main causes of uncertainty in demand. By incorporating uncertainty aspect of demand with this study s table management model, the following questions will be answered: (a) what policy should be adopted given customer population (i.e., how the party size is distributed)? and (b) when should the policies be applied, and when not (i.e., busy or slow)? This study examined whether restaurant table assignment policies help to improve system performance by specifically focusing on how to assign an incoming party a table location and how to combine tables to reduce customer waiting time. Our interest also lies in how variations in the level of demand would influence the impact of table assignment policies thus reducing waiting times. Demand level can be characterized by two factors: party size distribution and arrival rate. For the purpose of this study, a party is defined as an assemblage of customers who have come to the restaurant to be seated and served together as a group; the number of customers that make up a party is variable. Customer waiting time in this study is defined as the time each customer waits prior to seating. To address these research questions, a simulation model was developed that incorporated uncertain demand and the spatial priority of table assignments. Although many operational problems can be solved using an analytical approach, such approaches do not allow for the investigation of spatial priorities when tables are combined the major aspect of table management. Thus, a simulation study was used to find the best table assignment policy by taking into account the priority for table location. LITERATURE REVIEW Benefit of Restaurant Table Capacity Management Providing capacity through effectively managing restaurant tables can reduce customer waiting times, which eventually leads to increased customer satisfaction. The major benefit of table management is that additional capacity can be created without costly capacity expansion, such as adding space for additional tables. Other types of manageable capacity directly related to the quality of service include equipment, facility, and employees. These types of capacities are thoroughly discussed in Sill s (1991, 1994) and Sill and Decker s (1999) studies of Capacity Management Science (CMS).

Johye Hwang 337 Additional studies that focused on managing those types of capacities in improving a system s efficiency include Field, McKnew, and Kiessler (1997), Hueter and Swart (1998), and Thompson (2002, 2003). However, creating and adjusting capacity resources can be costly when they require additional space; for example, the addition of new equipment and the physical expansion of existing facilities. Therefore, managing table capacity can be a more effective and cost-efficient way to improve system performance. In addition to the benefit of reducing waiting time, managing restaurant tables can result in revenue enhancement. Matching a larger party of customers with combined tables can achieve higher seating occupancy, which eventually leads to higher revenue (Kimes & Thompson, 2004; Thompson, 2002, 2003). Restaurants configured with combinable tables offer the flexibility to serve larger parties. However, combinability may not be effective when two combined tables do not perfectly fit the size of the party (for example, combining two four-tops for a party size of five). In addition, labor is required to combine tables. Thus, managing table capacity should take into consideration the various demand factors, including party size distribution. Table Management and Performance Measurement Studies on table management are conducted mostly within the framework of revenue management. Kimes, Barrash, and Alexander (1999) suggested table management as one revenue management strategy for restaurants. Thompson s study (2002) determined whether dedicated tables or combinable tables make a difference in Revenue per Available Seat Hour (RevPASH). He found that the impact of the combinability of tables varied depending on restaurant size and mean party size. Combinable tables worked best in terms of RevPASH in small restaurants with small and medium mean party sizes, whereas a table dedicated for eight customers is not efficient in keeping the seat usage high. According to the result of Thompson s simulation study (2002), for a 50-seat restaurant, the 50% combinability level yielded higher RevPASH than did dedicated tables for 60% of the possible configurations. For a 200-seat restaurant, the 50% combinability level yielded higher Rev- PASH than did dedicated tables for 54% of the possible configurations. As an extension of the previous study, Thompson (2003) examined what table configurations resulted in better profitability. He focused on Contribution Margin per Available Seat Hour (CMPASH) instead of RevPASH, because RevPASH, as a measure, is limited to revenue maximization,

338 JOURNAL OF FOODSERVICE BUSINESS RESEARCH rather than profit maximization. The study found that the optimal table configuration for profit improvement is the configurations with longer sequences of smaller combinable tables. Kimes and Thompson (2004) examined the table mix for a specific mid-scale, full-service restaurant, and recommended and implemented the ideal table mix that resulted in more effective capacity and increased RevPASH with an increase in customer volume. Bertsimas and Shioda (2003) developed optimization models using mathematical models to determine when to seat a party to achieve higher revenue. All the aforementioned studies used revenue as the performance measurement. None of the studies focused on reduced waiting time. Their primary justification for the revenue approach was that the employment of their optimal policies and models did not increase waiting times. Our research focuses more on managing waiting times through the management of tables by addressing the sensitivity of different policies in assigning tables because we view waiting time performance as a key indicator of system performance for customer satisfaction. Our experimental study focused on how variations in the level of demand would influence the impact of table assignment policies, thus reducing waiting times. Demand level was characterized by two factors: party size distribution and arrival rate. The various attributes of the two factors are described in detail in the following section, Methodology. It is anticipated that a table assignment policy that produces minimum waiting times for large-size parties may not necessarily produce minimum waiting times for small-size parties. Large-size parties require more flexibility to combine tables than small-size parties, resulting in waiting times that could be significantly minimized. We also anticipate that a table assignment policy that can significantly produce minimum waiting times when a restaurant is busy may not necessarily work the same when a restaurant is slow. Overall, the best policy should result in effective capacity management. Psychology Behind Seating In general, environments influence people s behavior. Robson (1999) introduced some ambient factors (color, sound, lighting, and scent) and design factors (exterior features, restaurant layouts, furnishing, and materials) that influence restaurant table turnovers. With respect to seating, variables that influence customers length of stay were comfort (shape and material), and configuration and flexibility of seating (Robson, 1999). The

Johye Hwang 339 descriptive study of 10 restaurants by Robson (2002) found that most of the tables were anchored; the configuration of the tables was mostly faceto-face rectangular; the table sizes were within an appropriate distance for interaction with a companion. Another study by Kimes and Robson (2004) found no significant difference between anchored and unanchored tables in the combined measure of the length of stay and money spent. The study also found that table configuration (diagonal vs. rectangular) did not make any difference in the same measurement. Despite insignificant statistical differences, the study still affirmed that seats that provided higher privacy tended to result in a higher average check and a longer than average duration compared to tables that were more exposed to other people, a service area, or the kitchen. Although our focus is not on the study of psychological aspects of seating behavior, the table assignment policies used in this study are designed to capture customers seating preferences found in the aforementioned studies. The discussion on the table assignment policies is provided in the next section, Methodology. The two alternative hypotheses tested in this study were as follows: Hypothesis 1: The best table assignment policy resulting in maximum flexibility to combine tables and thus minimum waiting time varies by party size distribution. Hypothesis 2: The best table assignment policy resulting in maximum capacity and thus minimum waiting time varies by party arrival rate. Experimental Design METHODOLOGY Our experiment focused on three factors: table assignment policies, customer arrival rates, and party size distributions. Table Assignment Policies Four possible assignment policies were suggested: Front-to-back, Out-in, In-out, and Random (see Figure 1). These sets of table assignment policies were characterized by the different priorities for table location for

340 JOURNAL OF FOODSERVICE BUSINESS RESEARCH FIGURE 1. Table assignment policies in a restaurant consisting of 25 two-top tables. Policy 1 : Front-To-Back Policy 2 : Out-In Policy 3 : In-Out Policy 4:Random 1 1 2 2 1 * 4 * 4 3 3 * an incoming party. Detailed descriptions and incentives for these polices are as follows: 1. Front-to-back policy allowed customers to sit away from the back area of a dining room (i.e., kitchen or restrooms). These noisy areas might disturb customers when servers come and go and dinnerware is clinking. Thus, the front area was given a priority for seating customers. 2. Out-in policy allowed customers to sit near the window because customers might prefer or enjoy a great outside view, or being seated near a wall or a window to secure their privacy (Kimes & Robson, 2004; Robson, 2002, 2004). This policy seated customers in the outer area of a dining room and then moved to the center of the dining room. 3. In-out policy was the opposite of Out-in policy. In-out policy takes into consideration the situation when an attraction (such as a buffet station or performance) is located in the center and customers tend to want to sit near the interesting or engaging event or activity. Attractions include, but are not limited to, fireplaces or musical performances. 4. Random policy places equal probabilities on each seat in any area. Customer Demand Level In this study, the simulation model enabled us to find the optimal assignment policy resulting in minimum customer waiting time under different restaurant settings characterized by demand conditions. In particular, the impact oftwo prominent features of the demand was investigated on the selection of optimal policies: arrival rate and party size distribution. The best policy might be interactive with customer-arrival rate and party-size

Johye Hwang 341 distribution. Thus, the best table combination policy was selected by varying arrival rates and party-size distributions. Party-size distributions were classified as large, small, a combination of large and small, or equal party sizes, with the assumption that party size range was from one to eight customers. In practice, each operation may have various sizes of parties. For example, a fine dining restaurant that has a nice romantic ambience attracts more couples than large parties. However, a sports bar with good video and audio systems may attract large parties such as families or a group of friends to watch a sporting event together. Thus, the classification for the party-size distribution represents various sizes of parties that restaurants can have in practice. The four levels of party size distributions are as follows: 1. Level one: large-size parties composed of only six or seven customers; 2. Level two: small-size parties composed of only two or three customers; 3. Level three: mixed parties composed of only one or eight customers in each party; 4. Level four: equal parties composed of one through eight customers in each party with equal probabilities. Party arrival rates describe how busy a restaurant is using three typical levels: λ = 0.1 (slow), λ = 0.3 (moderately busy), and λ = 0.5 (very busy). Slow level (λ = 0.1) is defined as the arrival of each party every 10 minutes and represents a typical arrival rate during slow period such as the time period between lunch and dinner (i.e., 3:00 to 4:00 p.m.). Moderately busy level (λ = 0.3) is defined as the arrival of three parties every 10 minutes and represents busy hours, but not busiest of the busy hours. Very busy level (λ = 0.5) is defined as the arrival of five parties every 10 minutes and represents the busiest hours of the busy period. These three levels were selected due not only to their capturing three different periods of demand but also to their equal interval in the Lambdas. In demand level, reneging or balking behavior was not included, although this could be a significant variable of interest to be explored in a future study. Party size distribution and arrival rate were used as simulation input parameters. Simulation Model A hypothetical restaurant was created using a simulation. MATLAB 7.0.4 was used to program the model because it allows the incorporation of

342 JOURNAL OF FOODSERVICE BUSINESS RESEARCH spatial priority of table assignment (which tables in which area). The operational settings assumed that the demand stream followed Poisson distribution with arrival rate λ, and that dining duration followed uniform distribution of 40 to 45 minutes. The dining duration is equivalent to the duration that each table is occupied. The uniform-distribution assumption does not capture the variance in each party s stay duration. Each party s stay duration might be dependent upon the size of the party or their seating location. Using the uniform distribution allows this study to capture the volatile nature (i.e., larger variance) of stay duration better than other less variable distributions, such as the normal or exponential distribution. The downside of this choice is that the uniform distribution may overestimate the variability of the stay duration. However, even if the actual distribution of stay duration might be less volatile than the uniform distribution, our results can still serve as a more conservative estimate of the worst case analysis. The restaurant consisted of 25 two-top tables (i.e., 5[row] * 5[column]). The operation of the restaurant is modeled as a single queue/multiple server queuing system. Equal space was assigned for each seat. In combination of adjacent tables allowed for parties of more than two, optimization-based policy was considered, and the benefit of fairness of the First-Come, First-Served (FCFS) rule was kept as much as possible within the same party size. In other words, FCFS rule was applied as long as the size of available tables was equal to or larger than the size of the waiting party. For example, when two adjacent tables become available, a party of two waiting ahead of a party of four will get seated. However, the exception applies to situations where the size of available tables is smaller than the size of the waiting party. For example, when two adjacent tables become available, a party of four that is waiting behind a party of six will get the tables first. This optimization-based table-combination policy also reflects most common practice in the restaurant industry. Each statistic was obtained through 1,000 simulation runs with a 5-hour operational window in each run. The output system performance measures evaluated were average waiting time per customer, average waiting time per party, average waiting time per party size, and seat utilization. RESULTS AND DISCUSSIONS This study investigated the impact of various table assignment policies on restaurant performances including average waiting time per customer, average waiting time per party, average waiting time per party size, and seat

Johye Hwang 343 utilization. The four table assignment policies were classified into Frontto-back, Out-in, In-out, and Random policies according to table location priority for assigning and combining tables for an incoming party. The impact of those policies on performance was examined by varying customers demand level, which is characterized by party size distribution and arrival rate. Given arrival rate (λ = 0.3), the party size distributions were varied to examine the effects of the policies on the performances. An ANOVA test found that the policies made significant differences in average waiting time per customer depending on the party size distributions, although the policies did not make significant differences in average waiting time per party (see Figure 2). The result showed the statistically significant interaction existed (F = 21.045, p < 0.000; see Table 1). Thus, the first alternative hypothesis was supported. When the party sizes were large, Out-in and In-out policies worked best whereas Random policy resulted in the longest waiting time. When the party sizes were small, Front-to-back policy worked best, Inout policy was the worst, and Random policy had no substantial effects. When the party sizes were distributed equally, Front-to-back policy worked best and Random policy worked poorly. This case was investigated in more detail later in this study. When the party sizes were mixed with small and FIGURE 2. The impact of table assignment policies on waiting time performance with variance in party sizes. 60 50 b Avg.Waiting Time per Customer c a ab minutes 40 30 20 a ab b c a b c c Front-to-Back Out-In In-Out Random 10 0 a ab ab Large Uniform Small Mixed Party Size Distribution b a, b, c: The post-hoc test showed significant difference (p < 0.05)

344 JOURNAL OF FOODSERVICE BUSINESS RESEARCH TABLE 1. ANOVA Result: Impact of policies on average customer waiting time (ACWT) with variations in party size distribution (PS) Dependent Variable: ACWT Source Sum of squares df Mean square F Sig. Model 18447192.685(a) 16 1152949.543 11100.004.000 Party size 5035054.837 3 1678351.612 16158.304.000 Policy 12166.793 3 4055.598 39.045.000 Party size *policy 19673.708 9 2185.968 21.045.000 Error 1660246.734 15984 103.869 Total 20107439.419 16000 a R Squared =.917 (Adjusted R squared =.917). From The Analytic Hierarchy Process (p. 27) by T. L. Saaty, 1980, NY: McGraw-Hill Book Co. Adopted with permission of the author. TABLE 2. Best and worst policies depending on party size distribution Party size distribution Best policy Worst policy Difference in waiting time per customer (%) Large Out-in Random 8.32% Small Front-to-back In-out 14.84% Mixed Front-to-back In-out 15.13% Equal Front-to-back Random 5.14% large, Front-to-back policy performed best whereas In-out and Random policies performed poorly. Overall, the Front-to-back policy worked better than the others with the exception of large parties. On average, the best policy selected made approximately a 10 to 15% difference in the waiting times in comparison to the least efficient policy. This implies that the policies are effective in practical terms as well as statistically (see Table 2). The results indicate that Out-in policy worked better for larger size parties than other policies. This can be intuitively understood in light of higher spatial flexibility created by Out-in policy for combining tables. Unlike Out-in policy, In-out and Random policies worked poorly due to the lack of flexibility for combining tables. With equal probability of each party size, the arrival rates were varied to examine the effects of the policies on the performances. An ANOVA test found that the policies made significant differences in waiting times depending on the arrival rates (see Figure 3). Although there was no

Johye Hwang 345 FIGURE 3. The impact of table assignment policies on waiting time performance with variance in arrival rate. 60 Avg. Waiting Time per Customer 50 minutes 40 30 20 a ab b b Front-to-Back Out-In In-Out Random 10 0 a a b b Slow (λ = 0.1) Moderately Busy (λ = 0.3) Arrival Rates Busy (λ = 0.5) a, b: The post-hoc test showed significant difference (p < 0.05) TABLE 3. ANOVA Result: Impact of policies on average customer waiting time (ACWT) with variations in arrival rates Dependent Variable: ACWT Source Sum of squares df Mean square F Sig. Model 12474658.100(a) 12 1039554.842 16050.559.000 Lambda 4610331.378 2 2305165.689 35591.385.000 Policy 830.176 3 276.725 4.273.005 Lambda * policy 593.084 6 98.847 1.526.165 Error 776433.009 11988 64.768 Total 13251091.109 12000 a R Squared =.941 (Adjusted R squared =.941). statistical interaction (p > 0.05), there were main effects of the policies within each arrival rate (F = 4.27, p < 0.01; see Table 3). Thus, the second alternative hypothesis, The best table assignment policy resulting in minimum customer waiting time varies by party arrival rate, was supported. The result of a one-way ANOVA for each arrival rate showed

346 JOURNAL OF FOODSERVICE BUSINESS RESEARCH that the policies produced significantly different waiting times for slow and moderately slow demand but not for busy demand (p < 0.00, p < 0.01, and p > 0.05, respectively). Low arrival rates derived more sensitive model outputs. In other words, when the restaurant is slow, different policies resulted in greater differentiating effects on waiting times. According to the post-hoc analysis, with slow demand, Front-to-back policy produced the shortest waiting times whereas In-out policy produced the longest waiting times. When the restaurant was moderately busy, Front-toback policy performed best and In-out and Random policies performed poorly. Thus, no matter whether the restaurant was slow or moderately busy, Front-to-back policy resulted in the shortest waiting times with equal distribution of each party size. Unlike slow demand, when the restaurant was very busy, the policies did not make any significant difference in the waiting times. This suggests that the system reaches a point of saturation where there is no room to process incoming customers faster through applying any of the policies because there are no leftover tables available for seating customers. Therefore, the results imply that table assignment policies influenced system performance when the restaurant was either slow or moderately busy. For a slow and a moderately busy restaurant, the best policy selected made approximately a 34% and 5% difference, respectively, in the waiting times in comparison to the worst policy. The policies, again, are applicable statistically and in practicality (see Table 4). Interesting findings were obtained from examination of the impact of each policy on average waiting times per party size under the demand of equal probability of each party size. When average waiting time was disaggregated on the basis of each party size in the case of equal probability of each party size, the best and worst policy varied depending on party size (see Table 5). Overall, the larger the party size is, the longer the waiting time is. During the slow period (λ = 0.1), the four policies made significant differences in average waiting times for larger parties (party size: 5 6 and TABLE 4. Best and worst policies depending on arrival rate Arrival rate Best policy Worst policy Difference in waiting time per customer (%) Slow (λ = 0.1) Front-to-back In-out 34.10% Moderately busy (λ = 0.3) Front-to-back Random 5.13% Very busy (λ = 0.5) No difference No difference 0.01%

Johye Hwang 347 TABLE 5. Average waiting time (minutes) per party size given equal probability of each party size Party of 1 2 Party of 3 4 Party of 5 6 Party of 7 8 Slow *(λ = 0.1) Front-to-back 0.01 0.08 0.37 0.56 Out-in 0.01 0.05 0.36 0.70 In-out 0.01 0.05 0.53 0.91 Random 0.01 0.07 0.46 0.87 Average 0.01 0.06 0.43 0.76 Moderately busy (λ = 0.3) Front-to-back 3.84 12.69 30.92 41.79 Out-in 3.76 12.65 31.85 43.41 In-out 3.31 12.05 31.06 46.80 Random 3.32 12.77 32.19 45.54 Average 3.56 12.54 31.51 44.38 Very busy (λ = 0.5) Front-to-back 8.71 24.16 51.35 60.57 Out-in 8.12 23.54 52.63 61.64 In-out 7.70 22.94 52.02 64.17 Random 7.48 23.80 52.75 66.05 Average 8.00 23.61 52.19 63.11 *The policies made significant difference in average waiting time per partly (p < 0.000). Shaded area = The policies made significant difference in average waiting time per party size (p < 0.01). 7 8). For both large size parties, Front-to-back policy yielded shortest waiting time whereas In-out policy yielded longest waiting time (p < 0.01 for party of 5 6 and p < 0.000 for party of 7 8). During the moderately busy period (λ = 0.3), the four policies made significant differences in average waiting times for parties of one to two and parties of seven to eight. For small parties, Frontto-back policy produced longest waiting time whereas In-out policy produced shortest waiting time (p < 0.01). For large parties, the result was just the opposite: Front-to-back policy produced shortest waiting time whereas In-out policy produced longest waiting time (p < 0.000). A similar result was found during the very busy period (λ = 0.5): For small parties, Front-to-back policy produced longest waiting time whereas Random policy produced shortest waiting time (p < 0.000); for large parties, Front-to-back policy produced shortest waiting time whereas Random policy produced longest waiting time (p < 0.000). This discovery confirms the aforementioned finding that a good policy for a small-size party might be bad for large-size party in terms of waiting time. The finding also reveals that exponentially long waiting times of

348 JOURNAL OF FOODSERVICE BUSINESS RESEARCH large parties accounted for long waiting times per customer as a result of applying In-out or Random policy as compared to small parties. Significance also was found in the performance measure of seat occupancy depending on the policies. An ANOVA test for the representative case (λ = 0.3 and equal probability of each party size) found that the four policies made a significant difference in seat occupancy (p < 0.000). Frontto-back policy resulted in higher seat occupancy and served more customers within the operation window than In-out and Random policies. The result on seat occupancy confirms the logic that the best table assignment policy produces high flexibility of seating large parties and contributes to high seat occupancy by serving more customers. Our logic is consistent with the conclusion made in other studies that the best table mix resulted in more effective capacity and increased RevPASH with an increase in customer volume (Kimes & Thompson, 2004; Thompson, 2002, 2003). CONCLUSIONS AND IMPLICATIONS Bertsimas and Shioda (2003) developed mathematical models to assist in deciding when to seat an incoming party to enhance revenue. In contrast, our study places its focus on where to seat parties with respect to priority for table location and combinability of tables to improve service quality as defined in waiting time. This study answered the important managerial questions of table assignment: What policy should be adopted given party size distribution and when should the policies be applied [busy or slow]? The question of what policy should be adopted given party size distribution is concerned with who the customers are. Each establishment has a different customer population. Knowing the characteristics of the customer population, such as how the parties are distributed, will help determine which policy to use. This study showed that the optimal table assignment policy varied depending on party size distribution. Random or In-out policy resulted in poor system performance due to the lower flexibility to match the large party size with the restaurant table mix. This justification is confirmed by the long waiting time for large parties (i.e., parties of 5 8 in this study), which contributed to long average waiting time as well. Overall Front-to-back and Out-in policies resulted in better performance. This is good news not only in reducing waiting times but also in satisfying customers preferences. It is found in other research (Kimes & Robson, 2004; Robson, 2002) that customers are inclined to choose anchored seats against a wall or window or seats not exposed to a

Johye Hwang 349 service area or the kitchen. Thus, the result implies that higher operational efficiency can be insured without sacrificing customer satisfaction with seat location through managing seating assignments. Furthermore, according to the results of this study, the answer to the other question of when the policies should be applied is that the optimal assigning policy should be determined and adopted dynamically depending upon the level of business experienced by the restaurant. When the restaurant is slow or moderately busy, the optimal policy is Front-to-back. The worst policy (In-out or Random) varies depending upon the level of business experienced by the restaurant. The poor performance of Random policy implies seating customers without any plan for the table location can make customers wait even worse. The policies did not make a difference when the restaurant was extremely busy because the occupied tables did not produce any flexibility for seating or combining tables. However, caution has to be taken in interpreting extremely busy as defined in this study because each restaurant might have a different level for extremely busy depending on its size and demand. With the finding of relatively poor performance of the real restaurants in managing table capacity, in his report Thompson (2007) emphasizes significant potential for improvement in revenue by effective optimization of table mixes. As part of the efforts to assist effective capacity usage in the restaurant industry, this study can guide restaurant managers in developing a table management program that can (a) dynamically determine the best table assignment policy, (b) lower the time in making decisions, (c) reduce the time of having a table sit empty, and (d) lessen the number of decisions a host will have to make. Some restaurants still use a grease pencil board or wash-off markers on a plastic coated diagram of the restaurant s seating layout to manage seating and a waiting list. It takes great effort and time to coordinate many table assignments (Bendall, 1995). If customers are seated quickly, it can benefit both customers and managers. Customers may be more satisfied with their dining experience having experienced a short waiting time prior to being seated and served. For managers, it will increase seat turnover, which ultimately will help generate higher revenue. Our study results can be applied to establishments with diverse table layouts. LIMITATIONS AND FUTURE STUDIES Several limitations of this study should be recognized. This study did not take table design and psychological issues into consideration even though customer preference can vary. For example, the study did not

350 JOURNAL OF FOODSERVICE BUSINESS RESEARCH differentiate the type of seating, such as booth or free-standing table, and the shape of table, such as round or square. The optimal policy presented in this study may or may not satisfy the customer s preference for seating if the design aspects of tables were factored into the study. Customers stay duration can be influenced by the type of seating as well as the location of where they are sitting. Although the study s assumption of the uniform distribution for customers stay duration captures the volatile nature of stay duration, an actual stay-duration distribution needs to be used to prevent the overestimation of the variability of the stay duration and to capture customers real staying behavior. Incorporating these factors can extend this research. Future studies may want to address such issues as the size of the restaurant along with the different sizes of tables found within the restaurant. Another limitation can be found in relation to wait staff table assignment. A wait staff usually is assigned to a cluster of tables in a section of the restaurant. Figure 1 depicts that the Front-to-back, Out-in, and In-out policies lead to even loads for the wait staff, whereas Random policy causes difficulties with wait staff assignments. Efficiency of wait staff assignments should be explored in a future study. Last, but not least, a future study can incorporate factors such as customers balking or reneging behavior, customers willingness to wait, and reservations. REFERENCES Bendall, D. (1995). Table management tools. Restaurant Hospitality, 79(6), 102. Bertsimas, D., & Shioda, R. (2003). Restaurant revenue management. Operations Research, 51(3), 472 486. Durocher, J. (2005). Multiplication tables. Restaurant Business, 104(11), 66 68. Field, A., McKnew, M., & Kiessler, P. (1997). A simulation comparison of buffet restaurants Applying Monte Carlo modeling. Cornell Hotel and Restaurant Administration Quarterly, 38(6), 68 79. Hueter, J., & Swart, W. (1998). An integrated labor-management system for Taco Bell. Interfaces, 28(1), 75 91. Kimes, S. E., Barrash, D. I., & Alexander, J. E. (1999). Developing a restaurant revenuemanagement strategy. Cornell Hotel and Restaurant Administration Quarterly, 40(5), 18 29. Kimes, S. E., & Robson, S. K. A. (2004). The impact of restaurant table characteristics on meal duration and spending. Cornell Hotel and Restaurant Administration Quarterly, 45(4), 333 346. Kimes, S. E., & Thompson G. M. (2004). Restaurant revenue management at Chevys: Determining the best table mix. Decision Sciences, 35(3), 371 392.

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