Improving golf course throughput by modeling the impact of restricting early tee times to faster golfers.

Tiger, Andrew A. ; Salzer, Dave

ABSTRACT

A model-based decision support system (DSS) for operating and designing golf course systems is presented in this paper. The DSS is based on a simulation model that accurately represents the variability and interactions that impact pace of play on a golf course. Research shows the economic benefits of understanding the impact of policy and design on golf course play, specifically throughput (rounds played) and cycle time (round length). A specific policy, only allowing fast golfers to begin early in the day, was shown to improve both throughput and cycle time. A new statistic is proposed, the time handicap, which measures both a golfer and course's pace of play. The DSS model was developed using MS-Excel and @RISK, a Monte Carlo simulation package. Using MS-Excel offers a much greater degree of transferability and usability than traditional standalone discrete-event simulation software.

INTRODUCTION

The golf industry is big business. In 1999, golfers spent $16.3 billion on green fees (National Golf Foundation website, 2003). Because of the Tiger Woods effect on popularity, the number of golfers is increasing, creating the need for more courses. Over 400 new courses are being constructed per year (National Golf Foundation website, 2003). Golf courses, like most business operations, are designed and operated to be profitable. Many factors influence profitability. This paper focuses on improving profits by increasing throughput (the number of golfers playing golf per day) of a golf course. The approach used in this paper is unique in that we apply proven math-based modeling technology to model golf course daily throughput.

Daily golf course play is a stochastic system where random events (lost balls, weather, and poor shots) and interactions (waiting for the group in front of you) heavily impact the pace of play. Although complex, daily golf course operations are very similar to other complex systems such as:

 A manufacturing plant where parts are moving from production
 process to process A distribution network where transportation
 devices (trucks, boats, planes ...) move from location to location
 An emergency room at a hospital where patients wait for treatment

In all of these examples, performance is impacted by variability and interactions. However, these examples and other complex systems have been analyzed with math modeling. Therefore, a golf course system should be a candidate for math-based analysis.

A model-driven DSS that represents daily play at a golf course is beneficial for both designers and course managers. In both, qualitative measures and experience are the primary tools. Little empirical knowledge exists that provides the quantitative impact on throughput. For example, how much do the following impact throughput: fairway width, length of course, elevation changes, bunkers, green size ...? Certainly, designers know that the above impact pace of play. However, quantifying the impact is much more difficult. One study has shown that the number of bunkers and the hilliness of the course did not influence revenues (Schmanske, 1999). Similarly, course managers have questions regarding throughput. How much do the following impact throughput: tee-time intervals, shotgun starts, group size (2, 3, 4, 5...), carts vs. walking ...? Increasing throughput and controlling, or at least forecasting, cycle time are two of the most important factors in revenue management (Kimes, 2000).

Before proceeding, the first question to be addressed is 'Is there potential for math modeling to increase profits by improving throughput?' Consider a typical course with a $35 green fee, 12 hours of daily playing time, an average round taking 4.5 hours for a group of 4 golfers, and 144 busy golf days (weekends and holidays). Based on a 4.5 hour (270 minutes) round of golf, a group (on average) finishes a hole every 15 minutes. In a 12-hour day, 31 groups (124 golfers) complete a round of golf. A modest 10% improvement in round length (243 minutes vs. 270 minutes) yields a 16% increase in throughput (144 rounds/day vs. 124 rounds/day) and over $100,000 increase in annual revenue. Certainly, the potential exists.

This paper has three objectives. The first is to demonstrate a math-based model that accurately represents the daily play at a golf course that can be the basis for a design and operations improvement DSS. The second objective is presenting a specific analysis that shows a traditional dispatching rule, shortest processing time (SPT), commonly used in industry also improves throughput and cycle time in a golf course system. The third objective is introducing a new statistic for quantifying a golfer's ability to play fast: the time handicap.

To reach these objectives, we have represented golf course play with a math-based model. A model of systems allows studying the system without the consequences of experimenting on the actual system. The benefits are reduced time and costs and increased safety and creativity. If the model used only once to solve a problem, it has been a useful tool. If the model can be used again, in a changing environment, with several variables at the control of the user, the model is then a model-driven decision support system. The most used method for modeling systems with variability and interactions is discrete-event simulation (DES). In general, simulation refers to a broad collection of methods and applications to mimic the behavior of real systems. Simulation models can be physical or logical (mathematics).

DES is a venerable and well-defined methodology of operations research and many excellent explanatory texts exist (Hauge & Paige, 2001; Law & Kelton, 2000; Pritsker, 1995; Winston, 2001). The methodology is particularly useful in evaluating interdependencies among random effects that may cause a serious degradation in performance even though the average performance characteristics of the system appear to be acceptable (Shapiro, 2001). Additionally, simulation models are intuitive, which is an important reason for their longtime and continuing application to complex systems. The literature review found one published article where simulation was applied to modeling golf course play (Kimes, 2002). In this model, waiting occurred only on the first tee. In a real system, many opportunities exist for waiting, and not all of them occur at the beginning, i.e., on the first tee box. Waiting can occur anywhere a group's pace is dictated by the group prior. Therefore waiting can occur on all 18 tee boxes and in the fairways. The study also assumed that rate of play was normally distributed, and a skewed distribution is more likely. The time study used to build the simulation was based on one course. A new time study would need to be done for each course you wanted to analyze.

MODELING METHODOLOGY

A golf group consists of individual golfers, usually ranging from 1 to 5. Once set, the number of golfers in a group does not change. On each hole, the group begins on the tee box and hits one at a time. The group moves towards the green once all golfers in the group have hit from the tee box. Some golfers move to the green more quickly than others depending on many factors. Having reached the green, each golfer finishes by putting (one at a time) his/her ball into the hole. Once all golfers in the group have finished putting, the group proceeds to the next hole.

The group's pace is dictated not only by its own processing time, but also by the group's immediate predecessor and the type of hole (par 3, 4, or 5). A group must wait for its predecessor to be out of the way. For example on a par 4 (or 5), a group cannot begin to hit from the tee box until its predecessor is sufficiently out of range to prevent injury by hitting someone. Because of the short distance of a par 3, a group cannot hit from the tee box until its predecessor is off the green. On par 4/5's a safe distance is between 225 and 300 yards. We define the point that allows the group behind to safely hit as a gate and refer to waiting for the group ahead to be out of the way as gate management. Using gate management eliminates having to model every shot from every golfer. Rather, we focus on the time to reach gates and be out of the way.

On the tee box and green, individual golfers hit one at a time. Therefore, for the group, the processing times are additive. In the fairway, the Rules of Golf dictate that the ball farthest from the hole is played first (United States Golf Association website, 2003). However, golfers proceed to their ball in parallel; consequently, processing times are not additive, and the slowest golfer dictates the group's pace of play. A golf course is a terminal system. It has a definite beginning and ending as a function of daylight. For terminal systems, performance is very dependent on the system's initial conditions. For a golf course, a slow group early in the day often spells disaster for the remainder of the day in terms on the rounds played (throughput) and round length (cycle time).

The golf course system was modeled using MS-Excel and @RISK, a MS-Excel add-in. Although not a standalone discrete-event simulation software, MS-Excel has an assortment of functions that are quite capable of modeling a gate-management system. The add-in, @RISK, provided a concise method for modeling different scenarios and maintaining statistics for analysis.

The best way to illustrate the gate management modeling logic is through an example. Consider the first hole at the beginning of the day. The first two groups are modeled. Group one has the first tee time (time = 0), and group two's tee time is six minutes later. Table 1 shows the processing times for each group. Note that this table does not show event times, only processing times. Since hitting from the tee box is a serial process, times are additive, and group one takes 150 seconds. Before group two can hit from the tee box, group one needs to be out of the way. We define a gate 300 yards from the tee box that group one must be through prior to group two hitting.

The golfers in group one move to the gate at different speeds, and the slowest golfer (golfer 4 in this example) is out of the way in 140 seconds (after leaving the tee box). From this gate, golfers in group 1 proceed to the green. Golfer 3 takes the longest (200 seconds). Once on the green, putting time is additive; therefore, the total putting times is 180 seconds, and the group's total time to complete the hole is 670 seconds. Similar logic exists for group 2, except its pace is dictated not only by its tee time and processing time, but also by group 1's pace. Table 2 shows the event times. Group 2's tee time is six minutes after group 1. Since group 1 is through the gate at 290 seconds, group 2 does not need to wait for group 1 and begins to hit exactly at its tee time. However, group 2 is not as fortunate in the fairway. Group 2 takes 160 seconds to hit from the tee box and 100 seconds to reach the gate; therefore it is ready go through the gate at 620 seconds. However, it cannot get through the gate until 670 seconds because group 1 is still on the green. Therefore, group 2 waits in the fairway for 50 seconds. This delay does not prevent group 3 from hitting at its scheduled tee-time of 720 seconds; however, this can change as the day progresses. As often with queuing systems, once behind, it is very difficult to get back on schedule. For par 3 and 5 similar logic is needed, except par 3s have no fairway gate and par 5s can have two fairway gates.

The modeling approach used is gate management. In simulation modeling, gate management refers to controlling the flow of work items. Gate management has been used to model Kanban systems and drum-buffer-rope scheduling (Hauge & Paige, 2001). For accurately representing to-gate times, data were collected by a class of Operations Management students as a data analysis exercise. Four different types of data (500+ values) were collected from five different local courses. Each type of data fit a triangular distribution. See table 3 for the type of data and triangular distributions values for the minimum, mode, and maximum. Note that the tee box and putting values are times (minutes), and the other values are rates (yards/minute). The rates allow transit times to be determined on any hole on any course by dividing the hole-specific distance by the randomly generated rate. For example, consider a golfer leaving the tee box on a 400-yard par 4 hole. Assume that the out of the way gate is 300 yards from the tee box. To determine how long it would take for the golfer to be out of the way, a triangular distribution is sampled to get a rate. Assume the rate sampled is 75 yards per minute. If so, the time to reach 300 yards would be 4 minutes.

A good decision support system separates input data from modeling logic; thus, developing a tool that can be applied to many different systems. Our model-driven DSS separates course data from the modeling logic. Therefore, if a new course is to be analyzed, only the input data must be modified. The modeling logic takes into account which hole is a par 3, 4, or 5 and represents the gate management system accordingly. The input data structure used in this research is shown in Table 4. The first hole is a par 5. The first fairway gate is 250 yards from the tee box. The next fairway gate is 200 yards from the first fairway gate. The green is 50 yards from the second fairway gate, and the second hole's tee box is 50 yards from the first green. The second hole is a par 4; therefore, it does not have a second fairway gate. The third hole is a par 3; therefore, it does not have any fairway gates. Model assumptions are given in Table 5.

Although not modeled in this research, substantial opportunities exist for incorporating the assumptions as modeling parameters in subsequent research.

Validation, determining that the model accurately represents the real system, relied primarily on experience and expert judgment. Avid, if not talented golfers, the authors have a wealth of experience of how long a round can be played without waiting as a single or in a group. Results of a no-waiting analysis accurately depicted the authors' experiences and well established expectations. Similarly, the modeling of a busy course accurately reflected upwards of 5 hours for a weekend round of golf.

ANALYSIS OF RESTRICTING EARLY TEE TIMES FOR FASTER GOLFERS

A golf course is a terminal system. It has a definite beginning and ending as a function of daylight. For terminal systems, performance is very dependent on the system's initial conditions. For a golf course, a slow group early in the day often spells disaster for the remainder of the day in terms on the rounds played (throughput) and round length (cycle time). To prevent this, we tested the impact of restricting early times to faster golfers. This approach is taken from manufacturing system design research that used the shortest processing time (SPT) dispatching rule (Johnson, 1954; Lawrence & Barman, 1989) for system improvement.

A three-factor (three levels per factor) experiment was designed. Factor A defined the speed of a fast golfer as a percentage increase (0%, 25%, and 50%) of the base times/rates shown in Table 3. Factor B defined the length of the time (hours) from the beginning of the day that only allowed fast golfers to begin their round (none, 1, and 2). Factor C is the tee time interval (6 minutes, 8 minutes, and 10 minutes). Table 6 summarizes the factors and level values. Each trial was a 500-day simulation. Since the system is terminal, no warm up period was required. Figures 1 and 2 show the 27 average daily rounds played and round length, respectively.

[FIGURES 1-2 OMITTED]

In aggregate, both Figure 1 and Figure 2 provide intuitive results. Moving from left to right, tee time intervals move from 6 minutes to 10 minutes. Shorter time intervals increase throughput (rounds played) and cycle time (round length). As the interval lengthen, rounds played and round length decrease. Within each group of three, fast golfers rate increase from 0% to 50%. As expected, higher rates increase the number of rounds played and reduce the round length.

As we explore further, we see that the impact of a time window allowing only fast golfers to begin is the largest for a congested course (6 minute tee-time intervals) and provides minimal benefits for non-congested courses (10 minute tee-time intervals). Figures 3 and 4 highlight the circled areas from Figures 1 and 2, respectively. In Figure 3, the base case (no windows and no fast golfers) shows that the course averaged 157 rounds per day. However, if fast golfers could be identified and provided a one-hour time window that restricted the course to fast golfers, the average increased to 193 rounds per day (23% improvement) for golfers 25% faster and 214 rounds per day (36% improvement) for golfers 50% faster. For a 500-day simulation, the 90% confidence interval on average rounds played per year is the mean [+ or -] 3 rounds; therefore, the improvement is statistically significant.

[FIGURES 3-4 OMITTED]

Similarly, Figure 4 shows a reduction in round length from 301 minutes to 251 minutes (17% improvement) for golfers 25% faster and 225 minutes for golfers 50% faster (25% improvement). For a 500-day simulation, the 90% confidence interval on average round length is the mean [+ or -] 5 minutes; therefore, the improvement is also statistically significant.

The significance of this analysis is that improvements in the revenue-generating ability of a golf course exist without modifying the green fee structure, but by improving operations management.

INTRODUCING A MEASURE OF A GOLFER'S PACE OF PLAY: THE TIME HANDICAP

To insure that those beginning early in the day not delay those following, course managers have several options. One is simply communicating the importance of a quick pace through signs and quick speeches prior to beginning a round. Another is having the course marshal continually monitor the early groups' progress and pushing them to move quickly. A method we propose is using a golfer's time handicap as a restriction on those who can begin early in the day. Analogous to a golfer's scoring handicap that measures a golfer's scoring ability, the time handicap measures an individual golfer's ability to play quickly. The time handicap could also be applied to individual golf courses, as well as golfers.

Although nonexistent, consider its implications if a time handicap did exist. First, popular public courses, i.e., Pebble Beach, would have a quick method for allocating tee times that would improve profitability without modifying how much to charge in green fees. Secondly, time handicaps would provide the golfing industry a measure of the pace of play, which is a requirement for system improvement (Rath and Strong Management Consultants, 2002). Courses with notorious slow play will be punished, and courses that move golfers through quickly will be rewarded. Golfers want to play immaculately groomed courses, but a beautiful course that takes six hours to complete is inferior to the beautiful course that guarantees a four-hour round! Finally, the act of measuring often provides system improvement. A golfer wants to improve his scoring handicap. We believe a golfer would also want to improve his time handicap. Systemic improvement of the time handicap would benefit all those involved.

The time handicap formula would be similar to the United States Golf Association (USGA) Handicap System's[TM] (United States Golf Association website, 2003):

 The purpose of the USGA Handicap System[TM] is to make the game of
 golf more enjoyable by enabling golfers of differing abilities to
 compete on an equitable basis. The System provides fair Course
 Handicaps[TM] for players regardless of ability, and adjusts a
 player's Handicap Index[TM] up or down as one's game changes. At
 the same time, it disregards high scores that bear little relation
 to the player's potential ability and promotes continuity by making
 handicaps continuous from one playing season or year to the next. A
 USGA Handicap Index is useful for all forms of play. A basic
 premise underlies the USGA Handicap System, namely that every
 player will try to make the best score at each hole in every round,
 regardless of where the round is played, and that the player will
 post every acceptable round for peer review.

 A USGA Handicap Index compares a player's scoring ability to the
 scoring ability of an expert amateur on a course of standard
 difficulty. A player posts scores along with the appropriate USGA
 Ratings to make up the scoring record. A Handicap Index is computed
 from no more than 20 scores plus eligible Tournament Scores in the
 scoring record. It reflects the player's potential because it is
 based upon the best scores posted for a given number of rounds,
 ideally the best 10 of the last 20 rounds.

Mathematically, the Handicap Index[TM] is a function of the golfer's recent scoring history, course difficulty, and tee boxes used. A time handicap formula would need to be a function of the golfer's recent round length history, courses played characteristics (difficulty, course length, round length), group characteristics (number in group, walking/riding/combination), and the time of day that the round begins. Currently, no formula exists. Subsequent research is required.

CONCLUSIONS AND FUTURE RESEARCH

The significance of this analysis is that improvements in the revenue-generating ability of a golf course exist without modifying the green fee structure, but by improving operations management. In the past, little effort has been devoted to modeling a golf course system as a complex system impacted by variability and interaction. The DSS model was developed using MS-Excel and @RISK, a Monte Carlo simulation package. Using MS-Excel offers a much greater degree of transferability and usability than traditional standalone discrete-event simulation software. Future research is plentiful. For example, more detailed data would allow additional golfer and course characteristics to be evaluated; thus providing both course managers and designers feedback on policy and design decisions.

Obviously, implementation is another matter. Golf is a social system steeped in tradition and slow to change. However, demonstrable revenue-generating opportunities are not ignored in business, even in golf.

REFERENCES

Hauge, J. W. and K. N. Paige (2001) Learning Simul 8 The Complete Guide, Plain Vu Publishers, Bellingham, Washington.

Johnson, S. M. (1954) Optimal Two- and Three-Stage Production Schedules with Setup Times Included, Naval Research Logistics Quarterly, 3, 61-68.

Kimes, S. E. and L. W. Schruben (2002) Golf Course Management: A Study of Tee Time Intervals, Journal of Revenue and Pricing Management, 1(2), 111-120.

Kimes, S. E. (2000) Revenue Management on the Links: Applying Yield Management to the Golf-Course Industry, Cornell Hotel and Restaurant Administration Quarterly, 41(1), 120-127.

Law A. and W. Kelton (2000) Simulation Modeling and Analysis, McGraw-Hill, New York.

Lawrence, R. L. and S. Barman (1989) Performance of Simple Priority Rules Combinations in a Flow-Dominant Shop, Production and Inventory Management Journal, 3, 1-4.

National Golf Foundation Frequently Asked Questions. Retrieved June 26, 2003, from http://www.ngf.org/faq/

Pritsker, A. (1995) Simulation and SLAM II, John Wiley, New York.

Rath and Strong Management Consultants, (2002) Rath & Strong's Six Sigma Pocket Guide, Rath & Strong Management Consultants, Lexington, Massachusetts.

Shapiro, J. F. (2001) Modeling the Supply Chain, Duxbury, United States.

Schmanske, S. (1999) The Economics of Golf Course Condition and Beauty, Atlantic Economic Journal, 27(3), 301-313.

Winston, W. (2001) Simulation Modeling Using @RISK, Duxbury, United States.

United States Golf Association. Retrieved June 26, 2003, from http://www.usga.org/

Andrew A. Tiger, Southeastern Oklahoma State University Dave Salzer, E. & J. Gallo Winery

Table 1: Processing times for a Par 4

Group Golfer Time Time Time Time
 to through to to
 tee-off gate green putt

 1 1 60 110 70 70
 2 30 90 60 30
 3 20 100 200 (max) 10
 4 40 140 (max) 40 70
Group 150 140 200 180
 2 5 40 100 (max) 40 30
 6 40 60 60 40
 7 60 70 70 50
 8 20 80 80 (max) 40
Group 160 100 80 160

Table 2: Event times for a Par 4

Group Tee-time Off Through To Off
 tee-box gate green green

 1 0 150 290 490 670
 2 360 520 670 750 910

Table 3: Data Values

Data Type Description Min Mode Max

Tee box time The time for an individual 0.3 0.77 1
(minutes) golfer to address and hit the
 ball on the tee box. No
 waiting time included.

Tee box to gate After leaving the tee box, an 40 70 160
(yards/minute) individual golfer's rate while
 reaching an arbitrary (but
 identified) gate in the
 fairway.

Gate to green From an arbitrary (but 40 90 200
(yards/minute) identified) gate in the
 fairway, an individual
 golfer's rate while reaching
 the green.

Putting time The time for an individual 0.23 1.05 1.5
(minutes) golfer to complete putting
 and leave the green.

Table 4: Input Data

Hole Par Distance To To To To
 Gate Gate Green Next
 1 2 Hole

 1 5 500 250 200 50 50
 2 4 440 250 0 190 50
 3 3 160 0 0 160 50
 4 4 370 250 0 120 50
 5 5 500 250 200 50 50
 6 4 420 250 0 170 50
 7 4 350 250 0 100 50
 8 3 200 0 0 200 50
 9 4 370 250 0 120 50
 10 4 440 250 0 190 50
 11 5 520 250 200 70 50
 12 4 390 250 0 140 50
 13 4 340 250 0 90 50
 14 3 170 0 0 170 50
 15 5 560 250 200 110 50
 16 4 330 250 0 80 50
 17 3 200 0 0 200 50
 18 4 370 250 0 120 50

Table 5: Model Assumptions

1. Four golfers per group.

2. No play-through logic (same group order throughout the round).

3. Gates are hole-specific, not golfer-specific.

4. No golfer designation except quantity (golfers/group).
Carts/walking, fast/slow, good/bad, straight/erratic,
long/short ... are not included.

5. No course designation except par and distance. Course difficulty,
water, bunkers, rough height, elevation changes ... are not modeled.

6. No specific dollar values are modeled. We assume that daily
operating costs are fixed are only marginally increased if daily
throughput is increased. Therefore, we assume that increasing the
rounds played not only increases daily revenue, but daily profits.

Table 6
Experimental Design Factors and Levels

Factor Level 1 Level 2 Level 3

A: Fast golfer speed (% increase in 0 0.25 0.5
base speed)

B: Beginning of the day time window None 1 2
designated only for fast golfers
(hours)

C: Tee time interval (minutes) 6 8 10