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Exploring COFF[IE]: An Industrial Engineering Analysis
Kenneth Acquah Colin Courchesne Sheela Hanagal [email protected] [email protected] [email protected]
Kenneth Li Caroline Potts [email protected] [email protected]
Mentor: Juilee Malavade, Brandon Theiss, PE
RTA: Juilee Malavade
times in each restaurant, the simulation Abstract could be manipulated to change resource values and process orders, deriving an Waiting in lines for extended periods optimal model of increased efficiency and of time results in inconveniences and a increased profitability for both restaurants waste of what may be the most important which could potentially decrease wait times resource of all, time, for all consumers. for both Starbucks and Dunkin’ Donuts. Thus, reducing wait times within Starbucks and Dunkin' Donuts and optimizing a 1. Introduction simulation of the processes within those restaurants could result in shorter wait times Standing in queues is not only an for customers and larger profits for the inconvenience for customers everywhere, it restaurants. Data of the wait times in line is also costly to firms and to the overall and the service times were collected at economy. A person who spends five minutes Starbucks and Dunkin' Donuts restaurants waiting for coffee each day who otherwise within New Brunswick through ® earns ten dollars an hour would lose over observational studies. Minitab statistical three hundred dollars every year due to the analysis software was then used to analyze opportunity cost of waiting in line. When the data and obtain the probability this cost is applied to the three million distributions and descriptive statistics. The customers served in Dunkin' Donuts alone results from the Minitab software were then daily,1 millions of dollars are lost every year used to create simulations of the queuing due to Dunkin' Donuts coffee lines. processes for both Starbucks and Dunkin' ® Extending this to Starbucks restaurants and Donuts using Arena Simulation Software . customers as well, the loss only multiplies. The simulations were run and analyzed to Minimizing queue length by improving see whether the simulated data accurately efficiency and productivity in Starbucks and reflected the data which was collected at the Dunkin' Donuts coffee shops has the two restaurants. The simulated data reflected potential to save millions of people both some of the collected data but not all time and money. depending on what queue we were obtaining This research seeks to create a simulated data from. It was found that working simulation of both a Dunkin' queues in Starbucks were longer than the Donuts and a Starbucks restaurant and queues in Dunkin’ Donuts. Upon evaluation predict how the processes observed in each of the parameters which could shorten wait restaurant could be improved. A simulation perfect cup of coffee” for the consumers.3 that accurately represents the waiting and The service aspect of customer service was service processes in Dunkin' Donuts and also a main block of the new Starbucks Starbucks locations could be used to analyze model. Starbucks grew rapidly, recording ways to potentially increase efficiency and millions of dollars in sales from thousands decrease queue length. of locations annually. By changing parameters of an accurate simulation, one could analyze the 2.2 Starbucks Business Model additional costs and benefits of altering store operation systems, such as increasing or Starbucks is a coffee retailer that has decreasing the number of employees its main location in Seattle, Washington. working at the cash registers or making There are over twenty-two thousand specialty drinks. This would allow owners Starbucks restaurants worldwide. It reported to determine if a particular change would a net revenue of $12,977.9 million from improve or detract from the service provided company operated restaurants and $1,588.6 to customers without actually testing it in a million from licensed restaurants in 2014. real store, preventing a decline in the quality The majority of Starbucks’ sales come from and profitability of the company during the beverages, with company operated stores testing phase. To obtain data to compare to reporting this category to account for the values output by the simulation, data was seventy-eight percent of sales.4 In the United collected regarding the amount of time States, Starbucks has 7,400 co-operated customers waited to order and to receive restaurants and 4,823 licensed restaurants.5 their drinks at both a Dunkin' Donuts and a The 2014 net revenue from the Americas Starbucks restaurants located in New was $11,980.5 million.4 Starbucks focuses Brunswick, New Jersey. on expanding its geographic locations, having diversified products, and creating the 2. Background semblance of an authentic neighborhood coffee shop. 2.1 History of Starbucks Starbucks strives to be the place to which people retreat from home and work The first Starbucks was opened in and thus encourages customers to stay in- Pike Place Market in Seattle, Washington, in shop by providing attractive services, such 1971 by Jerry Baldwin, Zev Siegl, and as free WiFi, and a welcome atmosphere. Gordon Bowker. The company grew slowly To promote this atmosphere, Starbucks and soon hired Howard Schultz as Director emphasizes service and customer 6 of Retail Operations and Marketing in satisfaction. When it comes to beverage 1982.2 Schultz eventually bought the choices, Starbucks is well known for its company and, borrowing ideas from the wide, accommodating range. The drinks coffeehouse culture of Milan, Italy, worked available at Starbucks include hot drip to build a coffee shop that was more of a coffees, iced coffees, teas, Frappuccinos, restaurant than a retail store. He had a lofty espressos, lattes, cappuccinos, and clovers, vision for Starbucks; he wanted it to be a which are hot coffees that can be highly national company with values and ethics of specialized and are made in a machine that which employees could be proud and “to individualizes each cup. build a company with soul" by making sure The typical process once in a the company would never stop pursuing “the Starbucks is to wait in line (see 2 in Figure 2.2.1 below) and then place an order with a license franchises, consequently leading to cashier (5), who then passes the order on to the development and growth of the chain as the barista by marking a cup with the order a nationally recognized brand.1 if the order is not a drip coffee (7b). The Dunkin’ Donuts has since customer then pays (8b) and proceeds to the experienced exponential growth, leading to a designated pickup area (9b). The barista total of over 8,000 restaurants in the United then makes the coffee (10c) and hands it to States and 11,300 restaurants globally.1 the customer (11c). If the order is a drip Much of the recent growth can be attributed coffee, the cashier makes the coffee (8a) and to the brand’s recent shift away from food hands it directly to the customer (9a). Once items, namely donuts, and instead towards this occurs, the customer typically chooses coffee, effectively transitioning from being to stay in the shop and drink the coffee, mainly a restaurant to being mainly a coffee rather than leaving immediately. shop. The Starbucks business model This change is generally attributed to focuses on consumer satisfaction, increased CEO Jon Luther who, in 2003, was forced to distribution, partnerships, and international adapt to changing market tastes in order to expansion to encourage customers to stay keep afloat what was then a struggling with Starbucks as loyal customers. This business. Luther introduced a series of new model has worked well as the company’s coffee-based products, including espresso, annual growth rate from 2010 to 2014 was and expanded the menu to cater to a diverse eleven percent.7 range of customers.8 Dunkin’ Donuts has
Figure 2.2.1 – Process Map of Starbucks Operations
2.3 History of Dunkin’ Donuts since continued to follow this business model, which has brought it great success, The original Dunkin’ Donuts, almost doubling its stock price since its IPO excluding all affiliated brands such as in 2011.9 Dunkin’ Coffee and Baskin-Robbins, was started in 1950 by William Rosenburg in 2.4 Dunkin’ Donuts Business Model Quincy, Massachusetts. However, it was not until 1955 that Dunkin’ Donuts began to Dunkin’ Donuts focuses on service, amount of time to reach the counter, the emphasizing the quick delivery of food and customer served by one of two available drink items. The Dunkin Donuts system cashiers at either cashier’s earliest does not definitively delineate roles of convenience (3/4). The customer then cashier and barista; cashiers are proceeds to place his or her order simultaneously baristas. The workload is (5/6a/6b/6c), pay for the aforementioned often divided depending on the nature of the order and then wait for his order to be filled. drink, either hot specialty, cold specialty, or If the placed order is drip coffee or tea, drip, which is premade stock hot coffee. either cold or hot, the customer pays (7a) Dunkin’ Donuts does prioritize customer and is immediately served (9a). If the drink experience in the restaurant. Instead, service is a Coolatta®, or a frozen ice-based drink speed, convenience, and value are and the equivalent of a Frappucino® at prioritized, which can be seen in the brand Starbucks, the customer pays (7b), and the motto which is to “Make and serve the cashier then takes roughly three minutes to freshest, most delicious coffee and donuts personally make the drink (9b). If the drink quickly and courteously in modern, well- is a warm specialty drink, the order is passed merchandised stores.” This can also be seen down to a third employee who continually in the limited space inside restaurants which works the latte, cappuccino, and espresso indicates a model which primarily caters to machines (8). This worker then creates the customers who purchase food and drinks drink to give to the customer (9c), a process and then leave rather than those who stay in whose time depends on the type of drink the store after receiving their drinks and ordered. spend time socializing at the tables.8 Due to Dunkin’ Donuts currently focuses its high franchising rates, values and focuses business model on cost-optimization,
Figure 2.4.1 – Process Map of Dunkin’ Donuts Operations may deviate from store to store; however, seeking to capture a lower-income segment the original motto for the Dunkin’ Donuts of the market by offering products of similar brand remains expressly to "Make and serve quality to competitors for lower prices. the freshest, most delicious coffee and Though no official information has been donuts quickly and courteously in modern, released pertaining to profit margins per well-merchandised stores,” indicating that item, most speculate coffee to be the most speed, convenience, and value trump profitable item sold by Dunkin’ Donuts, customer experience.1 with economists believing that roughly 95% To begin the service process at a of coffee sales serving as pure profit.10 typical Dunkin’ Donuts store, customers Dunkin’ Donuts has also publically stated enter and begin queuing (see 1 and 2 in that it wishes to reach such cost optimization Figure 2.4.1). After waiting a variable through economies of scale, wherein the company is able to minimize the individual of roughly 3,000,000 customers daily.1 Their cost-per-unit by producing beverage and current menu offers an eclectic variety of food products in large quantities. This food and beverages, including upwards of minimization of cost allows Dunkin’ Donuts 50 donut options and over a dozen coffee- to reduce prices and therefore undercut based drink products. competitive companies while maintaining Overall, Dunkin’ Donuts is heavily healthy profit margins.11 franchised, has seen steady growth over the The growth of the Dunkin’ Donuts past 10 years, and has a business model companies has remained healthy over the centered on providing comparatively low past 5 years, namely thanks to the individual price items to undercut competitors and strength of the domestic Dunkin’ Donuts attract customers of a lower income bracket. brand. Sales for Dunkin’ Donuts brands, including Baskin-Robbins and international 2.5 Comparison of Starbucks and subsidiaries reached an annual total of Dunkin’ Donuts $748.709 million in 2014. Dunkin’ Donuts is heavily franchised, with roughly 7,000 of To elucidate the distinctions between current restaurants serving as franchises. Starbucks and Dunkin’ Donuts, this section Dunkin’ Donuts currently operates locally in will provide side by side comparison of 41 states while maintaining an international various aspects of the two chains (Figures presence in 36 countries, serving an average 2.5.1, 2.5.2).
2.6 Queueing Theory customer who arrives first receives service first, last in first out (LIFO), in which the Most businesses in the food industry customer who arrives last receives service deliver their products to customers through first, priority, in which some customers take service. The study of queueing theory can precedence over others, and random service be used to understand the different (RS), in which the order in which customers mechanisms used by companies to deliver are served is independent of arrival time or their products to customers. Queueing priority.15 theory is the mathematical theory and The notation used to identify analysis of waiting in queues. It was different types of queues is called Kendall’s originally used to optimize the number of notation. This notation follows the form telephone operators working at any given A/B/m where A is the type of arrival time; however, it can be applied to myriad process, B is the type of service process, and other industries including the food service m is the number of servers. The most industry and medical facilities. common model used to represent the arrival Mathematical models and operational process is called the Poisson Process. This measurements can then evaluate and process refers to a discrete model of arrival, increase customer flow.13 meaning that customers arrive as individual Results obtained through studies of units. Because customers cannot be queueing theory in the service industry can separated into non-whole number units, the improve everyday life of customers. By graph of arrival will not be continuous. The predicting wait times at various Poisson Process details the distribution of establishments, consumers can optimize events independent of each other as their time, a highly prized resource. exponential with a parameter λ. In Kendall’s Customer satisfaction from purchases is notation, the Poisson Process is represented largely dependent on queuing and by an M. An M can also be used to transaction time;14 therefore, minimizing represent an exponential distribution of waiting time through queueing theory can be service times. Service times can be very beneficial to companies. represented by a continuous exponential Queueing theory can be applied to distribution due to the ability to quantify the foodservice industry to analyze the time in very small increments.15 methods used by companies such as Dunkin’ One basic queueing model is the Donuts and Starbucks to deliver products to M/M/1 system. As the notation indicates, their customers. Random variables such as this refers to a queue in which customer arrival and service time along with details arrivals follow the Poisson Process, service concerning the method of delivering the times are exponentially distributed, and service characterize queueing models. It is there is one server. Variations of this model typically assumed that the system is include M/M/2, which is identical to the memoryless, in that each arrival is M/M/1 model except it includes two independent of the previous arrival, and that servers.15 the variables are identically distributed. The M/M/c system serves as an Queueing theory can be used to distinguish extension of the M/M/1 model, where c the sequence of requests for service and the represents a variable number of servers. order in which customers are served. There Variability of servers allows for idling when are numerous possibilities for serving order, the load is below c. such as first in first out (FIFO), in which the The M/G/1 system denotes a single server customer’s wait because the cashier has to with a general distribution time as opposed take time to write on the cup.16 to the memoryless service time model of This system also increases the M/M/1. The change in service time probability of needing to correct an error, as distribution indicates a different firm-side the presence of multiple servers adds response to the Poisson process. possibilities for mistakes.16 As was determined in a 2005 paper by Gregor Hohpe, the queueing process in 2.7 Similar Research coffee shops such as Starbucks is an example of an asynchronous processing Simulations have been used in model. The asynchronicity enters the model previous research to optimize processes in when the cashier places the cup in a various fast food restaurants.17, 18, 19, 20 secondary queue for the barista to make the Reducing Service Time at a Busy Fast Food drink. This allows the cashier to continue Restaurant on Campus indicated that serving customers when the barista is not simulations are a useful tool for accurately ready or multiple baristas to serve one line modeling and improving processes in a of customers, which increases the amount of restaurant.17 Additionally, Using Queueing customers that can be served in a given Theory and Simulation Model to Optimize amount of time. Additionally, the barista Hospital Pharmacy Performance revealed can begin to make the next drink in the that Arena Simulation Software is an queue before the customer retrieves the effective platform to construct simulations drink. In a process with one server per and that statistical analysis software is customer, also known as a two-phase- necessary to properly analyze queue commit approach, the process is linear, one distributions.13 Finally, the paper Computer step follows after another. This process is Simulation: An Important Tool in the Fast less efficient than an asynchronous model, Food Industry presented the technique of so it is not used in stores such as building a preliminary simulation and then Starbucks.16 adapting it by using observed data to set The asynchronous model results in parameters.18 This approach, as well as the the customers not necessarily receiving their use of Arena, was adopted in the research of orders in the same order in which they were Dunkin’ Donuts and Starbucks. placed. Because some drinks take longer to prepare than others, a drink that can be 3. Data Collection and Simulation prepared faster but was ordered later can be Creation delivered to the customer before a drink that has a longer preparation time but was 3.1 Data Collection Methodology ordered earlier. This creates a difficulty in matching the order to the customer; In order to collect the data needed to customers cannot simply wait in line for create simulations and analyze wait times, their drink to appear because the drink of trips to Dunkin’ Donuts and Starbucks shops someone behind them may appear before located in New Brunswick were taken. An their own. Starbucks resolves this equal amount of time of three days was complication by writing the names of the spent in both locations taking data. Tables customers on the cups and calling out the were set up in each location in order to name when the drink is ready. This collect data regarding the wait times of solution, however, adds time to the customers while in line and while waiting for an ordered drink. In order to get accurate them for easy access. The baristas are information, tables were chosen that were in located to the right with access to all of the view of the entrance of the shop, the other machines such as the Clover and cashier’s counter, and the waiting area. Espresso makers. The queue to order can be In order to record the times spent in seen below (represented by a black line). the queues within the store, a timing application was used. This application provided a timer that was pressed once a customer entered the store, once a customer ordered a drink, and once a customer received a drink. The total time a customer spends in the system is called the sojourn time. Also provided within the application was the ability to record which drink a customer recorded as well as a text box that allowed a description of the customer to be taken, which was helpful in ensuring that the data recorded using the timers was not mixed up between different customers. All Figure 3.1.1 – Starbucks Store Layout of the information being recorded was sent to a spreadsheet that organized each of the different categories. Recording the times The Dunkin’ Donuts store in New spent in queues allows analysis of wait times Brunswick that was visited to collect data that customers spend in each store. had a few tables for seating that were Recording the type of drink ordered was intended as a drink and then go accessory. also important because different drinks have As seen in Figure 3.1.2, when a person different average preparation times. Within comes into a Dunkin’ Donuts store, there are the application the drinks were separated cash registers located directly in front of the into categories that reflect similar customers. There are areas available for preparation times. The five options that seating on either side of the store although could be selected for drinks were Hot some of the tables are more isolated in a Drip/Tea, Ice Drip/Tea, Frappuccino, corner. The cashiers and baristas have Espresso/Latte/Cappuccino, and Clover. access to all of the machines, and the hot drip machines are located behind the cash 3.1.1 Store Layouts registers. The queue to order can be seen below in the figure. The Starbucks store in New Brunswick that was visited to collect data had a comfortable atmosphere with a strong coffee scent. There were many tables open 3.1.2 Errors in Data Collection and for seating and high-chair areas right next to Observation the barista’s coffee-making area. As seen in Figure 3.1.1, as soon as a person enters the When collecting data, there were Starbucks store, they can see the cash some variations in methodology from person registers in front. There are areas available to person. The first variation occurred with for seating on either side of the store. The differences in the interpretation of when a cashiers have the hot drip machines behind person counts as entering the store. Some applies to the order of beverages within Starbucks and Dunkin’ Donuts, data collected of people who entered the store only to use the toilet facilities and the data collected of people who ordered food rather than beverages had to be disregarded. Additionally, the researchers collecting data were inexperienced in this work which may have added to human error in the data.
3.2 Simulation Methodology
Rockwell Arena Simulation Queueing Software® is used for compiling and Baristas Line incorporating collected empirical data to Points of accurately create virtual simulations of Cashiers Observation / scenarios in businesses which can be Data Collection evaluated and manipulated. Simulation is a Figure 3.1.2 – Dunkin’ Donuts Store Layout method that presents information obtained from a constructed model based on observing work flow rotation from the current situation and other related data points were collected with the timer variables.18 being started when the customer opened the The three main components used in door and entered. Other data points were Arena simulations to represent various collected with the timer being started when components of actual operations are entities, the customer started to wait on line. The processes, and resources. Entities are the next variation occurred with differences in objects upon which processes are performed the interpretation of when a person was and must be defined first. Processes, which considered to have ordered a drink. Some act as operations performed upon the entities data points were collected with the timer and often incur delays within the queue, being pressed when a person told the cashier must be defined next. Lastly, resources the order. Some were collected when a must be created in order to perform the person paid the cashier. Another variation processes upon the entities. The nature of occurred when considering people who resources can be altered to allow for the ordered multiple drinks. Some data points prioritization of entities or to permit were collected when a person had finished multitasking. With proper classification of collecting all ordered drinks while others such objects, computer simulation provides were collected when a person got the first an accurate way to evaluate changes in the drink ordered. restaurant without disturbing the normal Some difficulties with the data day-to-day operations.18 In order for these collection included interpreting the start simulations to reflect the observed business time of timers, keeping track of customers operations, corresponding data and throughout the order process, and components must be inputted as factors of accounting for people who only entered the the simulated process. Since the average store for other purposes rather than ordering service times of different drink orders are beverages. Since the data collected only very different from each other, the Software was used to model these processes probabilities of each drink order are (Figures A.1, A.2). calculated to represent product variety at the respective stores. Furthermore, data 3.3 Data Analysis Methodology collected of service times for various observed drinks may reflect certain Microsoft® Excel was utilized in distributions. Thus, statistical evidence such order to sort all recorded data. After as probability distribution models and completing all necessary data certain respective parameters are required measurements, the resulting figures were for the simulation to adopt a specified then organized using a series of processes. distribution that would reflect firm Sort functions in the Microsoft® Excel operations based on empirical evidence. software were first used to organize the data For both restaurants, the simulation based on such parameters as alphabetic or consists of customers and drinks as entities, numeric order. Likewise, the “Delete drink production and cashier service as Duplicates” function in Excel was able to processes, and floor employees as resources. identify and delete any duplicate data. The simulations both begin through the Finally, manual sorting was also used to perspective of a customer but transition to determine any faulty or misrepresented data assume the position of a drink from its caused by human error in recording inception as an order into delivery to the procedures as well as any double-counted customer. As customers become largely data inherent to the data recording independent from the process after their techniques. For certain measurements, drink orders are processed, the drink including line waiting time and drink production process essentially equals the preparation time, the Excel software was length of the customer’s total wait after the also used to convert the times from order. Some processes involving cashier milliseconds to seconds. service after the order is placed are After sorting the data, Minitab accounted for as resource usage for more software, a conditionally free analytics than one process and can accurately be system, was then used to provide statistical represented in Arena although individual analysis for the data. Through data analysis, employee behavior cannot be modeled. one can identify patterns in data which may Since it had been decided that the simulation not be immediately obvious, then utilize of the ordering queue would be most such patterns to better understand the accurately represented by an M/M/c queue systems which produced the data. with a c-value of two, an Arena Simulation By entering the collected data points with two servers completing the process of and using the tools offered by the software, placing a drink order and a set queue with basic descriptive statistics were collected for values of wait times calculated with queuing each establishment, Dunkin Donuts and theory was created. Arena simulations apply Starbucks, as well as for each individual principles of queuing theory with statistical drink type. These statistics include mean, evidence that may accurately reflect real- median, maximum, minimum, standard time processes and components of the deviation, and quartile figures. Such Starbucks and Dunkin’ Donuts stores.21 statistics were found both for times spent Figures 2.2.1 and 2.4.1 show general flow waiting in line as well as time waiting for charts of service systems. Arena Simulation drinks to be prepared. Descriptive statistics can be used to determine, isolate, and analyze outliers in data as well as general 4.1 Starbucks Data trends, such as skewness or symmetry. Once such descriptive statistics were It is generally accepted in the study determined, the Minitab software was then of queueing theory that arrivals follow the used in order to perform significance tests to Poisson Process. This model assumes all determine appropriate probability arrivals to be independent, which can be distributions for the time spent in line at problematic in the case of the Dunkin’ each establishment as well as the required Donuts and Starbucks data because it was time to prepare each drink item, dependent observed that many customers did not arrive on the drink ordered as well as the independently; they either arrived with a restaurant. Minitab offers a total of 16 group of friends or would be drawn away possible probability distribution models, from or towards the store dependent on the including Weibull, Gamma, and Normal, size of the queue upon approach. The Chi- among 13 others. The appropriateness of square test for goodness of fit was used to each proposed data distribution model compare the distribution of arrival rates of comparative to the actual data distribution the observed data to the Poisson distribution. can be gauged by comparing the P-values By performing a Chi-square test in Minitab, and Anderson-Darling values provided by the p-value, or probability of independence, the software for each proposed distribution. can be calculated. A p-value of under 0.05 P-Values range between 0 and 1 and should generally indicates that the two inputs are exceed an arbitrary alpha value of between dependent on one another, while a p-value 0.05 and 0.10 to ensure that the distribution of over 0.05 indicates that the events are accurately represents the data. Meanwhile, independent. This means that a p-value of the Anderson-Darling Value can exceed 1 over 0.05 would be needed to conclude that but should be as low as possible, as the arrivals followed the Poisson Process relatively lower values comparative to other distribution. The p-value obtained from this distributions are indicative that the model test was practically zero, indicating that the more accurately reflects the data. The arrivals were not following the Poisson Anderson-Darling value can be used to Process. The results of the Chi-square test generally reaffirm the consensus indicated (Figure A.21) revealed that arrivals of four by the P-value. By using these two values in or more people weighed more heavily than it conjunction, one can find an appropriate should have, indicating that people did not probability distribution for any set of data. arrive independently and giving a possible Once the appropriate probability distribution reason why the Poisson Process would not was determined, the Minitab software was perfectly fit the data. When the expected then used to determine the parameters and observed counts were compared (Figure required by the Arena software in order to A.22) for every category, the number of run the distribution in the simulation. The times zero or three or more people arrived required parameters were dependent on the was too high, while the number of times one chosen probability distribution; however, or two people arrived was too low. This they were most often either mean and demonstrates that the arrival process does standard deviation or alpha and beta values not perfectly follow the Poisson distribution. for scale and shape. After analysis, it was determined that Starbucks queues followed a Weibull 4. Data Discussion distribution, demonstrating a strong right skew and a median value of 82.275 seconds, a maximum value of 325.024 seconds, and a median value of 80.629 seconds and a minimum value of 4.205 seconds. For all maximum value of 276.817 seconds (Figure distributions with rightward skew, median A.12). values of center will be used in order to compensate for the rightward skew, while 4.2 Dunkin’ Donuts Data mean values of center will be used for symmetric probability distributions. Queue Probability distributions for Dunkin’ wait time distributions also varied by day, Donuts wait times, both for queues and wherein observed Mondays displayed a drinks, differed from their Starbucks normal distribution, Tuesdays showed a counterparts, indicative of the manifestation gamma distribution, and Wednesdays of the previously outlined differences in the exhibited a Weibull distribution. Such business policies and structures for each differences can be attributed to differences respective company. Queues at Dunkin’ in customer inflow dependent on the day of Donuts had a gamma distribution, with a the week. However, it was found to be median value of 42.055 seconds and a appropriate to group data for all days into maximum value of 317.714 seconds. Like one collective data set, for both the data sets Starbucks, the queue wait time distribution of Dunkin’ Donuts and Starbucks, as not also varied depending on the day of the enough data was collected for each day to week. Mondays demonstrated a lognormal determine whether each day truly has a distribution, while Tuesday observations different probability distribution for queuing varied and were first believed to be gamma times, which could have been determined but were then seen to be lognormal. Lastly, with more observational studies, or if the Thursdays exhibited a gamma distribution. differences in probability distributions are Just as at Starbucks, drink wait times simply abnormalities in the regular flow of also varied depending on the type of drink business. ordered. Hot drip coffees were The probability distributions for each demonstrative of a lognormal distribution, Starbucks drink were variable. For hot drip which contains a slight rightward skew coffees, the data indicated a Weibull (Figure A.4). Hot drip coffee wait times had distribution, containing a strong right skew a median value of 59.838 seconds and a with a mean value of 69.093 seconds, a maximum value of 196.668 seconds. maximum value of 325.024 seconds and a Coolattas held a Weibull distribution with a minimum value of 8.028 seconds (Figure median value of 157.427 seconds and a A.9). Frappucinos demonstrated a gamma maximum value of 648.792 seconds (Figure distribution, which also contains a rightward A.6). Lattes showed a lognormal distribution skew but has a more severe skew with a median value of 102.919 seconds and comparative to the Weibull distribution an upper-bound maximum value of 267.075 (Figure A.11). Frappucino wait times had a seconds (Figure A.5). Finally, iced coffees median value of 78.888 seconds and a demonstrated a gamma distribution with a maximum value of 290.499 seconds. Lattes median value of 107.871 seconds and a exhibited a normal distribution, symmetric maximum value 350.140 seconds (Figure around the mean value of 94.656 seconds A.7). with a standard deviation of 64.194 seconds (Figure A.10). Lastly, iced coffee wait times 4.3 Starbucks vs. Dunkin’ Donuts demonstrated a Weibull distribution, once more showing a rightward skew with a Starbucks queue waiting times payments were averaged to gain the total tended to be generally longer than queue time of transaction inputted into the waiting times at Dunkin’ Donuts, as simulation. The paper listed the time for minimum, median, mean, and maximum cash as 28.86 seconds and it listed the time values for Starbucks queue waiting times for credit as 40.26 seconds.22 Therefore, the were all greater than their Dunkin’ Donuts time put into the simulation was an average counterparts. This data reflects Dunkin’ 34.56 seconds. Donuts’ devotion to quick service being In order to validate the simulation greater than that of Starbucks. Likewise, results in relation to the data collected preparation times for hot drip coffees were within the actual Starbucks and Dunkin’ longer at Starbucks than at Dunkin’ Donuts, Donuts stores, the two-sample Kolmogorov- wherein such aforementioned descriptive Smirnov test was used. This same test was statistics were all greater at Starbucks used by researchers who published comparative to Dunkin’ Donuts. However, Development and Application of a for all other drinks, including iced coffees, Validation Framework for Traffic lattes, and frappuccinos, Starbucks tended to Simulation and Statistical Validation of be quicker, exhibiting lower mean and Traffic Simulation Models. These two papers median values for all such drinks. Starbucks used the two-sample Kolmogorov-Smirnov also tended to be more consistent in its drink test to validate the traffic simulation models preparation times compared to Dunkin in relation to actual traffic.23, 24 Donuts as, for all drink preparation times When analyzing some of the results exclusive of hot drip coffee, standard of the simulation using the Kolmogorov- deviation values were lower at Starbucks Smirnov test, it was found that parts of the than at Dunkin’ Donuts. simulation did not accurately match the queue processes observed in the Starbucks 5. Simulation Results and Analysis restaurant. When running the simulations for Starbucks, there were some clear differences Simulating the processes within between the simulation results and the Starbucks and Dunkin’ Donuts requires collected data. The distribution for the input of the time it takes from entering the collected data of the Hot Drip was best fit store to ordering, the time it takes to mathematically by the Weibull distribution, complete a transaction with a cashier, and which provided the lowest relative P and the time it takes from ordering to receiving a Anderson-Darling values. Even though the drink. Data was collected on all of those Weibull distribution empirically provided processes except for the time it takes to the best fit for the data, the frequency complete a transaction with a cashier. Time histogram with fitted Weibull distribution Efficiency of Point-of-Sale Payment demonstrated that a Weibull distribution Methods: Empirical Results for Cash, Cards would not be appropriate for use within the and Mobile Payments relates data taken of simulation, as the aforementioned how long a transaction with a cashier takes. distribution would too heavily weight Hot The data in the paper is separated by Drip times trending around the zero value. payment method. It was observed while This would cause the mean values for hot collecting data that around half of the drip times to be unrealistically low; for customers paid with cash and half paid with example, a run of the simulation with the credit cards so the times given in the Weibull distribution as a parameter research paper for these methods of produced times of three seconds, which simulation results can be taken to accurately cannot be possible in reality. simulate the processes that take place within After matching the distribution for the two stores. Thus, analysis of the the data to the second-best mathematical fit, simulation data would be taken to reflect the an exponential fit, the distribution was more random queue processes that would occur reasonable, and, within the simulation, within the two stores. provided results more reflective of the For Dunkin’ Donuts and Starbucks, a observed data. The same error and analysis simulation was run of the sojourn time, the process was applied to the Iced Coffee data overall time from entering the store to for Starbucks, where the mathematically getting a drink. Running the Kolmogorov- appropriate distribution was forsaken in Smirnov test for the data in Minitab showed favor of a distribution which returned that the collected and simulated data had simulation results more reflective of real matching distributions for all of the data. Many of these errors could have been Starbucks data (Figure 5.1). The same test avoided had more data been collected; showed that the collected and simulated data however, time constraints rendered this for Dunkin’ Donuts had matching option an impossibility. distributions for only the Latte and the After making the necessary Coolatta (Figure 5.1). Whenever the K-S adjustments to the simulation probability value is less than the critical value, the distributions, the validity of the simulation distributions match. When the K-S value is results were tested by the Kolmogorov- greater than the critical value, the Smirnov test, which tests whether the distributions do not match, which happened distributions of two data sets match given with the Dunkin’ Donuts Hot and Iced certain parameters. Given that the Coffee. Another way to see whether the Kolmogorov-Smirnov test confirms the distributions match is by looking at hypothesis that the distributions match, the empirical cumulative distribution functions. Figures A.13- A.20 in the Appendix show cumulative distribution functions for the the empirical cumulative distribution simulated data and the collected data for functions side by side for the collected data Starbucks Espresso/Latte/Cappuccino and the simulated data which show the service time abide closely to the same difference in distributions for the other profiles. The Kolmogorov-Smirnov test was drinks. The Dunkin’ Donuts Hot and Iced run for the data, and the K-S value is 0.193 Coffee simulation data did not match what while the critical value is 0.225. Since the was collected in store because not all of the K-S value is less than the critical value, it is values inputted into the simulation were implied that the distributions for both sets of collected experimentally. Some of the values data match. The distribution for both sets of such as the time of the cashier transaction data is Normal. had to be taken from other sources such as Figure 5.1.2 shows both the established papers, which could have caused histogram curves and the empirical a difference in the simulation data versus the cumulative distribution functions for the collected data. simulated data and the collected data for Starbucks Frappuccino service time which abide closely to the same curves. The 5.1 Starbucks Service Time Simulation Kolmogorov-Smirnov test was run for the Analysis data, and the K-S value is 0.196 while the critical value is 0.269. Since the K-S value is Simulations were also run for the less than the critical value, it is implied that service times, the times from when the the distributions for both sets of data match. customer ordered the drink to when the The distribution for both sets of data is drink was received, in Starbucks and Gamma. Dunkin’ Donuts. Histograms, empirical As seen in Figure 5.1.3, both the cumulative distribution functions, and histogram curves and the empirical Kolmogorov-Smirnov tests were done for all cumulative distribution functions for the of the service time data for each of the simulated data and the collected data for drinks within each store. service time of Starbucks Hot Drip abide As seen in Figure 5.1.1, both the closely to the same profiles. The histogram curves and the the empirical Kolmogorov-Smirnov test was run for the
Figure 5.1.1 - CDF and Histogram for Starbucks Latte Simulated Data of Service Time vs Collected Data Figure 5.1.2 - CDF and Histogram for Starbucks Frappuccino Simulated Data of Service Time vs Collected Data
Figure 5.1.3 - CDF and Histogram for Starbucks Hot Drip Simulated Data of Service Time vs Collected Data
Figure 5.1.4 - CDF and Histogram for Starbucks Iced Drip Simulated Data of Service Time vs Collected Data data and the K-S value is 0.128 while the collected data is lognormal. Seen in the critical value is 0.262. Since the K-S value is histogram, the distributions are intuitively less than the critical value, it is implied that different, indicating that there exists a the distributions for both sets of data match. discrepancy within the structure of The distribution for both sets of data is simulation itself that does not affect service Weibull. time distributions of Iced and Coolatta As seen in Figure 5.1.4, neither the drinks to such a large degree. histogram curves nor the empirical Figure 5.2.2 shows both the cumulative distribution functions for the histogram curves and the empirical simulated data and the collected data for cumulative distribution functions for the service time of the Starbucks Iced Drip simulated data and the collected data for abide as closely to the same curve is service time, which do not abide closely to expected when the distributions match. The the same curves. The Kolmogorov-Smirnov Kolmogorov-Smirnov test was run for the test was run for the data and the K-S value is data, and the K-S value is 0.352 while the 0.220 while the critical value is 0.166. Since critical value is 0.215. Since the K-S value is the K-S value is greater than the critical greater than the critical value, it is implied value, it is implied that the distributions for that the distributions for both sets of data do both sets of data do not match. The not match. The reason for the difference in distribution of the collected data is weibull. distribution is that the process to make the Figure 5.2.3 shows both the Iced drip coffee is in the same queue as that histogram curves and the empirical of the Espresso drinks in the real world, but cumulative distribution functions for the this is not represented in the simulation. An simulated data and the collected data for espresso drink takes more time to make than service time, which do not abide closely to an Iced Drip Coffee (which is a relatively the same curves. The Kolmogorov-Smirnov short process), and the time spent in the test was run for the data and the K-S value is espresso queue substantially affects the 0.962 while the critical value is 0.163, amount of time between when the order is exemplifying a sharp distinction between the placed and when a customer receives the two data sets as the K-S value is larger than drink. the critical value by a large degree. The distribution of the collected data is 5.2 Dunkin’ Donuts Service Time lognormal. Simulation Analysis Figure 5.2.4 shows both the histogram curves and the empirical Figure 5.2.1 shows both the cumulative distribution functions for the histogram curves and the empirical simulated data and the collected data for cumulative distribution functions for the service time, which do abide closely to the simulated data and the collected data for same curves. The Kolmogorov-Smirnov test service time, which do abide closely to the was run for the data and the K-S value is same curves. The Kolmogorov-Smirnov test 0.080 while the critical value is 0.110. Since was run for the data and the K-S value is the K-S value is less than the critical value, 0.868 while the critical value is 0.227. Since it is implied that the distributions for both the K-S value is less than the critical value, sets of data do match. The distribution of the it is implied that the distributions for both collected data is gamma. sets of data do match. The distribution of the
Figure 5.2.1 - CDF and Histogram for Dunkin’ Donuts Latte Data of Service Time vs Collected Data
Figure 5.2.2 - CDF and Histogram for Dunkin’ Donuts Coolatta Data of Service Time vs Collected Data
Figure 5.2.3 - CDF and Histogram for Dunkin’ Donuts Drip Simulated Data of Service Time vs Collected Data
Figure 5.2.4 - CDF and Histogram for Dunkin’ Donuts Iced Drink Data of Service Time vs Collected Data results for Iced drink indicate that the These results in statistical matching of payment and ordering processes inaccurately sojourn and service times result in a diverse represented cashier interaction times in a set of combinations. While Latte and consistent manner as marked by a shift in Coolatta drinks matched for sojourn times, distribution curves (Figure ___ graph for they did not match for service times. While DD Iced sojourn time CDF). Thus, general Iced and Drip did not match for sojourn process of this production was correctly times, only Iced matched for service times. observed and translated yet payment and Thus, a case where a drink order fit both ordering processes could not be consistent distributions was nonexistent and implies a with this drink specifically. Such an error is considerable margin of error in this Dunkin’ coincidental in nature. As Drip does not Donuts simulation. Structurally, the DD match for neither sojourn nor service times, simulation is slightly more complex than there was quite possibly an unobserved that of Starbucks as the payment processes detail of workflow rotation and resource as observed were oriented towards management in the drink production that efficiency and frequent process overlaying, was distinct from that of all other drink which may be difficult to correctly replicate orders. Given the Drip product’s qualities given the flat, disassembled environment of itself and how they directly align with Arena. Since only sojourn times matched Dunkin’s expedited business model, a more with the Latte and Coolatta distributions, the complex or specialized process may have payment and ordering processes incorrectly actually been conducted. However, the same accounted for actual service times of those orientation of workflow rotation as in all drink orders that were not represented within other drinks was simulated, which may have the simulation. This discrepancy is more resulted in such deviated results. evident in the Latte (Figure 5.2.1) that Structural error implies that some exhibits a clear disparity in distribution, actual firm operations were unobserved or indicating that simulation structure directly unaccounted for when translating the deviated from actual operational structures. process onto the simulation platform. As the payment and ordering processes were Concepts such as worker rotation, general represented by constant delays, the simple workflow, and a behavioral aspect of translations in Coolatta service time employee behavior were unobserved and distribution (Figure 5.2.2) can be accounted thus not translated into the simulation. The for by said payment/ordering processes. The simulation employed default parameters to resource management which may directly and configured with analysis of relevant interfere with realistic modelling. Such data. The Minitab statistical package and inconsistency can propagate itself data analysis of queue times for individual throughout each of the simulated customers drink orders coupled with mutable modules and result in larger deficiencies in enabled simulations to be statistically distribution matching through such an accurate.The simulation can be tested for extended effect. In the case of workflow validity using the Kolmogorov-Smirnov test rotation, it is necessary to retain both a which compares distributions of the uniform and similar pattern within the simulated data to that of the collected data. simulation as the concept of queues itself Adaptable modules of the simulation allows requires arrival times via Poisson process. for alterations to experiment in resource As there are multiple processes as seen in utilization to increase efficiency and the simulation, irregular or distinct profitability. This modelling of firm workflow rotation affects the value of operations through simulations holds inputted distributions from data analysis. potential for such software and methodology The Arena Simulations for Dunkin that optimize usage of computational Donuts did not very accurately resemble the resources to apply from an industrial restaurant observed. While some of the engineering perspective that invites quality “time-to-make” simulation data came close control and other aspects. to achieving the goal of the Simulation, for Error is evident in some datasets but the most part they are not accurate enough to is conjecturally accounted for through sufficiently represent the restaurants. One extended analysis of empirical observations reason for this could be that our data set is and the issue with imposing such factors relatively small, especially once the data is into a simulation platform. It was recognized split into separate drink types. The lack of that employee behavior within each firm can data points prevented Minitab from be unpredictable and invites a larger degree accurately defining the distribution and of error and nonuniform resource parameters for the Dunkin Donuts management which opposes the consistent restaurant, and because of the low precision processes within the simulation. of these inputs into Arena the data points Furthermore, inconsistency in communal from the simulation lacked precision as well. data collection allowed for a larger degree of error that propagates into erroneous time 6. Conclusion distributions. Some graphs exhibit evidence that there exist distinct fundamental errors in A simulation that properly reflected simulation structure. Increased expertise the processes within Starbucks and Dunkin’ with the software that may enable more Donuts was created that could be altered to complex modelling is a valid method for accurately represent changes in firm future improvement. operations that may increase process A holistic analysis supported the efficiency and profitability without changing claim that Dunkin’ Donuts had lower queue actual employment or resource and service times following their expedient management.Process-charts representing the business model as opposed to the enriched- consumer purchase process were utilized to like nature of the Starbucks experience. It form simulation structures that were was observed within each site that the comprised of entities, processes, and amount of customer-oriented amenities were resources that mirrored that of actual firms representative of each firm’s business model and data analysis further corroborated the extend a special thanks to Deans Ilene notion that Dunkin’ Donuts operations are Rosen and Jean Patrick Antoine, directors of overall quicker than that of Starbucks in the New Jersey Governor’s School of light of business models. Engineering and Technology, for providing After confirming that the simulation the opportunity to perform this study. data accurately represents the processes Finally, the authors would like to within the stores, any occurrences in the acknowledge the New Brunswick Dunkin’ simulation after changes are made to it could Donuts and Starbucks establishments for be taken to accurately represent what would allowing the research to be conducted, actually happen in the restaurants. The Rutgers University and Rutgers School of simulation could be changed to allow for Engineering for hosting the Governor’s more efficient and profitable processes School program, as well as the State of New within the restaurants. These changes could Jersey for providing the necessary resources be implemented by testing different amounts to perform the study. of resources that are employed within the various processes. Changing the amounts of cashiers or baristas can result in changes within the queue times due to resources REFERENCES being employed in different areas. By 1 testing multiple variations of resources, an Dunkin’ Brands, “About Us,” 2014, optimal model for efficiency and
Appendix
Figure A.1 - Dunkin’ Donuts Arena Program
Figure A.2 - Starbucks Arena Program
Figure A.3 - Dunkin' Donuts (DD) Line Time Probability Distribution with Fit
Figure A.4 - Dunkin' Donuts Hot Drip Preparation Probability Distribution with Fit
Figure A.5 - Dunkin' Donuts Latte Preparation Probability Distribution with Fit
Figure A.6 - Dunkin' Donuts Frappucino Preparation Probability Distribution with Fit
Figure A.7 - Dunkin' Donuts Iced Coffee Preparation Probability Distribution with Fit
Figure A.8 - Starbucks Line Time Probability Distribution with Fit
Figure A.9 - Starbucks Hot Drip Preparation Probability Distribution with Fit
Figure A.10 - Starbucks Latte Preparation Probability Distribution with Fit
Figure A.11 - Starbucks Frappuccino Preparation Probability Distribution with Fit
Figure A.12 - Starbucks Iced Coffee Preparation Probability Distribution with Fit
Figure A.13 - CDF for the Espresso/Latte/Cappuccino Starbucks Simulation Data compared to the Collected Data
Figure A.14 -CDF for the Frappuccino Starbucks Simulation Data compared to the Collected Data
Figure A.15 -CDF for the Hot Drip Starbucks Simulation Data compared to the Collected Data
Figure A.16 -CDF for the Iced Drip Starbucks Simulation Data compared to the Collected Data
Figure A.17 -CDF for the Latte Dunkin’ Donuts Simulation Data compared to the Collected Data
Figure A.18 -CDF for the Iced Coffee Dunkin’ Donuts Simulation Data compared to the Collected Data
Figure A.19 -CDF for the Drip Dunkin’ Donuts Simulation Data compared to the Collected Data
Figure A.20 -CDF for the Coolatta Dunkin’ Donuts Simulation Data compared to the Collected Data
Figure A.21 -Chi-Square Value Graph
Figure A.22 -Observed vs. Expected Values Graph