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If the restaurant runs a sale and the customer arrival rate increases by 20%, how would this change the total time expected to serve a customer? How would this change the average number of cars in the drive thru-line?

If the restaurant runs a sale and the customer arrival rate increases by 20%, how would this change the total time expected to serve a customer? How would this change the average number of cars in the drive thru-line?

Practical Management Science
Practical Management Science
6th Edition
ISBN:9781337406659
Author:WINSTON, Wayne L.
Publisher:WINSTON, Wayne L.
Chapter12: Queueing Models
Section12.4: Important Queueing Relationships
Problem 6P
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Question #5: If the restaurant runs a sale and the customer arrival rate increases by 20%, how would this change the total time expected to serve a customer? How would this change the average number of cars in the drive thru-line?
Analytics Exercise: Processing Customer Orders Analyzing a Taco Bell Restaurant The following scenario was written by a reporter who became a Taco Bell worker for a few hours to experience what it's like to work at one of the most high-tech quick-serve res- taurant chains in the world. As you read, visualize how you could analyze a Taco Bell using the queuing models that we discussed in this chapter. After the scenario, we will give you some hints related to how you can model the Quick Service (QS) restaurant and then ask a series of questions related to your model. It must always be, "Hi, how are you today?" Never, "Hi, how are you?" "Hi, how's it going?" or "Wel- come to Taco Bell." Never, "What will it be today?" or, even worse, "What do you want?" Every Taco Bell Service Champion memorizes the order script before his first shift. The folks who work the drive-thru windows at the Taco Bell here in Tustin, California, about 35 miles south of Los Angeles, and everywhere else, are called Service Champions. Those who work the food produc- tion line are called Food Champions. You think you know it-"Hi, how are you today?" It seems easy enough. And you follow that with, "You can order when you're ready," never "Can I take your order?" The latter puts pressure on the driver, who might be a distracted teenager busy texting her friend or a soc- cer mom with a half-dozen kids in the van. "They don't need the additional pressure of a disembodied voice demanding to know their order," explains Mike Harkins. Harkins, 49, is vice-president of One System Operations for Taco Bell, which means he spends all day, every day, thinking about the kitchen and the drive-thru. He has been prepping me for my debut at the window. Getting ready, I wash my hands, scrubbing for the man- dated 20 seconds; slide on rubber gloves; and don the three-channel headset that connects me to the ordering station out in the lot, as well as to my fellow Champions. I take my place at the window. I hear the ding indicating a customer has pulled into the loop around the restau- rant, and I immediately ask, "Hi, how's it going?" It gets worse from there. As a Service Champion, my job is to say my lines, input the order into the proprietary point of sale (POS) system, prepare and make drinks like Limeade Sparklers and Frutista Freezes, collect bills or credit cards, and make change. I input Beefy Crunch Burritos, Volcano Burritos, Chalupas, and Gorditas. My biggest worry is that someone will order a Crunchwrap Supreme, a fast-food marvel made up of two kinds of tortillas, beef, cheese, lettuce, tomatoes, and sauces, all scooped, folded, and assembled into a handheld, multiple-food-group package, which then gets grilled for 27 seconds. This actually doubles the time it takes to prepare a normal order. An order for a Crunchwrap Supreme, the most complex item on the menu, sometimes requires the Service Champion to take up position on the
Transcribed Image Text:Analytics Exercise: Processing Customer Orders Analyzing a Taco Bell Restaurant The following scenario was written by a reporter who became a Taco Bell worker for a few hours to experience what it's like to work at one of the most high-tech quick-serve res- taurant chains in the world. As you read, visualize how you could analyze a Taco Bell using the queuing models that we discussed in this chapter. After the scenario, we will give you some hints related to how you can model the Quick Service (QS) restaurant and then ask a series of questions related to your model. It must always be, "Hi, how are you today?" Never, "Hi, how are you?" "Hi, how's it going?" or "Wel- come to Taco Bell." Never, "What will it be today?" or, even worse, "What do you want?" Every Taco Bell Service Champion memorizes the order script before his first shift. The folks who work the drive-thru windows at the Taco Bell here in Tustin, California, about 35 miles south of Los Angeles, and everywhere else, are called Service Champions. Those who work the food produc- tion line are called Food Champions. You think you know it-"Hi, how are you today?" It seems easy enough. And you follow that with, "You can order when you're ready," never "Can I take your order?" The latter puts pressure on the driver, who might be a distracted teenager busy texting her friend or a soc- cer mom with a half-dozen kids in the van. "They don't need the additional pressure of a disembodied voice demanding to know their order," explains Mike Harkins. Harkins, 49, is vice-president of One System Operations for Taco Bell, which means he spends all day, every day, thinking about the kitchen and the drive-thru. He has been prepping me for my debut at the window. Getting ready, I wash my hands, scrubbing for the man- dated 20 seconds; slide on rubber gloves; and don the three-channel headset that connects me to the ordering station out in the lot, as well as to my fellow Champions. I take my place at the window. I hear the ding indicating a customer has pulled into the loop around the restau- rant, and I immediately ask, "Hi, how's it going?" It gets worse from there. As a Service Champion, my job is to say my lines, input the order into the proprietary point of sale (POS) system, prepare and make drinks like Limeade Sparklers and Frutista Freezes, collect bills or credit cards, and make change. I input Beefy Crunch Burritos, Volcano Burritos, Chalupas, and Gorditas. My biggest worry is that someone will order a Crunchwrap Supreme, a fast-food marvel made up of two kinds of tortillas, beef, cheese, lettuce, tomatoes, and sauces, all scooped, folded, and assembled into a handheld, multiple-food-group package, which then gets grilled for 27 seconds. This actually doubles the time it takes to prepare a normal order. An order for a Crunchwrap Supreme, the most complex item on the menu, sometimes requires the Service Champion to take up position on the
food production line to complete it in anything like the 164 seconds that Taco Bell averages for each customer, from driving up to the ordering station to pulling away from the pick-up window. Above me on the wall, a flat-screen display shows the average time of the last five cars at either the order station or the pick-up window, depending on which is slowest. If the number is red, as it is now, that means one, or both, of the waits is exceeding 50 seconds, the target during peak periods. It now shows 53 seconds, on its way to 60, 70... and then I stop looking. The high-pitched ding that announces each new customer becomes steady, unrelenting, and dispiriting-85 cars will roll through over the peak lunch rush. And I keep blowing the order script. I fall behind so quickly and completely that restau- rant manager Amanda Mihal, a veteran of 12 years in the QSR business (Quick Serve Restaurant, the acronym for an industry that makes acronyms for everything), has to step in. "You'll get it," Amanda says as she fixes an order that I have managed to screw up. "Eventually," Every Taco Bell has two food production lines, one dedicated to the drive-thru and the other to servicing liner in the walk-up counter. Working those lines is no easier than wearing the headset. The back of the restaurant has been engineered so that the Steamers, Stuffers, and Expeditors, the names given to the Food Champions who work the pans, take as few footsteps as possible during a shift. There are three prep areas: the hot hold- ing area, the cold holding area, and the wrapping ex- pediting area. The Stuffer in the hot holding area stuffs the meat into the tortillas, ladling beef with Taco Bell's proprietary tool, the BPT, or beef portioning tool. The steps for scooping the beef have been broken down into another acronym, SST, for stir, scoop, and tap. Flour tortillas must be cooked on one side for 15 seconds and the other for five. When I take my place on the line and start to prepare burritos, tacos, and chalupas-they won't let me near a Crunchwrap Supreme-it is immediately clear that this has been engineered to make the process as simple as possible. The real challenge is the wrapping. Taco Bell once had 13 different wrappers for its products. That has been cut to six by labeling the corners of each wrapper differently. The paper, designed to slide off a stack in single sheets, has to be angled with the name of the item being made at the upper corner. The tortilla is placed in the middle of the paper and the item assembled from there until you fold the whole thing up in the wrapping expediting area next to the grill. "We had so many wrap- pers before, half a dozen stickers; it was all costing us seconds," says Harkins. In repeated attempts, I never get the proper item name into the proper place. And my bur- ritos just do not hold together. With me on the line are Carmen Franco, 60, and Ricardo Alvarez, 36. The best Food Champions can prepare about 100 burritos, tacos, chalupas, and gordi- tas in less than half an hour, and they have the 78-item menu memorized. Franco and Alvarez are a precise and frighteningly fast team. Ten orders at a time are dis- played on a screen above the line, five drive-thrus and five walk-ins. Franco is a blur of motion as she slips out wrapping paper and tortillas, stirs, scoops, and taps, then slides the items down the line while looking up at the screen. The top Food Champions have an ability to scan through the next five orders and identify those that require more preparation steps, such as Grilled Stuffed Burritos and Crunchwrap Supremes, and set those up before returning to simpler tacos and burritos. When Alvarez is bogged down, Franco slips around him, and slides Crunchwrap Supremes into their boxes. At the drive-thru window in Tustin, I would have shaken off the headset many orders ago had it not been for manager Mihal's support, but I'm hanging in there. After a while, I do begin to detect a pleasing, steady rhythm to the system, the transaction, the delivery of the food. Each is a discrete, predictable, scripted interaction. When the order is input correctly, the customer drives up to the window, the money is paid, the Frutista Freeze or Atomic Bacon Bombers (a test item specific to this Taco Bell) handed over, and you send people on their way with a smile and a "Thank you for coming to Taco Bell," you feel a moment of accomplishment. And so does Harkins, for it has all gone exactly as he has planned. Then a ding in my headset. "Um, hello?" Idiot, I think to myself, I've blown the script again. Source: Karl Taro Greenfeld, Bloomberg Business Week Features Section, May 5, 2011 Modeling the Restaurant In the scenario, they indicate that it takes about 164 seconds on average to serve a customer during the busy lunch hour period. Put yourself in the seat of your car getting food at the FS restaurant. Let's assume you are using the drive-thru window and that you will pick up the food and take it home to eat with some friends. You drive into the restaurant lot and notice there is a line of cars that has formed at the order kiosk. You wait for your turn to talk to the Customer Service Champion so that you can place your order. The menu is sitting there in clear view, so you can see exactly what you want. Soon it is your turn and you quickly place your order, learn what the bill will be, and move your car to the line at the drive-thru window. While waiting, you get your money out and count out the exact change you will need. After a short time, it's your turn at the window and you give the Service Champion your money, take your drink and food, and carefully drive out of the parking lot. 242 section 2 . MANUFACTURING AND SERVICE PROCESSES Think about what happened at the restaurant. First, you waited in two lines. The first was at the order kiosk and the second at the drive-thru window. Next, consider the work that the restaurant needed to complete to process your order. The Service Champion took your order and entered it in the POS system, prepared your drink, and then when the food was ready, collected your money, and delivered your drink and food. One of the Food Champions prepared your food using information from a screen that shows orders as they are entered by the Service Champion. The total time that it takes between when you arrive at the restaurant until you leave is made up of the following elements: 1 The service time for the Service Champion to process your order 2 The service time for the Food Champion to prepare your order 3 The waiting while the Service Champion and Food Champion served other customers To model this using the queuing models in the chapter assume that you have two totally independent service processes. The first process is the Service Champion and the second is the Food Champion. Each process has potentially a different mean service time per customer. The Service Champion must serve each customer and they arrive at a particular rate. The Food Champion prepares the individual items on the order such as a burrito, taco, chalupa, or gorditas taco. As the orders are taken, each individual item appears on a monitor telling the Food Champion what should be made next. The average time for a customer to run through the system is the sum of the average service times (time to take the order by the Service Champion and time to make the order by the Food Champion) plus the sum of the expected waiting times for the two processes. This assumes that these processes operate totally independent of each other, which might not be exactly true. But we leave that to a later discussion. Assume that the queues in front of each process are large, meaning that there is plenty of room for cars in the line be- fore and after the order kiosk. Also, assume there is a single Super Quiz 1 Service systems can be generally categorized ac- cording to this characteristic that relates to the customer. 2 A framework that relates to the customer service sys- Service Champion and two Food Champions each operat- ing independently and working just on the drive-thru orders. Also, assume that the arrival pattern is Poisson, customers are handled first-come-first-served, and the service pattern is exponential. Given this, answer the following questions: 1 Draw a diagram of the process using the format in Exhibit 7.3. 2 Consider a base case where a customer arrives every 40 seconds and the Customer Service Champion can handle 120 customers per hour. There are two Food Champions, each capable of handling 100 orders per hour. How long should it take to be served by the restaurant (from the time a customer enters the kiosk queue until her food is delivered)? Use queuing mod- els to estimate this. 3 On average, how busy are the Customer Service Champions and the two Food Champions? 4 On average, how many cars do you expect to have in the drive-thru line? (Include those waiting to place orders and those waiting for food.) 5 If the restaurant runs a sale and the customer arrival rate increases by 20%, how would this change the total time expected to serve a customer? How would this change the average number of cars in the drive- thru line? 6 Currently, relatively few customers (less than 14%) order the Crunchwrap Supreme. What would happen if the restaurant ran the sale, demand jumped on the Crunchwrap Supreme, and 30% of the orders were for this item? Take a quantitative approach to answer- ing this question. Assume that the Customer Service Champion never helps the Food Champions and that these two processes remain independent. 7 For the type of analysis done in this case, what are the key assumptions? What would be the impact on our analysis if these assumptions were not true? 8 Could this type of analysis be used for other service- type businesses? Give examples to support your answer. 6 Consider two queuing systems identical except for the service time distribution. In the first system the service time is random and distributed according to a Poisson distribution. The service time is constant
Transcribed Image Text:food production line to complete it in anything like the 164 seconds that Taco Bell averages for each customer, from driving up to the ordering station to pulling away from the pick-up window. Above me on the wall, a flat-screen display shows the average time of the last five cars at either the order station or the pick-up window, depending on which is slowest. If the number is red, as it is now, that means one, or both, of the waits is exceeding 50 seconds, the target during peak periods. It now shows 53 seconds, on its way to 60, 70... and then I stop looking. The high-pitched ding that announces each new customer becomes steady, unrelenting, and dispiriting-85 cars will roll through over the peak lunch rush. And I keep blowing the order script. I fall behind so quickly and completely that restau- rant manager Amanda Mihal, a veteran of 12 years in the QSR business (Quick Serve Restaurant, the acronym for an industry that makes acronyms for everything), has to step in. "You'll get it," Amanda says as she fixes an order that I have managed to screw up. "Eventually," Every Taco Bell has two food production lines, one dedicated to the drive-thru and the other to servicing liner in the walk-up counter. Working those lines is no easier than wearing the headset. The back of the restaurant has been engineered so that the Steamers, Stuffers, and Expeditors, the names given to the Food Champions who work the pans, take as few footsteps as possible during a shift. There are three prep areas: the hot hold- ing area, the cold holding area, and the wrapping ex- pediting area. The Stuffer in the hot holding area stuffs the meat into the tortillas, ladling beef with Taco Bell's proprietary tool, the BPT, or beef portioning tool. The steps for scooping the beef have been broken down into another acronym, SST, for stir, scoop, and tap. Flour tortillas must be cooked on one side for 15 seconds and the other for five. When I take my place on the line and start to prepare burritos, tacos, and chalupas-they won't let me near a Crunchwrap Supreme-it is immediately clear that this has been engineered to make the process as simple as possible. The real challenge is the wrapping. Taco Bell once had 13 different wrappers for its products. That has been cut to six by labeling the corners of each wrapper differently. The paper, designed to slide off a stack in single sheets, has to be angled with the name of the item being made at the upper corner. The tortilla is placed in the middle of the paper and the item assembled from there until you fold the whole thing up in the wrapping expediting area next to the grill. "We had so many wrap- pers before, half a dozen stickers; it was all costing us seconds," says Harkins. In repeated attempts, I never get the proper item name into the proper place. And my bur- ritos just do not hold together. With me on the line are Carmen Franco, 60, and Ricardo Alvarez, 36. The best Food Champions can prepare about 100 burritos, tacos, chalupas, and gordi- tas in less than half an hour, and they have the 78-item menu memorized. Franco and Alvarez are a precise and frighteningly fast team. Ten orders at a time are dis- played on a screen above the line, five drive-thrus and five walk-ins. Franco is a blur of motion as she slips out wrapping paper and tortillas, stirs, scoops, and taps, then slides the items down the line while looking up at the screen. The top Food Champions have an ability to scan through the next five orders and identify those that require more preparation steps, such as Grilled Stuffed Burritos and Crunchwrap Supremes, and set those up before returning to simpler tacos and burritos. When Alvarez is bogged down, Franco slips around him, and slides Crunchwrap Supremes into their boxes. At the drive-thru window in Tustin, I would have shaken off the headset many orders ago had it not been for manager Mihal's support, but I'm hanging in there. After a while, I do begin to detect a pleasing, steady rhythm to the system, the transaction, the delivery of the food. Each is a discrete, predictable, scripted interaction. When the order is input correctly, the customer drives up to the window, the money is paid, the Frutista Freeze or Atomic Bacon Bombers (a test item specific to this Taco Bell) handed over, and you send people on their way with a smile and a "Thank you for coming to Taco Bell," you feel a moment of accomplishment. And so does Harkins, for it has all gone exactly as he has planned. Then a ding in my headset. "Um, hello?" Idiot, I think to myself, I've blown the script again. Source: Karl Taro Greenfeld, Bloomberg Business Week Features Section, May 5, 2011 Modeling the Restaurant In the scenario, they indicate that it takes about 164 seconds on average to serve a customer during the busy lunch hour period. Put yourself in the seat of your car getting food at the FS restaurant. Let's assume you are using the drive-thru window and that you will pick up the food and take it home to eat with some friends. You drive into the restaurant lot and notice there is a line of cars that has formed at the order kiosk. You wait for your turn to talk to the Customer Service Champion so that you can place your order. The menu is sitting there in clear view, so you can see exactly what you want. Soon it is your turn and you quickly place your order, learn what the bill will be, and move your car to the line at the drive-thru window. While waiting, you get your money out and count out the exact change you will need. After a short time, it's your turn at the window and you give the Service Champion your money, take your drink and food, and carefully drive out of the parking lot. 242 section 2 . MANUFACTURING AND SERVICE PROCESSES Think about what happened at the restaurant. First, you waited in two lines. The first was at the order kiosk and the second at the drive-thru window. Next, consider the work that the restaurant needed to complete to process your order. The Service Champion took your order and entered it in the POS system, prepared your drink, and then when the food was ready, collected your money, and delivered your drink and food. One of the Food Champions prepared your food using information from a screen that shows orders as they are entered by the Service Champion. The total time that it takes between when you arrive at the restaurant until you leave is made up of the following elements: 1 The service time for the Service Champion to process your order 2 The service time for the Food Champion to prepare your order 3 The waiting while the Service Champion and Food Champion served other customers To model this using the queuing models in the chapter assume that you have two totally independent service processes. The first process is the Service Champion and the second is the Food Champion. Each process has potentially a different mean service time per customer. The Service Champion must serve each customer and they arrive at a particular rate. The Food Champion prepares the individual items on the order such as a burrito, taco, chalupa, or gorditas taco. As the orders are taken, each individual item appears on a monitor telling the Food Champion what should be made next. The average time for a customer to run through the system is the sum of the average service times (time to take the order by the Service Champion and time to make the order by the Food Champion) plus the sum of the expected waiting times for the two processes. This assumes that these processes operate totally independent of each other, which might not be exactly true. But we leave that to a later discussion. Assume that the queues in front of each process are large, meaning that there is plenty of room for cars in the line be- fore and after the order kiosk. Also, assume there is a single Super Quiz 1 Service systems can be generally categorized ac- cording to this characteristic that relates to the customer. 2 A framework that relates to the customer service sys- Service Champion and two Food Champions each operat- ing independently and working just on the drive-thru orders. Also, assume that the arrival pattern is Poisson, customers are handled first-come-first-served, and the service pattern is exponential. Given this, answer the following questions: 1 Draw a diagram of the process using the format in Exhibit 7.3. 2 Consider a base case where a customer arrives every 40 seconds and the Customer Service Champion can handle 120 customers per hour. There are two Food Champions, each capable of handling 100 orders per hour. How long should it take to be served by the restaurant (from the time a customer enters the kiosk queue until her food is delivered)? Use queuing mod- els to estimate this. 3 On average, how busy are the Customer Service Champions and the two Food Champions? 4 On average, how many cars do you expect to have in the drive-thru line? (Include those waiting to place orders and those waiting for food.) 5 If the restaurant runs a sale and the customer arrival rate increases by 20%, how would this change the total time expected to serve a customer? How would this change the average number of cars in the drive- thru line? 6 Currently, relatively few customers (less than 14%) order the Crunchwrap Supreme. What would happen if the restaurant ran the sale, demand jumped on the Crunchwrap Supreme, and 30% of the orders were for this item? Take a quantitative approach to answer- ing this question. Assume that the Customer Service Champion never helps the Food Champions and that these two processes remain independent. 7 For the type of analysis done in this case, what are the key assumptions? What would be the impact on our analysis if these assumptions were not true? 8 Could this type of analysis be used for other service- type businesses? Give examples to support your answer. 6 Consider two queuing systems identical except for the service time distribution. In the first system the service time is random and distributed according to a Poisson distribution. The service time is constant
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