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A fast-food franchise is considering operating a drive-up window food-service operation. Assume that customer arrivals follow a Poisson probability distribution, with an arrival rate of 26 cars per hour, and that service times follow an exponential probability distribution. Arriving customers place orders at an intercom station at the back of the parking lot and then drive to the service window to pay for and receive their orders. The following three service alternatives are being considered. 1. A single-server operation in which one employee fills the order and takes the money from the customer. The average service time for this alternative is 2 minutes. 2. A single-server operation in which one employee fills the order while a second employee takes the money from the customer. The average service time for this alternative is 1.25 minutes. 3. A two-server operation with two service windows and two employees. The employee stationed at each window fills the order and takes the money from customers arriving at the window. The average service time for this alternative is 2 minutes for each server. The following cost information is available for the given fast-food franchise. • Customer waiting time is valued at $25.00 per hour to reflect the fact that waiting time is costly to the fast-food business. • The cost of each employee is $12.75 per hour. • To account for equipment and space, an additional cost of $20.00 per hour is attributable to each server. What is the lowest-cost design for the fast-food business? (Express the total cost per hour in dollars. Round your answers to the nearest cent.) for system 1, $ The total cost per hour, i.e. the combined time value of the customer and the business, is $ for system 2, and for system 3, respectively. Therefore, system? is the most economical.

A fast-food franchise is considering operating a drive-up window food-service operation. Assume that customer arrivals follow a Poisson probability distribution, with an arrival rate of 26 cars per hour, and that service times follow an exponential probability distribution. Arriving customers place orders at an intercom station at the back of the parking lot and then drive to the service window to pay for and receive their orders. The following three service alternatives are being considered. 1. A single-server operation in which one employee fills the order and takes the money from the customer. The average service time for this alternative is 2 minutes. 2. A single-server operation in which one employee fills the order while a second employee takes the money from the customer. The average service time for this alternative is 1.25 minutes. 3. A two-server operation with two service windows and two employees. The employee stationed at each window fills the order and takes the money from customers arriving at the window. The average service time for this alternative is 2 minutes for each server. The following cost information is available for the given fast-food franchise. • Customer waiting time is valued at $25.00 per hour to reflect the fact that waiting time is costly to the fast-food business. • The cost of each employee is $12.75 per hour. • To account for equipment and space, an additional cost of $20.00 per hour is attributable to each server. What is the lowest-cost design for the fast-food business? (Express the total cost per hour in dollars. Round your answers to the nearest cent.) for system 1, $ The total cost per hour, i.e. the combined time value of the customer and the business, is $ for system 2, and for system 3, respectively. Therefore, system? is the most economical.

Practical Management Science
Practical Management Science
6th Edition
ISBN:9781337406659
Author:WINSTON, Wayne L.
Publisher:WINSTON, Wayne L.
Chapter12: Queueing Models
Section12.5: Analytic Steady-state Queueing Models
Problem 9P
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A fast-food franchise is considering operating a drive-up window food-service operation. Assume that customer arrivals follow a Poisson probability distribution, with an arrival rate of 26 cars per hour, and that service times follow an exponential probability distribution. Arriving customers place orders at an intercom station at the back of the parking lot and then drive to the service window to pay for and receive their orders. The following three service alternatives are being considered. 1. A single-server operation in which one employee fills the order and takes the money from the customer. The average service time for this alternative is 2 minutes. 3. A two-server operation with two service windows and two employees. The employee stationed at each window fills the order and takes the money from customers arriving at the window. The average service time for this alternative is 2 minutes for each server. The following cost information is available for the given fast-food franchise. $ 2. A single-server operation in which one employee fills the order while a second employee takes the money from the customer. The average service time for this alternative is 1.25 minutes. • Customer waiting time is valued at $25.00 per hour to reflect the fact that waiting time is costly to the fast-food business. • The cost of each employee is $12.75 per hour. • To account for equipment and space, an additional cost of $20.00 per hour is attributable to each server. What is the lowest-cost design for the fast-food business? (Express the total cost per hour in dollars. Round your answers to the nearest cent.) for system 1, $ The total cost per hour, i.e. the combined time value of the customer and the business, is $ for system 2, and for system 3, respectively. Therefore, system ? ✓ is the most economical. tA
Transcribed Image Text:A fast-food franchise is considering operating a drive-up window food-service operation. Assume that customer arrivals follow a Poisson probability distribution, with an arrival rate of 26 cars per hour, and that service times follow an exponential probability distribution. Arriving customers place orders at an intercom station at the back of the parking lot and then drive to the service window to pay for and receive their orders. The following three service alternatives are being considered. 1. A single-server operation in which one employee fills the order and takes the money from the customer. The average service time for this alternative is 2 minutes. 3. A two-server operation with two service windows and two employees. The employee stationed at each window fills the order and takes the money from customers arriving at the window. The average service time for this alternative is 2 minutes for each server. The following cost information is available for the given fast-food franchise. $ 2. A single-server operation in which one employee fills the order while a second employee takes the money from the customer. The average service time for this alternative is 1.25 minutes. • Customer waiting time is valued at $25.00 per hour to reflect the fact that waiting time is costly to the fast-food business. • The cost of each employee is $12.75 per hour. • To account for equipment and space, an additional cost of $20.00 per hour is attributable to each server. What is the lowest-cost design for the fast-food business? (Express the total cost per hour in dollars. Round your answers to the nearest cent.) for system 1, $ The total cost per hour, i.e. the combined time value of the customer and the business, is $ for system 2, and for system 3, respectively. Therefore, system ? ✓ is the most economical. tA
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