Lines at Loaf N' Latte

CASE DESCRIPTION This case applies queuing theory in a small business. Students gain an appreciation for the usefulness as well as the difficulties of producing appropriate data and analyses rather than working text problems that contain only summary measures. Specifically, students analyze interarrival and service times collected during a five day period. (Values are included and can be changed to renew and reuse the case.) The case has a difficulty level between three and four and can be completed by Junior and senior level undergraduate students in introductory quantitative analysis, operations research, or management science courses in 2 - 3 hours time. Analysis can include computation of the current situation at the business as well as explorations of alternative arrangements. CASE SYNOPSIS Like many entrepreneurs, Anna Jamison believed she had an idea that would prove to be a viable and sustainable business. She created a coffee shop and vegetarian restaurant in a small college town. She succeeded. The business became a favorite among professors and college students. The alternative menu appealed to this demographic. It offered customers a variety of vegetarian items and baked goods that could not be found in other food establishments near the campus. Additionally, the relaxing atmosphere allowed customers to work and study, so students and professors spent hours in the restaurant drinking coffee and working on projects. Ms. Jamison appreciated these customers despite the limited space. In the past, long lines were never a problem, but recently several complaints surfaced, and some customers even walked out rather than wait in the long lines during lunch periods. Anna wishes to address this problem before Loaf n' Latte develops a reputation for slow service. She would like to evaluate options and remedy the situation. INSTRUCTORS' NOTES Recommendation for Teaching Approaches The project offers opportunities to appreciate difficulties as well as benefits of applying quantitative models in the real world. Specifically, the project investigates queuing models and cost effectiveness of different queuing systems for a small eating establishment. There are actually three stages or levels of this project. We describe the first two as background for instructors who wish to pursue data collection and individual projects rather than employ the actual aggregate data available with this case. During the first week of class, students initially encountered the business itself, its queuing system, and the participants (customers and servers). With minimal background information and instruction, they observed and recorded interarrivai times and service times over a short time period. The students also noted aberrations that made it difficult to measure these times, such as servers who do something else in the middle of serving a customer, customers who balk or renege, or customers who arrive in groups. (We actually set up an extreme case with colleagues who arrived at different times and broke in line.) Class discussion based on their observations yielded a protocol and consensus on how to define and consistently measure arrival intervals and server times. Student benefits from their experiences in the shop and with these technical aspects of the project include: * Increased awareness of the messiness of real world data and, consequently, the need to define and consistently measure variables as well as treat resulting computed value more warily, and * Impressions of queuing systems and increased attention to actual queues, both of which motivate further study of queuing models and recognition of technical terms. * Even professors who do not proceed with the next stage may want to heighten student interest and understanding by requiring that they visit actual businesses to observe and collect data (however roughly). Following their data collection, students did individual analyses of the queuing situation and its cost effectiveness based on their individual data sets and their personal observations. …