Menya Sora Ramen Queueing Case: Operations Management Individual Assignment 2 2026

This operations assignment uses a small ramen restaurant to test queueing theory. Students first estimate the average number of customers in the store, the expected wait for a seat and the queue length under simple arrival and service assumptions, then repeat the analysis with a month of real lunch-service data, and finally judge whether a web-based ordering system that shortens but adds variability to time in store is worth the investment.

Case Background

Menya Sora was a popular restaurant in Fukuoka specialising in Hakata-style ramen, open only for weekday lunch. It served a small menu of ramen bowls prepared to order. Business had grown steadily over the past year, but owner Hironobu Kisaragi had begun receiving complaints about long waits during service.

The restaurant had only 22 counter seats arranged along an open kitchen. Typical customers were office workers who visited individually. An arriving customer was seated immediately if a seat was free; otherwise they joined a queue outside. On a typical weekday the restaurant opened at 11:00am and accepted any arriving customer until 2:00pm, after which no one could join the queue. Once in the queue, customers generally did not leave, and they were not picky about seats.

When a customer sat down, staff cleaned the counter space and explained the ordering process, which took around one minute with very little variation. The customer then ordered, waited for and ate the meal, paid and left, freeing the seat for the next customer.

Questions

Hironobu felt it was reasonable to assume that customers arrived at precise intervals of exactly one and a half minutes, and that each customer’s time in the store (from being seated to leaving) followed an exponential distribution with a mean of 30 minutes. Use these assumptions for Questions 1 and 2.

1. On average, how many customers are inside the restaurant at any point in time?
2. For a customer who has just arrived, use the current assumptions to estimate (a) their average waiting time for an available seat and (b) the expected number of customers in the queue.

Hironobu then collected customer data for all weekday lunch services in July 2026, recorded in the appended spreadsheet. Use these data for all subsequent questions.

3. For a customer who has just arrived, use the data to estimate (a) their average waiting time for an available seat and (b) the expected number of customers in the queue.
4. Hironobu is considering a web-based ordering system that would reduce customers’ time in store by half a minute but increase its standard deviation by around 3 minutes. He feels it is worth it if it reduces customers’ expected waiting time in the queue by 40% or more. Should he do this?

Assignment Instructions

• You may discuss the assignment with no more than 3 classmates, but each student must write up independently and list the classmates consulted.
• Do not give only final numerical answers; briefly explain the intermediate steps and rationale. Full credit requires both a correct explanation and a correct answer.

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