Operations Management – Homework Assignment 1

3.2) At the drive-through counter of a fast-food outlet, an average of 10 cars waits in line. The manager wants to determine if the length of the line is having any impact on potential sales. A study reveals that, on average, 2 cars per minute try to enter the drive-through area, but 25 percent of the drivers of these cars are dismayed by the long line and simply move on without placing orders. Assume that no car that enters the line leaves without service. On average, how long does a car spend in the drive-through line?

Answer:
Based on problem data we have to use Little’s Law in order to solve the problem.
We have the I (average inventory) and T (average flow) and we need to
All data conform to planners’ expectations except for one set—the classifications made by the nurse practitioner. Assume that the triage nurse has been sending 91 percent of all patients to the Simple Prescription area when in fact only 90 percent should have been so classified. The remaining 1 percent is discovered when transferred to the emergency area by a doctor. Assume all other information from Exercise 3.5 to be valid. On average, how long does a patient spend in the ER? On average, how long does a Potential Admit spend in the ER? On average, how many patients are in the ER? Assume the process to be stable; that is, average inflow rate equals average outflow rate.

Answer: Based on the problem description the following flow can be plotted (assumed that the triage takes 1 minute).

Based on the problem description the values in green boxes are given. The values in yellow boxes were calculated based on Little’s Law formula (T = I / R). The value in blue were calculated based on the patient’s flow over the process (91% or 10% based if they are going to be prescribed or admitted on hospital – including the mistake on the triage process).

How long, on average, a patient spends in the ER equals to 55.32 minutes. Since 90% of the patients spend 53.3 minutes, 9% of the patients spend 71.2 minutes and 1% of the patients spend 94.2 minutes.

Patients prescribed flow over the activities 1, 2, 3, 4, 5