Operations Management

Topics: Normal distribution, Department store, Queueing theory Pages: 2 (594 words) Published: November 27, 2012
Caroline Walsh
Assignment # 4 Due: Monday November 12th ‐ 5:00 PM
(a)  A study‐aid desk manned by a graduate student has been established to answer student’s questions and help in working problems in your OM course. The desk is staffed eight hours per day. The dean wants to know how the facility is working. Statistics show that students arrive at a rate of four per hour, and the distribution is approximately Poisson. Assistance time averages 10 minutes, distributed exponentially. Assume population and line length can be infinite and queue discipline is FCFS. Using this information, answer the following questions. i. Calculate the percent of utilization of the graduate student

P= 4/6 = 2/3 = .6667 percent utilization
ii. Determine the average number of students in the system
λ= 4 per hour
μ= 6 students helped an hour
Ls= 4/ 6-4 = 4/2 = 2 students in the system on average.
iii. Calculate the average time in the system
Ws= 1/ 6-4 = ½ = .5 hours average time in the system
iv. Find out the probability of four or more students being in line or being served
P0= 1 – 4/6 = 1- 2/3 = .33 probability that there are 4 or more students being in line or being served. v. Before a test, the arrival of students increases to five per hour on the average.  Compute the average number of students waiting under this scenario.

Lq= 4^2 / 6 (6-4) = 16/ 12= 1.33 student waiting in line on average.
(b)  What are the three characteristics of a waiting‐line system? 1. Arrivals or inputs to the system: these have characteristics such as population size, behavior, and a statistical distribution. 2. Queue discipline, or the waiting line itself: characteristics of the queue include whether is it limited or unlimited in length and the discipline of people or items in it. 3. The service facility: its characteristics include its design and the statistical distribution of...