You must work on the project by yourself, including solving problems and designing and writ-
ing all of your own programs. You may only discuss the project with me (Prof. Nakayama).
You can ask me to clarify problems; however, I might not answer questions on how to solve
On the rst page of the solutions you hand in, you must include a signed and dated statement
saying, \On my honor, I pledge that I have not violated the provisions of the NJIT Academic
Honor Code." If your solutions do not include this pledge, then you will receive a 0 on the
project. Anyone caught violating the NJIT Honor Code will be immediately reported to the
dean of students.
The questions below ask you to solve problems, give algorithms (i.e., pseudocode) and write
programs to simulate various models.
Hand in hardcopies of the solutions to your problems, printouts of your programs and
printouts of your relevant output. (Do not hand in printouts of the outputs from every
replication.) If you do not hand in the required hardcopies, then you will receive 0 on
Also, you must e-mail me all your programs (source code only) as a single compressed
(.zip or .rar) le. If you do not e-mail me your programs, then you will receive 0 on
All of the required hardcopies and your e-mail of your programs must be received by
the due date/time to avoid any lateness penalties. Late projects will be penalized at
a rate of 25 points per 24-hour period, and lateness penalties will continue accruing
until I have received all of the required materials. For example, if the last thing you
turn in gets to me between 5:01pm on May 1, and 5:00pm on May 2, then you will
lose 25 points. If the last thing you turn in gets to me between 5:01pm on May 2, and
5:00pm on May 3, then you will lose 50 points.
For any problems that require providing pseudocode, you may assume that you have at your
disposal a uniform[0; 1] random number generator and a method to generate independent
standard normal random variates. Problem 1 requires that you write Arena programs, and
for this problem you can use any of Arena's built-in functions. For problem 2, you need
to write programs, which you may do in a high-level language (e.g., C, Java or Matlab) or
If you implement a program in Excel, be sure to specify all of the formulas used
in the cells and hand in only enough pages so that all of the formulas appear for
one replication. You may generate a standard normal in Excel using the command
If you write a program in a high-level language, you can generate standard normals
using the Box-Muller method or any other built-in exact method or numerical approxi-
mation (e.g., like normsinv in Excel, but not a crude approximation, such as averaging
12 independent uniforms).
1. [50 points] Consider the following model of a call center for a small airline. (All times
in this problem are expressed in units of minutes, and all specied random variables
and events are mutually independent.) The call center is open for 720 minutes each
day from 8am to 8pm, and let t = 0 denote 8am, so, e.g., time t = 60 is 9am. From
8am to 8pm, calls arrive according to a nonhomogeneous Poisson process with rate
(t) = 2:5 + 2 sin(2t=720):
After placing a call, a customer hears a recorded message asking him/her to \press 1"
(denoted \option 1" or \type 1") to buy a plane ticket, or to \press 2" (denoted \option
2" or \type 2") for all other inquiries. The caller spends a random amount of time
to choose an option, where the time follows a triangular distribution with parameters
(0:1; 0:2; 0:4). The call center can handle an unlimited number of incoming calls, so
there is no queueing at this point. Sixty percent of callers choose option 1, and the
rest choose option 2.
After an option is chosen, the call is routed to one of two pools of operators to handle
the two types of calls. Calls of customers who select option 1 are switched to o