# the NJIT Honor Code homework

Bajet £20-250 GBP

Instructions

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

a problem.

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

the project.

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

the project.

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

1

to write programs, which you may do in a high-level language (e.g., C, Java or Matlab) or

Excel.

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

normsinv(rand()).

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).

Problems

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

function

(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