**Question one**

Range

Range is the difference between the maximum and the minimum values within a particular set of numbers. To calculate range, we subtract the lowest value from the maximum value. For example from the data we have we can calculate the range by taking (146-4) = 142.

Range explains how values in a given set vary from each other. Adding and dropping of courses should be done within the acceptable ranges.

Mid spread values and the inter-quartile range eliminate the outliers (extreme values that appear to be inconsistent with other values in the data set). Quartile range is obtained by subtracting the lower quartile from the upper quartile. The main objective of calculating range is to establish how numbers (values) vary from each other.

**Question two**

Step 1 Generate time randomly and set arrival time= between

Step 2 Initialize every output value

HARTIME = unload, MAXHAR = unload, WAITIME = 0, MAXWAIT = 0 IDDLETIME=0. MAIN=0, DATAENT = 0

Step 3 Compute the finish time for emptying the ship

Finish = arrival + unload

Step 4 For i=2,3……..,n

Step 5 Generate random numbers of integer pairs drop and between over a given time period.

Step 6 Assume that the time clock starts at t=0. compute the ship’s arrival time

Arrival = arrive + between

Step 7 compute the difference between the arrival time of ship and the finish time of dropping the ship that came before

Timediff= arrive – finish

Step 8 for time that is non-negative, te unloading facility is idle

Idle = timediff and wait =0

For negative timediff, ship must be in a waiting line before it is dropped

Wait = -timediff and idle = 0

Step 9 Compute the starting time for dropping ship

Start= arrive + wait

Step 10 Compute the finish time for dropping the ship

Finsh = start + unload

Step 11 Calculate time in harbor for ship

Harbor = wait + unload

Step 12 Sum harbor, in total harbor time HARTIME for averaging.

Step 13 If harbor > MAXHAR then set MAXHAR = harbor, otherwise leave MAXHAR as it is.

Step 14 Sum wait, the total waiting time WAITIME for averaging

Step 15 Sum idle, the total idle time IDLETIME

Step 16 If wait > MAXWAIT then MAXWAIT = wait otherwise we set HARTIME = HARTIME/n. WAITIME = WAITIME/n and IDLETIME = IDLETIME/finish

Step 18 OUTPUT (HARTIME,WAITIME, MAXWAIT, IDLETIME)

STOP

**Question three**

We collected data on waiting time when adding or dropping a course. The data provided guidelines for effective planning and management in the school. From the data we developed a simulation and optimization model (OSM). The model had three important elements (Addiscott, 2007). First, its interface was user friendly and it gave students and school administration an easy time to operate it. The data provided a model that could be easily edited incase information about a particular student was wrongly entered. Secondly the model provided an appropriate waiting time that scheduled module that minimized the waiting time.

The model is comprised of four modules that can be described in the following sections.

MAIN sub model

This sub model directs the operation of the by the model by giving the students and the administration the ability to choose subsequent sub models and load the sample data in the computer.

DATAENT sub model this sub model enable the students to edit and enter their primary data to enhance the operation of one or two operating scenarios. Primary data encompasses project site and functioning data, command area data, adding and dropping courses.

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**Question four**

the steps below can be used to generate accurate simulation models.

Calibration

Computer simulation are the best at comparing scenarios. A base model is created and calibrated so that it has similar data as the area being studied. The calibrated model is therefore verified to ensure that the model is functioning as required basing on the inputs. Once model is verified, the ultimate step is to validate it by comparing the outputs to previous data in the area of study. This is achieved by using statistical methods to ensure that we have appropriate R-squared value.

The process of calibration can be achieved changing the parameter available to change how the model functions and stimulate the process. A good example is the traffic simulation where the parameters include car flowing sensitivity, headway discharge and look away distance. These parameters influence the character of drivers such as how and when the driver takes should change from one lane to the other, the distance a driver should leave between his/her vehicle with the other vehicle (Addiscott, 2007).

Model verification

It is achieved by getting the out data from the model and compares it with what is expected in the input data. In traffic simulation, the volume of cars can be verified to ensure there is actual volume throughout the model (Vose, 2006). Simulation model usually deals with model input differently and in most cases you may find out that vehicles do not reach their desired destinations. Furthermore, the traffic that wants to join the network may find it difficult to do so because of congestion.

Validation

Validation is achieved by comparing the finding with what is required basing on the previous information about from the area of study. Validation always produces results similar to previous results obtained from historical data. The results is verified using R-squared. This statistic measures the portion of variation that is accounted by the model. Large R value doesn’t mean that the model fits well. Graphical residual analysis is the other tool that is used to validate the model (Vose, 2006). Whenever the output data is different from historical data and thus this means that there is an error in the model.

**Question five**

I will consider increasing the number of counselors because more counselors would mean more students would be served quickly. The waiting lines would reduce because, and the students would take minimum time to be served and congestion in the office will reduce.

Reference

Addiscott, T. M. (2007). Simulation modeling and soil behaviour. *Geoderma*,*60*(1), 15-40

Vose, D. (2006). *Quantitative risk analysis: a guide to Monte Carlo simulation modelling*. John Wiley & Sons.

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