California State Polytechnic University, Pomona

Department of Industrial and Manufacturing Engineering

Dr. Parisay

IE 429

January 26, 2011

Example 5 - Travel Delay

Group 7:

Tamara Vail

David Trigg

Chad Creason

Explanation:

We were given two models to explain to the class; Example 5 - Travel Delay and

Example 6 - Travel Station. Both of these models are based off a previous model that we have

discussed in the class, Example 3 – Travel Process. The two models both have the same output

as the one previously discussed because all three models accomplish the same thing. The only

difference between them is the way that they are modeled. The purpose of the two models is to

incorporate travel time into the model. This is because in most processes a travel time is

unavoidable; the parts somehow have to get from one station to the next.

Travel Delay is a “delay” selected from the advanced process panel rather than a

“Process” selected from the Basic Process panel. Its function is to incorporate a delay due to

travel time in the system. An example of this could be time needed for a part to get from one

station to the next. This delay can have a variety of distributions associated with it. Some

examples are normal [NORM(1,2)], exponential [EXPO(1)], uniform [UNIF(0.5, 1.5], triangular

[TRIA(0.5,1,1.5)] etc…

Travel Station utilizes the Advanced Transfer panel in Arena and specifically the Station

and Route functions. A station is a sort of check point that in the case of the example model is

used when the parts enter the system and after the parts are received from routing. A route is

something used to tell the parts were to go and with what distribution. One of the benefits of

using a route in arena is that you do not have to connect the route to its destination, as in the

example model given. Instead the route lets you send it to the proper station just by use of the

name. An example of this that is helpful is if you have a very large model the benefit of not

having to make a connection creates a model with less clutter.

Example Problem

Premier Packing Co. receives shipments of two parts from an outside supplier. Part AA arrives to

the facility at an exponentially distributed rate with a mean of 16 minutes. Part BB arrives to the

facility at an exponentially distributed rate with a mean of 15 minutes. Both parts must be

received at a Check In Station in which each part will be routed to one of two processes

depending on what type of part it is. Part AA travels to its next destination which is uniformly

distributed with a minimum time of 2 minutes and maximum time of 5 minutes, whereas, Part

BB travels to its next destination which is uniformly distributed with a minimum time of 3

minutes and maximum time of 6 minutes. Part AA then arrives at Station 1 where it prepares to

undergo a Special Packing process. The Special Packing process requires one Machine 1 and one

Worker 1 and is exponentially distributed with a mean time of 2 minutes. Part AA will next

endure an inventory delay, where the finished packaged part will be waiting to be shipped out to

Supplier 1. This delay is uniformly distributed with a minimum of 2 minutes and a maximum of

4 minutes. On the other hand, Part BB will arrive at Station 2 where it will prepare to undergo a

Wrapping process. The Wrapping process requires one Machine 2 and one Worker 2 and is

exponentially distributed with a mean of 3 minutes. Part BB will also be held up by an inventory

delay, where the finished product will be sent out to Supplier 2. This delay is exponentially

distributed with a mean time of 1 minute. Run the simulation for 10,000 minutes.

The first step is to attach the Advanced Processes and Advanced Transfer Tab

A panel will appear on the screen and you can add the tabs which are required for creating the model in arena.

These new tabs will appear on the left side of the screen in the “Project Bar”

Creating the Arena Model

The first station parts AA and BB arrive to is a “Check in” station:

Shown below in tabular form:

After the parts have been checked in, they will be routed to their designated stations which will send them to the respective process plans:

Shown below in tabular form:

Adding the Travel Delay

Shown below in tabula form at the bottom of the window

Arena Simulation Results

Summary Table:

Entity/ProcessPerformance

Measure

Distribution Observed Value

Acceptable Range

Comments

Input Part AA Expo(16) --- --- ---Part BB Expo(15) --- --- ---

Travel AA Unif(2,5) --- --- ---Travel BB Unif(3,6) --- --- ---

Special Packing

Expo(2) --- --- ---

Wrapping Expo(3) --- --- ---Delay AA Unif(2,4) --- --- ---Delay BB Expo(1) --- --- ---

Output Part AA TIS --- 8.76 min --- ---Part AA WIP --- 0.61 AA --- ---Part AA VAT --- 2.00 min --- ---

Part BB TIS --- 9.35 min --- ---Part BB WIP --- 0.65 BB --- ---Part BB VAT --- 3.08 min --- ---

Machine1 ρ --- 13.9% 90% - 95% Extreme lowMachine1 Wq --- .266 min ≤ 1 min GreatMachine1 Lq --- 0.02 AA ≤ 2 AA Great

Machine1 Max Lq

--- 2 AA ≤ 6 AA On track

Worker1 ρ --- 13.9% 70% - 90% Extreme lowWorker1 Wq --- .266 min ≤ 1 min GreatWorker1 Lq --- 0.02 AA ≤ 2 AA Great

Worker1 Max Lq

--- 2 AA ≤ 6 AA On track

Machine2 ρ --- 21.4% 90% - 95% Extreme lowMachine2 Wq --- .788 min ≤ 1.5 min GreatMachine2 Lq --- 0.05 BB ≤ 3 AA Great

Machine2 Max Lq

--- 4 BB ≤ 6 AA On track

Worker2 ρ --- 21.4% 70% - 90% Extreme lowWorker2 Wq --- .788 min ≤ 1.5 min GreatWorker2 Lq --- 0.05 BB ≤ 3 AA Great

Worker2 Max Lq

--- 4 BB ≤ 6 AA On track

Summary Verification:

Part AA enters the system with an inter-arrival time of 16 minutes and Part BB enters the

system with an inter-arrival time of 15 minutes. Assuming there were no bottlenecks in the

system then, whenever Part AA enters a process it will leave also the process and whenever Part

BB enters a process it will also leave the process. According to this then the inter-arrival time

should be equal the time it takes between departments (inter-depart time). The average service

time for worker 1 is 2 minutes and the total time is 16 minutes. If you divide the values to find

utilization you get 2

16x100=12.5 % which is close to our observed value of 14.0%. The average

service time of worker 2 is 3 minutes and the total time is 15 minutes. If you divide the values to

find utilization you get 315x100=20.0 % which is close to our observed value of 21.4%. Since

our simulation was run for 10000 minutes and part AA arrived at an average of 16 per minute,

we should expect to see 10000

16=625 parts enter and exit the system. This is close to our

observed values of 698 parts entering and 695 parts exiting the system. Also, using the same

idea for part BB which arrived at an average of 15 minutes we should expect to see

1000015

=666.7 parts which we would round to 666 parts entering and exiting the system. This is

close to our observed values of 696 parts entering and exiting the system. The reason that we

chose to round down to 666 parts is because you cannot have 0.7 of a part leave the system. The

differences between our observed values and calculated values can be attributed to randomness

and can be considered negligible for our purposes.

Report to Manager:

Dear Manager,

Per your request we have observed our packing facility in order to find solutions and to

make recommendations for optimization in the Special Packing and Wrapping Stations. With the

use of the Arena Simulation software I have modeled our packing system and have noticed the

following conditions:

Personnel Utilization

Personnel UtilizationWorker One 14.0%Worker Two 21.4%

As shown, the utilization of each worker is extremely low. We feel that the acceptable

range should be 70%-90% because although a worker needs breaks by law they also still need to

be productive. We would recommend using only one worker between both the Special Packing

process and the Wrapping process. Our goal of this would be to increase worker utilization to

have it as close as possible to the range of 70%-90%.

Machine Utilization

Machine UtilizationMachine One 14.0%Machine Two 21.4%

As shown, the utilization of both machines is extremely low. We have set an acceptable

range for the machines to be between 90%-95%. We believe that the range can be this high due

to the fact that machines do not need breaks like humans. There is not much we can do about the

under-utilization of the machines. We suggest that one worker can operate both machines given

that the utilization of each machine is extremely low. Also do to the fact the worker utilization is

so low.

Average Station Wait Time

Stations Wait Time (minutes)SpecialPacking .266Wrapping .787

As shown the wait times at the stations are extremely low. One suggestion that we would

make is to increase the frequency of the parts coming into the system.

More analysis is needed to fully prove this; however we believe that the suggestions

provided will improve the overall utilization of the system.