Queueing Theory - Required Time to Load a Container

O

Osman

#1
Queuing theory

Hello Dears

Can you help in this case which related to logistic (loading a container?)
I have to load a container which has a capacity of = 2184 cubic ft,
((L x W x D) = 39’ x 7’ x 8’). To load the container I’ll use a trolley which has a capacity of = 230 cubic ft, I also designed a ramp so that the trolley will elevate or lift up to the container.

I calculated following timings
Trolley loading time = 4 mints
Trolley traveling time from warehouse to dock area = 1.20 mints
Trolley lift up time (thorough ramp) to container = 30 sec (0.5 mints)
Trolley unloading time = 3 mints
Trolley lift down (thorough ramp) from container = 15 sec
Total time = cycle time of one trolley = (4 + 1.20 +0.30 + 3 + 0.15) = 8.65 mints.

 I want to calculate the required time to load the whole container, now current loading time of container is 2.5 hours (without the ramp) by hands. And I has been asked to make it in 15 mints onlyyyyyyy !!!!!

 How money trolleys I will need for this task

 Note I have 6 to 10 manpower (loaders).

waiting for your advise
thanks
 
Last edited by a moderator:
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BradM

Staff member
Admin
#3
Re: Queueing theory

Queuing theory

Hello Dears

Can you help in this case which related to logistic (loading a container?)
I have to load a container which has a capacity of = 2184 cubic ft,
((L x W x D) = 39’ x 7’ x 8’). To load the container I’ll use a trolley which has a capacity of = 230 cubic ft, I also designed a ramp so that the trolley will elevate or lift up to the container.

I calculated following timings
Trolley loading time = 3 mints
Trolley traveling time from warehouse to dock area = 1.20 mints
Trolley lift up time (thorough ramp) to container = 30 sec (0.5 mints)
Trolley unloading time = 3 mints
Trolley lift down (thorough ramp) from container = 15 sec
Total time = cycle time of one trolley = (3 + 1.20 +0.30 + 3 + 0.15) = 7.65 mints.

 I want to calculate the required time to load the whole container, now current loading time of container is 2 hours (without the ramp) by hands. And I has been asked to make it in 15 mints onlyyyyyyy !!!!!

 How money trolleys I will need for this task

 Note I have 6 to 10 manpower (loaders).

waiting for your advise
thanks
I have a couple of questions regarding assumptions.

1) Are you sure loading/ unloading times are identical? I would think loading would take a bit longer.

2) Is the rail system circular? Saying, when a trolley is unloaded, does it immediately proceed where it can be loaded again?

3) Does 3 minutes include the time to procure raw material for packing?

4) It just seems (and it very well may be) there are no bottlenecks in the system-unlimited materials, plenty of packers, no obstructions for unloading, etc. How will you keep the trolleys from stacking up?

5) Also, did you calculate Mean Time Between Failures and such? Surely the trolley system does not work perfectly, and it will be down every now and then for repairs.

6) When you measured the times, how did you do that? Saying, keep in the the John Henry theory (or Hawthorne; take your pick:D) that the times you saw may be ideal; and not represent the realistic time frames. I would also surmise that the loading times will be slower end-of-day than start of day.

I'm just thinking of some variables with the process. If you have adjusted for everything, I think the value Randy gave would be optimal.

About 1.25 hours (72 minutes give or taking time for people to catch their breath)
Not bad for an old man.:tg::lol:
 

Steve Prevette

Deming Disciple
Staff member
Super Moderator
#4
One consideration - you did refer to this as "queuing theory". Generally in queuing theory we model the processes with homogeneous or non-homogeneous poisson processes - that is - taking into account the variability of the timesm and generally related to random arrival processes (which I assume you don't have here).

Have you collected enough data that you could also give the standard deviations of the times? Whether Poisson or not, I assume you want to account for variablity. Your AVERAGE cycle time may work out to be a certain value, but you may want to specify you want to be better than a certain cycle time 95 percent of the time . . .
 
O

Osman

#6
Hi again
thanks Randy, Steve Prevette & Brad for giving time and advising.

I posted the same case in other forum at the same time … but no one replied me till now , if that show some thing, it shows that elsmar is a unique and its uniqueness come from the professionals like you :applause:.. (I hope my English is understood:tg:)

Randy I will be thankful if you show me how you calculated the time.
To get the required trolleys I divided container capacity on trolley capacity and I have got around 10 trolleys … to load the container …then I selected 3 trolleys only so the time calculated was around 120 mints :bonk: I think I have to increase loaders! To minimize the time

Brad … I have studied trolley and container loading time again... You were right loading time is longer than unloading
About other factors like bottleneck and material availability, these do not exist, but I have to consider the fatigue factor/ allowances.

Steve Prevette
Your right….. Variability in arrival time of trolleys almost not exists.
But do you think arrival of trolleys can take any distribution form ?!

Thanks
 

Randy

Super Moderator
#7
All I did was divide the total container size (2184 cu/ft) by the size of the material you could load (230 cu/ft) and that gave me 9+ a bit more (I rounded up to 10 for ease) I then multiplied that by the total time you said the operation took for 1 complete cycle (7.65 min). All the other information was nice but totally non-essential and wasted effort... I just rounded everything off a bit to ease the calculations.

cycle time (X) # of cycles = Total time
 
R

RLewing

#8
I do not get a good grasp of your arrangement, but if you can have only one trolley unloading at one time, then you need at least 10*3 minutes for unloading, and even then you need some arrangement where you can switch to another trolley in "no time" (double ramps or something).

If you need to get the time down to 15 minutes, then 30minutes/15minutes = at least 2 trolleys unloading simultaneously (and no time needed for changing trolleys -> 3 ramps).

Is it possible to build some kind of intermediate storage which you could then "dump" to the container?
 

Steve Prevette

Deming Disciple
Staff member
Super Moderator
#9
Steve Prevette
Your right….. Variability in arrival time of trolleys almost not exists.
But do you think arrival of trolleys can take any distribution form ?!

Thanks
An initial assumption of Poisson for arrival times is reasonable. Recognize that you might be able to decrease the variability through control of the system. You may want to try to gather data from an existing setup, if one exists and is willing to share data, in order to determine what would be good distributional fits. The you could run a computer simulation to see what the extreme values (not just the steady state rate) are.
 

BradM

Staff member
Admin
#10
Osman, may I ask a question... What exactly is your goal, here? How accurate are you wanting to get with your estimation? Are you needing this for project justification?

Steve has provided you some valuable information regarding distributions and the like. However, your numbers (and assumptions) seems overly simplistic.

Just saying, you can just add the numbers up, and depending on how conservative (or liberal) you were with your estimates is whether that value would be ideal or average.

Do you have constant arrival rates, or will the arrival rates represent Poisson (or another) distribution? Will all workers be exactly the same in their time? I would think some are slower than others. What about different shifts? What about different demand rates?

I'm just wanting to see how detailed (and thus more realistic) your estimate needs to be. Or just take Randy's estimate, multiply by 1.5, and state that as the average.

As far as the assumptions, I just cannot believe there will not be any bottlenecks anywhere in this process. It may not be obvious now; but will present itself once you are set up.

After everything gets put into place, you can always monitor the times and get a much better approximation of the average time.

In addition to calculating the exact time, I would think you would have additional benefits including better conditions for the workers.
 
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