Math formula to calculate throughput

With what you have given, we can determine that the vehicle takes 200*60/90 seconds to travel the length of the lane, and 2*60/90 seconds to travel the width of a stop, but there is no given information to say how that relates to the time to store/retieve a box

ozo

I am looking for average time for the vehicle to retrieve a box or store a box in a given lane of length L feet. Obviously if one were to do this problem by hand, then one can generate all possible store & retrieval time combination and then average the time out. Instead I am looking for a math formula that can calculate this number elegantly provided the input parameters

what are the input parameters?
 length of a storage lane, width of each stop with the lane,  and speed of the vehicle
alone don't tell you much

are we meant to assume that a box is stored and retrieved as a vehicle passes a stop at 90 feet/min?  if so, it must do it in 1 1/3 seconds

ozo
I am sorry, but what other inputs are you expecting ? I thought one can calculate the time it takes to 'visit' any stop given those input parameters.  If you are referring to the time it takes for the vehicle to transfer the load then - I apologize for omitting that as input. I was going to assume that the time to transfer the load onto and off the vehicle was fixed constant, say 5 seconds. Thus it does not affect the formula

I took my two formulas and put one in column A (location of each stop) and the other in column B (the time between them). I then copied the formulas down for 1000 rows and averaged the results in column B. Since the column A formula depended on a random number, I was basically doing a Monte Carlo simulation. For 999 trials I examined, the average distance was 70 feet and the average time 0.78 minutes.

byundt:
Thanks for attempting the solution. What changes are needed in your formula if the vehicle is asked to do single action vs dual action, meaning either visit a stop to store/retrieve a box (single cycle) or visit a stop for store and after storing , retrieve another box from nearby stop (dual cycle). I know I am introducing complexity to the original simple problem and I appreciate all attempts to solve the problem.

I thought time to transfer the load onto and off the vehicle was what you were asking to calculate.
If you just want time to reach a stop, it is just distance to stop/speed of vehicle assuming that the vehicle can accelerate instantaneously.

ozo
Yes. I am aware of the formula to figure out time to reach a single stop. The problem I have is given just the above input parameters, is there an efficient way to calculate the average response time for all possible stops. I think byundt approach of a monte carlo type might work here. Of course I am no 'Expert' at this hence my question in this forum

if the entire lane is filled with non overlapping stops, and each of 100 possible stops is equally likely, and you start at one end of the lane then the average is the same as the time to get to the middle of the lane.  again assuming instantaneous acceleration

and the average time to get from one random point to another, is the time to go 1/3 the length of the lane

ozo
I am an extremely dense learner: so I will use the QBE technique here to understand your solution:
If
L=200; stops=100;speed=90fpm;
then
timetostore/retrieve anywhere in this lane = (200/2) / 90 = 1.111 minutes
time to move between any two random points = (200/3)/ 90 =  0.74 mintues.

Is my understanding correct ?

choochim,
Could you elaborate a little more on the underlying problem? I assume this is a homework assignment of some type. If so, for which subject?

The reason I ask is that I want to give you the help you need without getting you in any kind of trouble with your prof.  also want to gear the suggestions at the right level.
Brad

byundt:
I am a bit flattered that you consider this a homework assignment for my prof. I wish it was that simple. Unfortunately this problem is a small puzzle of a much larger complex piece of engineering puzzle I am involved with at my place of work. I am trying to create a blackbox that would produce math based responses to input parameters for a simulation model in AutoMod. This was a simple test to see whether any experts would bite such problems. Now that I have found two - namely you and OZO, I can confidently post other puzzle pieces to solve the rest of the mystery.

choochim,
The third take-away from this discussion should be that both Ozo and I were trying to avoid giving a completely worked out solution to something that looked like an academic problem. Had you posted the discussion about AutoMod in your original question, you might have gotten a formula from him and a sample workbook from me.

Brad

Alas
Pardon my ignorance. this is my first week after I signed up for VIP access and I am still wading the waters. Point duly noted and I will be more thorough next time. Now that there is an offer of workbook and formula, can I please have such outputs to test the solutions?

Thanks for all the help

Brad

Thanks for the starter kit. Will try to develop from here.

In case either of you have any more pointers for me on this problem. Please send them to my email ID directly.

choochim,
As an additional bit of information, none of the experts have access to your e-mail address unless you post it in your member profile.

The site discourages exchanging information by e-mail because:
1) It puts experts not involved in the exchange at a disadvantage in trying to offer help
2) It diminishes the value of the Experts-Exchange database because valuable information may not be captured in posted Comments

For these reasons, if either ozo or I have further thoughts, we will post them in this thread.
Brad

byundt, you didn't need to do a simulation to get these figures (which aren't 100% correct either) :

>> For 999 trials I examined, the average distance was 70 feet and the average time 0.78 minutes.

    The average distance travelled is 200 / 3 = 66.67 feet
    The average time is (200 / 3) / 90 = 0.74 feet/minute

(as ozo already said)

Or, probably more accurate :

    The average distance travelled is 198 / 3 = 66 feet
    The average time is (198 / 3) / 90 = 0.73 feet/minute

since at the beginning and end of the lane, there's 1 feet that isn't used, since the vehicle stops in the middle of the "stop".


Btw, this does not take into account that the box needs to be delivered somewhere too. Neither does it take into account the acceleration of the vehicle, or the time to retrieve/store a box.
It also doesn't account for storage management. By doing proper storage management, you might be able to optimise these figures, by storing the boxes close together on either side of the lane (or at least close to the delivery point).

There are so much variables that aren't covered, but I'm sure you're aware of that.

Infinity08:

You have rightfully pointed out all the other variables in this problem that are not presented here. Yes I am well aware of those variables. I am not trying to optimize the operation here, just getting a feel for automating an input parameter to a sim model, given only those initial parameters.  The box needs to be delivered to a fixed location usually assumed to be a constant stem distance from the start of the lane. The time to retrieve/store is also a constant  as I had posted earlier to Ozo's similar followup question. Storage management is beyond the scope of this project requirement right now as the solution is being 'engineered' as I am writing this. So the natuaral assumption is within the length of the lane, the box can be stored anywhere.