Crap. I can't figure this out. (Math)

O no.

It was a TV documentary. The American inventor had the brilliant idea of making his designs free to all, and so the idea was taken up fast.
He had a trucking company, so was mainly interested in logistics.
Lucky for the rest of us.
The basic design hasn't changed much over the years, so everone's containers will lock with everybody else's.
The first container-packed cargo to leave the UK was Scotch whisky from the port of Leith, and it was the first-ever cargo of whisky to arrive undamaged and unpilfered at its USA destination.
Slam-dunk, is that the correct expression?

Some great ideas do come out of the US that impacts the world's economies.


Gotta agree, that one was an excellent one! After all, it saved all that Scotch whisky. I purchased a bottle of Johnny Walker gold when I was on my last trip to the Dalmatian Coast, and paid US$21 for one. The cheapest I can find stateside is $72. Shudda bought 3-bottles.

yes.
Joe(Now if we can teach you how to pronounce 'schedule'.)Nation

Okay. Now here's where we are. Here's how I crunched the numbers:
A= (35.5*31.5*21.5)/1000000= .024cbm
B=(41.5*38.5*23.5)/1000000= .0375cbm
C=(41.5*38.5*23.5)/1000000=.035cbm
D=(47.5*45.5*27.5)/1000000=.059cbm

If we take what they was "a full container" for each value, you get this:
1160 pieces of A = 27.84 cbm
474 pieces of B= 28.04cbm
830 pieces of C= 29.17cbm
480 pieces of D= 28.52cbm

They are all supposed to equivalent,.....so I averaged them 28.3cbm

So, now I've got
.24A + .037B + .035C + .059 D = 28.3

Solve so that, in each category, the numbers are the lowest possible, but are approximately the same as each other.

My first guesstimate was:
200 A+ 200 B + 200 C + 150 D = 28.3
(200*.24)+(200*.037)+(200*.035)+ 150*.059)
4.8 + 7.5 +7.0 +8.85 =28.15 close but not perfect.

That looks good, but is there a way of solving for those multipliers, rather than just guessing and punching in other numbers until you arrive at the actual correct solution? (If I raise D to 160 and lower the rest to X.... .)

Is the fun of math devising the formula, because it sure isn't the calculating.

Joe(time for lunch)Nation

to get the same number of boxes you would simply let X = the number of boxes

.024X + .0375X + .035X + .059X = 28.3
Which works out to 165.9 = X

The only issue is based on dimensions vs cubic size will they fit?

The container is always the same size so it is always at least 29.17cbm. It's only a question of how the boxes can be stacked.

You just need a software that does that for you such as this one
http://3d2f.com/programs/46-781-cargo-optimizer-download.shtml

http://www.scientificamerican.com/podcast/episode.cfm?id=DD5541C2-E7F2-99DF-3E4D2546AC400A79

there's a podcast with the author of the book at this link

ah!
Thanks,

I knew I could get a program to do it (and I am saving that one for downloading later, but I wanted to figure it out on my own

joe(or with a little help from my friends)Nation

Thanks EVERYONE!

Before you purchase the commercial software, ask your shipping department if they are going to pack a container per some optimal, but not necessarily simple arrangement that the program kicks out. Or, should you be making some simplifying assumptions like:
- Each box of a given type (A-D) will be oriented a specific way in the container.
- The container will be filled with horizontal layers of the same box type.
- The container will be filled with vertical columns of the same box type.

Your four variable equation will work great for liquids. However, it won't generally work with boxes.

You stated that the customer wanted the most of each type (likely maximizing the minimum). If that's true, this is a one-time problem with a single solution - no formula required. Is that still the case, or do you now want to be able to handle different mixes of the boxes which would require a formula or an algorithm?

You bring up some good points; different size boxes for different size containers can vary with how many of each size box you wish to ship or store.

Maximum utilization will require including different size boxes in the same container, so one must be able to know what the variables will be. Only in this way can one expect to determine what size containers will be most efficient.

What a good point, Markr, the liquids vs solids.....makes sense.

The original numbers were the ones that the shipping department sent on to me. They assume that everyone will fill containers with single items (we generally sell 5-6000 pieces of each model to a user, so this question of stuffing a container with lots of different boxes kind of threw them.)

It could be partially due to a language barrier.

Not buying the software. My engineer assures me that this will not be a problem in the future. This example was only for a particular type of product and we have many others, in many other sizes, shapes and weights.

So, I think my exercise here was just that, some exercise for my head, and I will leave the packing to those who pack.

Just curious though, what would a formula for solids look like?

Same assumptions: four sizes of box, container of a particular shape and size, looking to maximizing the minimum.

Cheers
Joe(now it's time for afternoon tea)Nation

You also need to get some very short but very strong guys to load the top layer right to the back of the container.

One would have to know all the possibilities of all the box sizes available - including the combination of sizes and maximum capacity.

Thanks ehBeth.

The tv documentary I saw was British, at least with a British narrator, but maybe it was re-packaged for the UK market. Much of the film was European- Rotterdam, Immingham, Antwerp.
It was full of fascinating facts and stories. Like for example, ship captains used to reckon on a few days in each port, time off for playing golf and sightseeing, but now even the biggest container ships are turned round in one tide or so.