Saturday, June 29, 2013

The Shopping Cart Paradox

We all have done it thousands of times. But I have thought it through only now. There is a serious issue.
A paradox, I'd say. The shopping cart paradox...  The more you buy, the more pronounced this paradox becomes. You pay at the cashier, bag all your groceries and carefully place them in the shopping cart arranging the heaviest items on the bottom and anything breakable, smashable, squeezable on the top. If you do your family shopping only once a week and especially if you have diaper-age kids, chances are your cart is full to the top.

top: anything fragile, smashable, squeezable
bottom: heavy items

Now, you come to your car and start transferring the bags into your trunk. What bags are on top of the cart? The bags with the breakable, smashable, squeezable items!  The only choice you have is to put them at the bottom of your trunk. What goes next? The bags with the heavy items that will undoubtedly break, smash and squeeze the bread, yogurts, eggs and peaches on the bottom. You see the flipping grocery cart-car paradox? Of course you are aware of this. So, you naturally try to sort the bags as you place them, spreading the bags around the trunk or the shopping cart. Some of us are even using the ground or a second cart as a temporary placeholder, flipping the bag order once again: lighter to the ground, heavier in the trunk, then placing lighter ones on top. We make it work, but it is far from optimal. It seems that some creative solution is required here to save us all from this ridiculous weekly process.

Your thoughts and suggestions are accepted any time until midnight Eastern Time on Sunday, on our Family Puzzle Marathon.

Image by Polycart used under CCL.


Kalonni said...

I usually shop alone so I place the soft items into the front seat, then the rest in the main area of my minivan. Anything especially large or cumbersome is placed in the rear compartment.

Jill said...

when we load the cart if possible we put the eggs and bread in the 'top' of the cart where a kid might go. If that's not possible, then we open the car doors (gotta get the kids in anyway), put the eggs and bread on the seat or floorboards up front by adult feet and then put the heavy stuff under the car seats.

Tom said...

Just put the light and fragile stuff on the left side, and the heavier things to the right?

Jerome said...

I did try to answer last week's problem. I did not have as neat a solution as those you got. It was an interesting problem. I was at my daughter's and using her computer. It blocked me from getting through and you did not get the answer I wrote which I could not correct until Monday and by then I felt that my answer was not nearly as good as those you got. I knew that daughters and sons could be math phobes, but I did not think that true of computers.

It is odd that this week's puzzle is one we were talking about last Wed.

I on occasion did the shopping in our household and when I did, I always took the kids. My wife (quite correctly I think) didn't come with us. We were just becoming Vegetarians then and nothing was too small to leave out of our discussion of what to buy and what not. It drove other customer's nuts I'm sure, but we enjoyed it.

The packing problem actually came up more than once. It was my daughter who solved the problem. She would come along with a second cart and we'd put all the drinks (in bottles) like milk and all the boxes of oranges etc in my cart and she had all the bamamas and peaches and perishables in hers. When it was rung through and bagged it was more or less in the right order and classified the right way.

anne-marie said...

One idea is to use a trunk organizer and sort out the items from the cart to the trunk.
I am not organized with my shopping but I do not break the items. My trunk is little and there's always something inside so I use the back seats and kind of sort out the items on the go, a real mess but no broken items.

Maria said...

I love your answers - spread the purchases all around the car: trunk, available seats, floor. I also place eggs and any extra fragile stuff on the seat next to the driver and had forgotten them there on a few occasions.

Utilizing big kids and getting multiple carts is a great trick.

But shouldn't it all be easier? And I talk large size shopping for a big family for a week.

Our dentist passed away this year. And he was a very creative guy who tended to my husband's teeth since his childhood. Dr Bahar. He once mentioned to my husband that this problem could be solved if car manufacturers designed a car with a shopping cart detachable from the car's trunk. You part at the store, open your trunk, wheel out the cart, shop till you drop, wheel the filled cart back attaching it to the trunk (inside) and drive home. No grocery flipping, no cart return. And at home you could wheel the cart right to your kitchen (assuming no stairs).
I would buy such a car.

Puzzle point for everyone who shared. See you next week.

Edith.morris said...

They are now coming up with a phone app where you check out the items as you pull them off the shelf and put them in your bags and into your cart and then as you leave the store you can check out by not emoting your cart, but instead by the list you scanned on your phone. Wouldn't help with the loading of your car, but would take away one step of unloading and loading it back onto the cart.

Anonymous said...

Hi there.

This is a typical optimisation problem.
If you're OK with differentiation and derivatives, I propose following:

Firstly -

formulate a function of perishability, weight, stowage-ability and space or volume

lets call it p(x), w(x), s(x) and v(x) respectively

Now you have three functions that need to be optimised wrt v(x)
simplest way to optimise would be to form a statistical plot of all functions and finding the local maxima and minima and then optimise to v(x)
Some optimisation techniques suitable in this case are
Multi-objective optimization
Main article: Multi-objective optimization (on the Wikipedia)

or multi-modal (also on wiki)

Me thinks, they explain it better than I would in this short space, so check out the above techniques

Post a Comment

Note: Only a member of this blog may post a comment.