|By Michael Nir||
|July 7, 2014 02:03 PM EDT||
So there you are, living in New York City - well actually it is Queens, but still... You're planning an extended weekend escape from city.
You booked a great vacation in the Caribbean.
Your flight is early next morning. You are in your bedroom packing.
Considering the current restrictions, you are allowed only one piece of luggage and a small carry on to take onboard.
You have only tonight to decide what to pack. You want to make sure, that you're packing just what you need.
You remember how you've missed a proper mosquito repellant last year on your excursion to Alaska. Who would've known that the mosquito is their national bird?
Maybe a helmet is in order - did you know that the common belief that dozens, if not hundreds of people die of coconuts falling on their heads, is no more than an urban fairytale?
There you are in your bedroom, surrounded by your carry-on and bag open, awaiting. Looking at your huge closet unsure what you really need to take.
The thing is that, each and every item has a certain utility or in other words, has a certain benefit. At the same time, each and every item has a certain volume, or bulk. The transportable storage space is constrained.
You're inspecting the items you'd like to take. Definitely you need a pair of running shoes for aerobics, your second pair of leisure pants just to be on the safe side, your teenage days weightlifting shirts that shows the biceps, and your moisture repellant cross training sweater. These are already inside.
You might go snorkeling, so you should pack the lovely snorkeling mask with the fish pattern that was your 21st birthday gift and which you've always cherished.
The hard copy of the Silent Influencing book that you've started reading, with those cool illustrations and creative concepts, is a must.
The check-in bag is bursting, and you haven't even packed the casual evening dress and an extra pair of pants. You decide that probably the snorkeling fins should stay and that you don't really need your water purification bottle.
You land in Nassau only to discover that you've left your bathing suit on the top drawer, as you were making room for your ukulele...
This problem which we all faced at one point or another is also a well-known complex problem. Unfortunately, it is not one of those, plug in a formula and get a solution type of problem.
It seems that even the most mundane and seemingly easy problems are really difficult, challenging and complex. The packing your bag to go on a vacation problem is known as the knapsack or rucksack problem.
According to Wikipedia:
The knapsack or rucksack problem in combinatorial optimization: Given a set of items, each with a mass and a value, determine the number of each item to include in a collection so that the total weight is less than or equal to a given limit and the total value is as large as possible. It derives its name from the problem faced by someone who is constrained by a fixed-size knapsack and must fill it with the most valuable items.
The knapsack problem has been studied for more than a century, with early works dating as far back as 1897 and even before.
It has plagued knights on pilgrimages, and mid age's ships exploring the globe. Due to shortage in haul space, the ships didn't pack any fruit which resulted in nasty health problems to the sailors... only towards the end of the millennium, did a British physician recommend packing fruits and vegetables on long sea excursion as a cure against Scurvy; changing the priorities of items to be packed on ships forever.
We understand that there are two types of problems. Ones which are easy to solve they are known as Polynomial problems. We studied about them in school, sometimes we had formulas to solve them; in general they are not representative of the challenging business and personal problems that we face in our lives.
The second types of decision-problems are complex, confusing and constitute the majority of business and personal decision-problems we face. The number of possible solutions is enormous and grows exponentially with the problem size. Since we can't really calculate the total number of solutions, we opt for rules of thumb for deciding on the best course of action.
More - an Ulitzer article here: