why sales reps pose a hard problem
To measure the intensity of X-, scientists have to move the crystals in thousands of different directionsRay diffraction
The manufacturer has to move a bit around the circuit board to make thousands of holes.
The sales representative must count dozens of cities.
If they want to do these things in the most economical way, all three have to solve what a mathematician calls a travel salesman problem.
The problem, which first appeared in the United States, was solved by mathematical analysis in a new discipline in its 1930 s-later known as operational research.
The original version was about a sales rep who had to visit multiple cities.
If the representative starts from a city and visits another City before returning to the starting point, in which order should they be visited so that the total distance of the trip is as short as possible?
In the manufacturing process of the circuit board, the city represents the holes to be drilled. In measuring X-
X-ray diffraction, the city corresponds to the orientation of the crystal, and the distance corresponds to the time required to reposition the diffraction instrument between the two measurements.
It may be simple to ask this question, but it turns out to be difficult to solve.
Despite the efforts of several generations of mathematicians and computer scientists, no one has found a complete solution.