Why does the salesman have to travel, when he can sell everything from home ?

On Wednesday, October 29, 1997 at 10:00:00 AM UTC+2, Tim Bagot wrote:
> On Wed, 29 Oct 1997, Dario Diogo wrote:
> >
> > Hello, I have a problem and I wonder if anyone out there can help me with ...
> > It's like this :
> >
> > A travel salesman stands at a store D, he has to visti some clients
> > from 1 to n and then returd to the store D. To all clients there is a
> > proift associeted, Li. The travel salesman has to return to store D with
> > an aculmulated profit > B units. We wanna find the minimum cost circuit,
> > where each circuit implicates the cost of the arc used and the acumulated
> > profit of the circuit.
> >
> > Now what is asked is a mathematical formulation of the problem and an
> > heuristic to solve it...
> >
> > Any help with it will be precious.....
> >
> > Thanks In Advance
> The only way to be certain of finding the best circuit is to evaluate
> every possible circuit. Unfortunately this takes a very long time aven
> for relatively small n. (It is usually possible to make some modifications
> so that some possibilities can be ignored, but it would still be far too
> time-consuming).
> It is, however, possible to get very close to the optimum (except in
> rather contrived cases) in a reasonable time. I suggest a method like the
> one given below, though I am sure it can be improved:-
> * A good starting point can be obtained by use of the 'Greedy' algorithm -
> i.e. the salesman always chooses as his next destination the point which
> will give maximum profit for that leg of the journey.
> * Next (optional), you could use gradient descent - i.e. simply choose
> changes to the route at random, and keep them if they improve it.
> * Finally, employ simulated annealing, which can almost always get within
> 1 or 2 per cent of the optimal situation relatively quickly. Essentially
> the method is the same as for gradient descent, with this modification: if
> a change does not make an improvement, it should be accepted anyway with a
> probability exp(-E/(kT)), where E is a measure of how much worse it makes
> the route, k is Boltzmann's constant (not strictly necessary), and T is a
> metaphorical temperature, which should gradually be reduced towards 0.
> This has the advantage of not getting stuck at local maxima. A search on
> the Web should find you some more detailed information if you need it.
> Tim Bagot

On 6/19/2023 6:49 PM, V õ l u r wrote:
> Why does the salesman have to travel, when he can sell everything from home ?
[...]

How does it get delivered to the customer? Say the deliver man has many
deliveries. What is the optimal path?