How to create a distance matrix in matlab

Hello,

I want to determine what the shortest route is to pick multiple items in a warehouse. However, I do not want to use a standard distance matrix, but I want to compute the distances between two items myself. Does anyone know how to create an distance matrix with the shortest distances between items in the same picking order?

Answer 1

[Bob Thompson]

What do you mean by 'picking order'?

I have no experience actually doing this, but my first thought would be to create a matrix of ordered pairs which represents all pickup locations within the warehouse. For making the distance matrix itself you could then use a for loop to loop through all locations and identify the distance required to reach any other point.

A sample code of what I'm thinking is below. I literally threw it together right here, so no testing or thurough thinking has gone into it.

pickups = [7,1;14,1;4,2;9,3;13,7;4,8;7,8;5,9;11,9;8,11;5,12;13,12];
np = length(pickups);
distancemat = zeros(np);

for i = 1:np;
    for j = 1:np;
        if pickup(i,2)==pickup(j,2); % Same columns READ NOTE AT END
            distancemat(i,j) = abs(pickup(i,1)-pickup(j,1));
        else % Different columns
            % Account for rows
            if pickup(i,1)<=15 & pickup(j,1)<=15
                distancemat(i,j) = min([abs(pickup(i,1)-pickup(j,1)),30-(pickup(i,1)+pickup(j,1))]);
            elseif pickup(i,1)>15 & pickup(j,1)>15
                distancemat(i,j) = min([30-abs(pickup(i,1)-pickup(j,1)),60-(pickup(i,1)+pickup(j,1))]);
            else
                distancemat(i,j) = abs(pickup(i,1)-pickup(j,1));
            end % Row check
            % Account for columns
            distancemat(i,j) = distancemat(i,j) + 2*abs(pickup(i,2)-pickup(j,2));
        end % Column check
    end % Columns loop
end % Rows loop

Note: As I have this currently written, it does not account for two columns being accessible at once. I do not have a good solution for this off the top of my head, but it should at least get you started.

[Lisa de Boer]

Thank you bob for your help. It helps me a lot.

[Image Analyst]

It's sort of like the traveling salesman problem, but not quite - it has a twist. Once you go down an aisle, you must stay in that aisle.

I don't see how the circles in diagram (b) correspond to the black squares in column (a), so I can't refer to them.

But, since you're committed to going down a aisle, if you were in aisle 4 and just got the black item in the third row, since you have to stay in that aisle, you can't then next grab the item in aisle 5, 4th row down, even though just looking at (x,y) coordinates, the one in aisle 5 is closest.

Another twist is that you can backup. For example you might head down a row but if there is only one item to be picked up in it, and it's close to the beginning of the aisle, it might be best to go in and grab it, then back out the same way you came in if there are no other items deeper into that aisle.

Answer 2

[Image Analyst]

Did you see this link on the Traveling Salesman Problem?