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Geographically splitting a problem into smaller chunks, produces lower total impedance.

JakeForsey

We are trying to create a fixed number of facilities across a region to service a bunch of demand points.

After we ran the problem we summed the total amount of length in the problem.

We then ran the problem again but with the facilities and demand points broken up into smaller regions.

The problem is: when the total length in all of the smaller problems is summed together the result is lower than in the single larger problem.

Our premise that makes us think this is a problem is: the larger problem contains the solutions of the smaller problems, so the algorithm should be at be able to at least match the solution.

Is our premise wrong, or is there some limitation of the algorithm that we are not aware of?

Many thanks.

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JaySandhu

What solver are you using? Location-Allocation? If yes, it uses heuristics to solve the problem. If you change problem space, you may get a slightly different answer. From your post, it is not clear how you model it "broken into smaller parts". Are the number of candidates still the same? Are cutoffs still the same? How different are the results?

Jay Sandhu

JakeForsey

Sum of all the travel in Run 1 consistently exceeds sum of all the travel in Runs 2 a and b.

Hi Jay,

Thanks for taking the time to reply to my question.

I've tried to make a picture that explains what I mean.

I'm using location allocation (I've tried both maximise capacitated coverage and minimise impedance), I keep all the parameters the same between runs (this is being run in a Python script so is easy to do).

The results are approximately 5% worse in scenarios without the breakdown (at this point we have tried quite a few runs with different setups).

Hope this helps you understand our position.

Thanks again,

Jake

JaySandhu

I see the picture with the subset. It is solving quite a bit different problem so there is no guarantee the solution will be the same. However I am not sure you will consistently see an improvement by doing subsets. So given the above picture, you are solving for 2 and then in the subset you are solving for 1 each?

How are you comparing the results? What metric? Do you take the chosen facilities from the subsets and make them required in the whole and resolve to compare?

Do note that Maximize capacitated coverage has a different objective then minimize impedance. Sometimes they give the same answer. (for coverage the goal is to cover the most demand within the cutoff honoring facility capacities).

JakeForsey

Hi Jay,

The total number of facilities chosen is the same between run 1 and run 2 (so yes, for example in run 1 we would solve for two, then run 2 we would solve for 1 in a and 1 in b).

We are checking the sum of the impedance and the average impedance in run 1 vs run 2 (both are improved in the subsets).

No we are not fixing any of the facilities at any point (not sure what this would show?).

I think I understand the differences between the two problem types, for the sake of understanding lets stick to minimize impedance. (we are not setting an impedance cutoff, so were hoping that maximise capacitated coverage would be optimising purely the impedance whilst honouring capacity caps).

As of yet, every run we have done has seen an improvement in the subset (which is why we are confused).

Many thanks,

Jake

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