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Assume that I have data about a regular big company (not a salesman problem). data contains of every department's (marketing, finance, production, etc.) vehicle size, GPS track values, duration of using vehicles, etc.

I want to optimize the fleet management.

First option: there will be a (one or more) vehicle pool, and every department will make a car reservation from the pool when they need it.

Second option: allocate certain number of cars to every department based on the data

Third option: mix of first and second.

Is there any model for optimization? I'm sure the problem isn't clear enough and it's hard to say for sure without seeing the data. But I need a starting point. Also, I will be glad if there is a paper about this kind of problem.

EhsanK
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maxime
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2 Answers2

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If the use of vehicles by departments is deterministic (which I find very unlikely), then scenarios 2 and 3 can be approached as integer programming models. You might be able to do that with random vehicle usage by plugging in averages, but I would be suspicious of the results. There are also scenario-based approaches to stochastic optimization.

If the data is robust enough to allow you to estimate probability distributions for things like time between vehicle requests for each department, you could try building a discrete event simulation. Once you had validated that under the current vehicle rules (whatever they are) the output resembled the historical data adequately, you could try running various scenarios (single pool, allocate this many cars to each department, allocate a different fixed number of cars to each department, allocate some cars and keep the rest in a pool) and let the simulation results guide you to an "optimal" policy. This can be done just by doing a lot of runs and comparing their results, but there are more scientific ways to do it.

Under any approach, you will need to answer some additional questions, including what happens if a department requests a vehicle when none is available (do they wait and, if so, for how long) and, importantly, what you criterion for a "good" result is (your objective function).

prubin
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  • Thanks for the answer. My goal is; the vehicle request of each department must be met within 1 hour at the latest. I was thinking of constraints as; the number of vehicles used by each department at the same time during the day and their usage times. – maxime Apr 24 '22 at 08:49
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    If vehicle requests occur randomly, it is possible that your one hour time limit could only be met with a certain probability (e.g., requests are met within one hour with probability 0.9) unless you are willing to invest in a very large fleet. You might want to do a search on "chance constrained programming" or "chance constrained optimization" (constraints satisfied with a certain probability and "stochastic programming/optimization with recourse" (specifying a backup plan when a constraint is violated, such as calling a cab if no vehicle is available within an hour). – prubin Apr 24 '22 at 15:41
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Based on what you described in the question, the problem you are facing is a variant of the vehicle routing problem. If you have faced some uncertainty, as Prof. Rubin mentioned too, the simulation technique would be useful. Also, some of the references that might be close to your problem are:

A.Omidi
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  • I'm not convinced this is a variant of the vehicle routing problem. It seems to be about booking cars from pools, but there's no consideration of travel between locations (or even locations that need visiting). – Open Door Logistics May 01 '22 at 10:01
  • @OpenDoorLogistics, If the questioner had already given more details about the problem, one more likely could be able to answer precisely. Please, feel free to pin your answer as it might be interesting to other members. – A.Omidi May 02 '22 at 05:03