My question is related to freight transportation, but I am stuck on the logic. So, I am considering a path between two points $(a, b)$ where I am sending $n$ trucks where the capacity/truck is $k$. The distance is $d$ and the truck speed is $v$. Let's say that I am trying to get the time required to transport one unit of freight, do I use the standard $ t_{a,b}=\frac{d_{a,b}}{v}$ or do I consider road capacity (i.e., $path \ cpty_{a,b} =\frac{60}{headway}$)? If I consider $ t_{a,b}=\frac{d_{a,b}}{v}$, and assuming that $n$ vehicles are not simultaneously dispatched, then which is it ? The time to transport one unit of freight, $k$ units of freight ? Finally, do I need to use queuing theory to compute the total time to transport $k \times n$ units of freight ?

An example would be a minimum flow time model where the objective function is to minimize the total amount of transit time or $Min \ Z= \sum_{a \in O}\sum_{b \in D}t_{a,b}x_{a,b}$, where $t_{a,b}$ is the average time to transport 1 unit of flow over any $(a,b) \in A$ and $x_{a,b}$, the total flow transiting through any $(a,b) \in A$. If I have to solve it, I would need to be able to accurately define a function to compute $t_{a,b}$.

  • 1
    $\begingroup$ Welcome to ORSE. I think more context would be needed to answer the question. If you could dispatch all $n$ trucks more or less simultaneously, I would say $d_{a,b}/v$ would be the time to transport up to $k\times n$ units of freight. $\endgroup$
    – prubin
    Apr 14, 2022 at 15:27
  • $\begingroup$ Hi, thanks for your response. In fact, I am trying to create a model where I am minimizing the average travel time in a flow network. Therefore, I needed to know whether the time per unit of flow is $t=\frac{d}{v}$. The assumption is that $n$ trucks aren't dispatched simultaneously, therefore the mentioned formula would not be applicable. $\endgroup$
    – Bree
    Apr 14, 2022 at 15:57
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    $\begingroup$ We might need to see the full model to give a useful answer. Based on your edit, I would suggest just tracking the transit time $d/v$ for each truck and sum those up if the total amount of flow (across all routes/trucks) is fixed. $\endgroup$
    – prubin
    Apr 14, 2022 at 16:26
  • $\begingroup$ Thank you, I will try that and see how it works out. $\endgroup$
    – Bree
    Apr 14, 2022 at 16:29
  • $\begingroup$ @Bree, Out of curiosity, Why you don't try to use real-time by asking a driver that drives many times this specific road? $\endgroup$
    – A.Omidi
    Apr 14, 2022 at 18:23


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