transport network

[tomauro]

Greetings Tom (et al)...been a while since I've been doing SD, so I'm a little rusty. Hoping to get to the conference in Boston next year and catch up.

Got a network modeling problem where Supply A,B,C needs to go to Demand X,Y,Z respectively. In between A,B,C origins and X,Y,Z destinations is a transportation network that the goods can be shipped. The path that goods can take depends on capacity of nodes/connections between cities. How do I "tag" each product A,B,C to be delivered to destination X,Y,Z only?

I've currently modeled the problem using a two stocks called Network and Customer with volume originating at a network node located at A,B,C. The volume loops around as it's traversing through the network (dictated by a matrix of 1's and 0's) and it needs to "exit" when it gets to it's destination node.

I somehow feel this is a basic problem, but I'm just not seeing the solution. Thanks for any suggestions. I can provide the model if desired.

[tomfid]

This is a nontrivial problem. For the commodity case, like electricity where you don't care which electron ends up where, it can be solved with FIND ZERO. However, I'm not sure that's true here.

Are ABC and XYZ the same set of cities, or do the paths include additional nodes?

[tomauro]

Hey Tom,

ABC and XYZ are different cities. It would be like NY,DC,Boston shipping to LA,SF,Seattle respectively. NY all has to go to LA and so on...but they can traverse the same connections on the way based on shortest path, available capacity, priority, etc.

Perhaps it might be best to keep the supply and demand stocks seperate but present the same "network paths" to them (Supply->Network->Demand)? Could LPALLOC/LPSOLVE possibly handle this? I remember you added that like 10 yrs ago because I was asking for it. I'll play with it and let you know if I get it.

Lou

[tomfid]

This is definitely an LP-type problem. I'm not sure the LPSOLVE integration is complete enough to handle this "off the shelf" but it's certainly a possibility.

[tomfid]

Do the shipment paths include movement within ABC, XYZ, or do they pass through a distinct set of cities unrelated to the endpoints (StLouis, Denver, Omaha)?

(I'm just looking for a special case here.)

[tomauro]

Tom,

Turns out that the volume traversing the network can be homogenous and well-mixed for now (like your electon example). Otherwise, I think I'd need a seperate "network" for each To-From pair and control the network flow by aggegating that somewhere else in the model, like I suggested (worry about that later).

The From nodes can start anywhere on the network and volume from other From nodes can pass through them on their way to the To nodes. Think of it as having a network node on top of every To/From node and we just want to say how much volume originates at the From nodes as well as how much is required at the To nodes. Much simpler right?

Take a look at the attached toy model. It seems to work pretty well and I can divide up the flow any way I want with the matrices in Data20Nov24.xlsx. Curious though why a couple stocks still have a smidge of volume in them at the end. I'll keep playing till I get it perfect.

Lou

[tomauro]

Btw, do you know anyone at Sage Analysis Group? They're an MIT spin-off with offices in Boston, MA and Arlington, VA. I sent them a resume because they were advertising positions on the SD.org site. Hoping to talk to them about possibilities.

[tomauro]

Tom,

Here's a better version where I've replaced the file references with ?Data (same data file)...all you need to do is modify that one pointer in the Model Settings. Also, replaced the Supply, Transit and Demand with Binomial distros controlled by *Prob sliders which adds some variability/reality. My goal is to run sensitivity analyses for each and plot drawdown profiles to show resilience of various network configurations.

The important thing is that supply is now traversing the network based on the Network connections table in Data20Nov24 and showing up at the assigned Demand stocks in the expected quantities. It's interesting to note that if I reduce Supply Prob, that actually reduces the end quantities (because it's an Initial), whereas even if I reduce Transit Prob and Demand Prob the quantities still show up (because they're calculated at each time step)...it just takes longer.

Cheers,
Lou

[LAUJJL]

Hi Lou

To get help it would be useful if you put units in your model: We don't know if you're talking about sausages or aircraft carriers.

Second, the files are usually downloaded to the same download directory. However, in the model, the Excel file is in a directory that must be created and in which the Excel file must be copied, not to mention that I do not have a D disk. It's really not practical.

Thirdly, why not start with 2 cities and once you understand this simpler case, move on to 3 etc.. ?

Yours truly.

JJ

[tomauro]

Hey Tom and JJ, been doing a bit more work on this model since last post. I put in units ("widgets" meant to represent generic data) and quadruple subscripted to track Product (P) at Origins (O) through a Network (N) to Destinations (D). I actually submitted this as a paper (attached) to the society for consideration at the upcoming conference in Boston. I'm currently reviewing 3 other papers and volunteering. Hope to see you both again in August! Let me know what you think.

[tomfid]

Nice!