How can I set a progressive rate per mile in cost attribute?

Question

Hi, I want to use location-allocation model by minimizing total costs (dollars).  However, instead of a flat rate per mile, I would like to set a progressive rate.

For instance, if total miles (from facilities to demand points) are less than 50 miles, cost per mile is 0.5 dollars.  If total miles are greater than 50 miles but less than 100 miles, cost per mile is 0.75 dollars.  If total miles are greater than 100 miles, cost per mile is 1 dollar.

Or I want to set cost per mile is 0.5 dollars for the first 50 miles, then it is 0.75 dollars for the 50th-100th mile, and so on.  Either of these is good to me.

Is there any way to set cost attribute like this?

JaySandhu · Answer

Network analyst works on one impedance attribute at a time. So the distance decay will apply to whatever cost is returned from the network edges. You can have a network built with different modes like road, and rail and have a way to return the appropriate cost of transferring from one mode to another. The solver cannot work on minimizing two different impedances at the same time.

Location-Allocation does not model any extra fixed costs for facilities.

For the gravity model based models, Maximize Market Share and Target Market share, if competitor facilities are present then your candidate facilities can have a weight associated with them. Higher weight means the facility is more attractive. e.g., stores with larger area can be modeled this way.

Perhaps you can describe exactly what you are trying to model and solve and maybe I can suggest some methodology. Regards,

Jay Sandhu

OranuchW · Answer

Unfortunately, I have more than one facilities and they are close to each other so I can't use the polygon barriers.  Can you describe more about distance decay functions?  I'm wondering if I can specify the distance decay function on a particular mode of transportation (among many modes).  If I can, it may also works for my research.

Additionally, do you know if I can add a fixed cost for each mode of transportation?  In other words, there are additional costs for multimodal transportation.  If possible, I also want to add a specific fixed cost for each facility.

JaySandhu · Answer

if you only have ONE facility or if all the facilities are more than 100 miles away then you can use scaled cost barriers. That is, generate a service area with breaks at 50 and 100 miles. Assume that the cost if $1 per mile for the network. Then you can load the service area polygons as polygon barriers and set to be scaled cost and not restrictions. Scale the outer polygon (50 to 100) as .75 and the inner polygon (0 to 50) as .5

Now all the edges within 50 miles will have a cost of $.5, to 100 miles will be $.75

Note this only works if the polygon barriers do not overlap as they are addative.

Also, you could model the distance decay functions to increase cost further your drive.  But these are continuous, i.e. linear or power or exponential decay functions and not step functions.

Jay Sandhu