I am wondering if it is possible in ArcGIS 10.3 to customize the location-allocation network analyst or use other tools to find the location of a facility which minimize the costs and not the distances?
In other words, instead of minimizing the sum of the weighted transport distances from candidate facilities to the demands to find the best location(s), I would like to:
1) associate a cost to each demand (different between the demands)
2) associate a cost to the facilities (different between the facilities)
3) associate a cost which is a function of the distance between them
4) find the location which give me the minimum of the sum of the cost
All of network analysis is based on minimizing a "cost" on each edge. This does not have to be distance. It can be travel time or it can be travel cost. You just need to set up an attribute in the network dataset that is based on your cost. So yes, you can use a cost instead of distance.
Location-Allocation first finds the minimum cost matrix between all facilities and demand locations and then minimize the weighted cost. The weighted cost is weight at the demand location times the cost to reach that demand location from the facility. You load in the weight for each demand location when you load in these locations into a LA demand point layer. The facilities too have a weight that can be loaded. BUT, the facilities weight is NOT used by the normal minimize weighted impedance (P-Median) solver. The facility weight is ONLY used by the Maximize Market share and Target Market share solvers. In those instances, the huff model or gravity model is used to determine the interactions between demand and facility (candidates and competitors) to determine the best location.